Foam films drawn from dispersions Citation for published version (APA): Baets, P. J. M. (1993). Foam films drawn from dispersions. Technische Universiteit Eindhoven. https://doi.org/10.6100/IR406827 DOI: 10.6100/IR406827 Document status and date: Published: 01/01/1993 Document Version: Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication: • A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, please follow below link for the End User Agreement: www.tue.nl/taverne Take down policy If you believe that this document breaches copyright please contact us at: [email protected]providing details and we will investigate your claim. Download date: 10. Feb. 2022
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Foam films drawn from dispersions
Citation for published version (APA):Baets, P. J. M. (1993). Foam films drawn from dispersions. Technische Universiteit Eindhoven.https://doi.org/10.6100/IR406827
DOI:10.6100/IR406827
Document status and date:Published: 01/01/1993
Document Version:Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers)
Please check the document version of this publication:
• A submitted manuscript is the version of the article upon submission and before peer-review. There can beimportant differences between the submitted version and the official published version of record. Peopleinterested in the research are advised to contact the author for the final version of the publication, or visit theDOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and pagenumbers.Link to publication
General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.
• Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal.
If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, pleasefollow below link for the End User Agreement:www.tue.nl/taverne
Take down policyIf you believe that this document breaches copyright please contact us at:[email protected] details and we will investigate your claim.
de Rector Magnificus, prof.dr. J.H. van Lint, voor
een commissie aangewezen door het College
van Dekanen in het openbaar te verdedigen op
vrijdag 17 december 1993 om 16.00 uur
door
PETER JOHANNES MARIE BAETS
geboren te Grathem
Dit proefschrift is goedgekeurrt
door de promotoren
prof.dr. H.N. Stein
en
prof.dr. W.G.M. Agterof
CONTENTS
Chapter 1: Introduetion
Objective of the thesis ...................... 1
Mechanisms of foam destruction ............... 2
Disproportienation of gas bubbles .......... 2
Spreading .................................. 5
Drainage of horizontal faam films .......... 5
Drainage of vertical faam films: ........... 7
marginal regeneratien
Influence of solid particles .............. 12
Film rupture of horizontal films .......... 13
Rheological properties ...................... 14
Foam destructien in practice ............... 18
References .................................. 19
Chapter 2: Drainage of CTAB films containing solid particles
Abstract .................................... 25
Introduetion ................................ 26
Theory ...................................... 27
Experimental methods ........................ 28
The apparatus ............................. 28
Film thickness measurements ............... 30
Light scattering measurements ............. 30
The preparation of the PS particles ....... 31
The characterization of the PS particles .. 32
Results ..................................... 33
Discussion .................................. 38
Conclusion ................................. 40
References .................................. 41
Appendix 2A ................................. 42
Chapter 3: The influence of glass particles on the foam stability
of CTAB solutions
Introduet ion ................................ 44
Experiment al ................................ 44
Method .................................... 44
Materials ................................. 45
Results and discussion ...................... 46
Conclusions ................................. 48
References .................................. 49
Chapter 4: Influence of surfactant type and concentratien
on the drainage of vertical liquid films
Abstract .................................... 51
Introduet ion ................................ 52
Bxperimental section ........................ 53
Materials ................................. 53
Apparatus ................................. 53
Results ..................................... 55
Discussion .................................. 60
Conclusions ................................. 62
Acknowledgement ............................. 62
References .................................. 62
Appendix 4A ................................. 64
Appendix 48 ................................. 71
Chapter 5: Surface rheology of surfactant solutions
close to equilibrium
Abstract .................................... 74
Introduetion ................................ 74
Experimental ................................ 75
The apparatus ............................. 75
Data processing ........................... 77
Experimental errors ....................... 79
Materials ................................. 81
Results ..................................... 82
Discussion .................................. SS
Diffusion of surfactant to the surface .... 87
Electrastatic repulsion between .......... 88
the head groups
Impurities ................................ 89
Micelie/Surface layer interaction; ........ 93
Surface ordering
Conclusions ................................. 94
Acknowledgements ............................ 9S
List of symbols ............................. 96
References .................................. 98
Appendix SA ................................. 10 0
Appendix SB ................................. 101
Chapter 6
Conclusions ................................ 104
Summary .................................... 108
Samenvatting ............................... 112
Curriculum Vitae ........................... 116
Dankwoord .................................. 117
OBJECTIVE OF THE THESIS
The present
dispersions.
theoretica!
investigation
This subject
problems. The
CHAPTER 1
INTRODUCTION
is devoted to the study of foam films in
has connections with both practical and
conneetion with practical problems arises
because foams in dispersions are frequently encountered in a large
nuffiber of situations and applications, such as the preparatien of foamed
concrete, food products and in faam fighting techniques. A closely
related topic is the stability of thin liquid films separating air
bubbles from the surrounding air, e.g. in the manufacture of coatings.
In some cases foam is a problem, in other cases foam is the desired
product. Cantrolling the stability of foam is therefore very important,
and faam stability is determined by the behaviour of the thin liquid
films in them. In theoretica! respect, the study of thin liquid films
containing solid particles is important since it enables us to
differentiate between the influence of bulk rheological and surface
rheological properties on film drainage, as wil! be argued in more
detail in chapter 2.
Foam films break after they reach a critica! thickness as proposed by
Scheludko 1• This thickness has a value between 100 and 500 Á according
to Vrij 2. The time necessary to reach this critica! thickness, is
determined to a large extent by film drainage. Thus drainage of thin
liquid films is important for foam stability.
The aim of this work is to obtain a better understanding of foam
drainage. We are interested in the influence of solid particles wi th
various volume fractions on the drainage ( see chapter 2, 3) . We also
studied the behaviour of solid particles with different partiele
diameters in a faam film (see chapter 2). The drainage rate of various
surfactant solutions (free from particles) at different concentrations
was investigated in chapter 4. With regard to the influence of the type
of surfactant solution, the relation between drainage on the one hand
1
and interfacial and bulk rheological properties on the ether, was
investigated (chapter 5) . The shear stress in a mobile soap film, as can
be calculated according to Mysels' model of marginal regeneration, was
measured and compared to theory (see chapter 4). Calculations on the
persistenee of spots formed by marginal regeneratien are given in
chapter 4.
HECHANISHS OF FOAH DESTRUCTION
A faam is a dispersion of gas in liquid. Th is is a thermodynamically
unstable system. There are two types of foams, depending on the volume
fraction of gas. A low volume fraction of gas will give a dilute faam,
with round gas bubbles. A high volume fraction of gas will give a
polyhedral faam, in which bubbles are pressed against each ether so that
planar films are formed between them. In this stage, Plateau borders
(the liquid canals generated at lines along which three films come
together) play an important rele in the drainage of the films. Examples
of a dilute faam are hair-gel and ice cream, whereas shampoo and coffee
faam (after sufficient drainage has occurred) are polyhedral.
Several mechanisme of faam destruction of polyhedral foams are given
below.
Disproportienation of gas bubbles
Disproportienation is a process, in which large bubbles grow at the
expense of smaller ones. The reasen for this growth is diffusion of gas
through films because of preesure differences between the bubbles. These
pressure differences exist because of differences in bubble size.
Important physical parameters for this process are: the diffusion
coefficient of the gas in the liquid phase, the (dynamic) surface
tension, the solubility of the gas in the liquid, and of course the gas
composition. Apart from that, the film thickness is a very important
geometrical parameter.
For liquid films with a purely elastic surface, Gibbs 3 pointed out that
2
disproportienation can be inhibited by the surface elasticity E if
E>7 /2, where 7=Surface tension. The surface elasticity is defined as
E=d7/dln(A), where A is the total area.
Ronteltap c.s. 4'
5 developed a model which describes the shrinking of a
single bubble floating on a liquid, taking into account the physical
parameters as mentioned above. The model was verified experimentally.
Two dimensional foams are interesting model systems, especially for
investigating the mechanism of coarsening processes. The meaning of a
'two dimensional foam' as used in the work mentioned below, is in fact a
monolayer of foam bubbles between two parallel walls as illustrated in
figure 1.
Fig.l An example of a two dimensional foam between two parallel walls.
Measurements on two dimensional foams were performed by Smith6, and a
linear relation between the average cell area and time was found. From
later work by Aboav7
, can be concluded that the second moment of the
number of sides per cell ~2 increases linearly with time. Here, ~2 is
defined as follows:
~2 = fi (n-6)2*f(n), were f(n) is the fraction of cells having n sides.
3
Recently experimental work on two dimensional foams was reported by
Glazier c.s. 8 • Experimentally hardly realizable parameters like: 't~' and •number of cells~~, can be approximated with computer
simulations~- 13 The influence of the Plateau borders was not introduced
into computer simulations as a physically reliable mechanism of the
influence of Plateau borders on the film drainage is lacking.
It can be shown that bubbles with less than 6 sides shrink and
disappear, and that bubbles with more than 6 sides expand. Six sided
bubbles do not change in area. This rule is called Neumann's law14, and
is aften used in simulations of two dimensional foams. Neumann' s law
prediets a linear increase or decrease of surface area with time, and
only accounts for coarsening due to diffusional processes.
Attempts were made to simulate the topology of a soap froth in two
dimensions~ 13 However, such simulations can give erroneous results, as
can be concluded from Contradietory results obtained about the
development of the second moment of the number of sides per cell ~2 with
increasing time. For example, D.Weaire c.s~ 1 conclude that ~2 increases
linearly with time, whereas Stavans c. s ~ 3 find that ~2 goes to a
constant"'l. 4 as time increases. Monte Carlo simulations 1 0 confirm the
asymptotic behaviour of ~2, being finally 1. 4. Beenakker9 showed that
the average bubble size area increases linearly in time, in agreement
with Neumann's law.
The simulations so far do not account for changes in film thickness or
differences in surface tension due to expanding/shrinking surfaces. The
influence of the Plateau border suction therefore also was neglected. In
spite of that the calculations seem to agree quite well with von
Neumann's law, and with the experiments. It is (as far as we know)
generally accepted that the behaviour of a two dimensional faam with
respect to disproportienation as t~ is : A-t and ~2=Constant. Here A is
the average cell area.
Advanced simulations of two-dimensional networks have been publisbed by
D.Weaire12, in which the influence of the liquid fraction on the
coarsening process was incorporated. Plateau borders appeared to
decrease the amount of film area significantly if the liquid fraction is
high. This reduces the disproportionation-rate.
Experimental research (with three dimensional foams) has been done by
Durian c.s. 15 who used laser light scattering techniques for the
determination of the average bubble si ze. The average bubble size was
found to increase with the square root of time.
Spreading
Another mechanism to destray foams is the spreading mechanism, which was
first discussed by Ross: 6 Oil draplets or particles which contain
surface active material spread over a faam film and destray it by so
doing. A droplet will spread over a film if the sum of the interfacial
surface tensions -r re sul ts in a net force on the oil phase: rr> ( ror +
-rol (see Ross 16). The sub-scripts are defined as r:foam film/air,
or: faam film/oil droplet and o: oil droplet/air. The spreading process
has been described later by Prins~ 7 Kulkarni c.s: 8 propose a mechanism
in which silica particles are dispersed over film surfaces by the
spreading of an oil. The particles deplete the film of surfactant
(locally), and cause rupture.
Drainage of horizontal faam films
Films in polyhedral foams drain, because of the suction of the Plateau
borders, until the film reaches the critica! thickness where it breaks.
This means that a delay in the drainage process, will increase the foam
stability. The driving force for drainage of horizontal films is a
pressure difference between the film and the surrounding Plateau
borders. In the film, the pressure is uniform across the film, and equal
to that in the adjacent gas phases because of the virtual absence of
surface curvature;in the Plateau border, there is a lower pressure than
in the surrounding gas phases because the surface curvature in the
Plateau border is directed that way. This pressure difference is, when
the border is connected with a bulk liquid phase, in final resort due to
gravity. Drainage of horizontal films differs from that of vertical
films, because in the farmer there is no "marginal regeneration". This
5
is a special
{margins) of
drainage phenomenon, which can occur at
vertical films. We will discuss marginal
the borders
regensration
later. The drainage of horizontal films is thus a simplified case of
drainage. We therefore will deal first with drainage of horizontal
films.
Reynolds' equation has been employed to describe film drainage in
cylindrical horizontal films in numerous publications~ 9 21 This equation
reads as follows:
-dh/dt (1)
Equation (1) relates the thinning of the film to the film thickness h,
the bulk viscosity ~. the film radius R and the capillary pressure AP.
Apart from the lubrication assumption three other important assumptions
were used in relation [1] . The film is supposed to have a rigid surface,
and is supposed to be plane parallel. A cylindrical shape was assumed
for the film because this shape is most frequently encountered in
experiments on horizontal films.
However, major discrepancies between theory and experiment were reported
by Radoev c.s: 2 and, Manev c.s~;· 24 especially for films with a large
radius. Manev c.s. found a dependenee of the film thinning rate on the
film radius with a power R-o.e rather than R-~
Radoev c.s~ 5 presented a theory on the drainage of a plane parallel film
with mobile surfaces. They concluded from this theory that the drainage
rate can be considerably higher than the drainage predicted by Reynolds'
equation because of the mobility of the surface.
Sharma and Ruckenstein26 therefore developed a theory in which the
assumption that the film is plane parallel was avoided, by assuming
non-homogeneities to be superimposed on a plane parallel film with rigid
surfaces. An average drainage rate is calculated, and good agreement
with experiment is found, with regard to the drainage times of a
SDS/NaCl salution as a function of the film radius of horizontal films.
However only asymmetrical nonhomogeneities will cause deviations in
thinning rates from Reynolds' law, and at present there is neither a
6
theoretica! basis nor experimental evidence for the asymmetry in the
nonhomogeneities. The agreement with the experimental data of Radoev22
on the film thinning rate dependenee of R does not follow from the
theory rigorously. Experimental data were used (viz. the correlation of
the experimental amplitude of the hydrodynamic nonhomogeneities with R) ,
in order to derive the drainage rate to be proportional to R-o.s.
Nonhomogeneous mobile films were discussed by Sharma and Ruckenstein 27
and Ivanov c.s~ 8
However, the theories mentioned above only describe small fluctuations
in film thickness. Dimple formation was studied by Joye c.s~ 9 Here the
complete drainage process of rigid films is given for horizontal films,
starting with a certain (circular) profile, including the contact angle
with the measuring apparatus. Van der Waals attraction and electrastatic
repulsion are taken into account. Joye c. s~ 9 report good qualitative
agreement between simulation and experiment for bath low and high
electrolyte concentration; the formation of thin annular rings could be
simulated. Finite contact angles were observed, indicating that Van der
Waals attraction and electrastatic repulsion play an important role. The
values of the film thickness in their simulation are in between typical
values of the black film and 1.3 ~m.
Calculations on horizontal films can give only partial information about
the drainage in vertical films. The formation of thin film parts and the
formation of dimples can be predicted. In a gravitational field, these
film parts would move up or down until they reach the height were the
film has the thickness of the rnaving film part, due to surface tension
gradients in the film. This phenomenon is similar to Archimedes' law.
Drainage of vertical faam films : marginal regeneratien
Numerous experimental and theoretica! investigations were performed on
horizontal films: 9-
29 However, the fact that gravity does not cause
differences across a horizontal film, in contrast with the situation in
vertical films, severely reatricts the information which studies of
horizontal drainage can give on drainage of vertical films. The drainage
of mobile vertical films is predominantly determined by the phenomenon
7
of marginal regeneration, which is the turbulent motion visible in the
film along the Plateau borders. Marginal regeneratien ie not obeerved in
horizontal films: 0
The drainage of a vertical rigid film in the absence of Plateau borders
can be described analytically (see Mysels c.s. 30
), and the profile of
the film is then parabol ie. The thickness d is a function of the
distance to the top of the film z, time t, viscosity ~. density p and
gravity.
d2 = (4Z'l'j) I (pgt)
The assumption of absence of the Plateau
justified in view of the great importance
borders.
borders however
of the vertical
(2)
is not
Plateau
In the Plateau borders an underpressure is created by gravity, and
causes the drainage and in some cases marginal regenerat ion. Marginal
regeneratien was already reported by Gibbs 31 (see also Overbeek32). Thin
film parts are created along the sides of the film. These parts rise,
while the central portion becomes thinner. That this mechanism can be
the dominating one for film drainage (see Mysels c.s: 0) was confirmed
much later by Hudales c.s:3
Mysels c. s7° was the first who reported about the different drainage
regimes in vertical soap films. They distinguished rigid, simple mobile,
irregular mobile films, and films with an intermedia te behaviour. We
will restriet here the discuesion to drainage of films in the early
stages of a polyhedral foam, in which the thickness of the film is such
that Van der Waals attraction and electrastatic repulsion in the films
play a minor role. We then can simplify the drainage regimes. We will
distinguish between rigid and mobile films, and films with an
intermediate behaviour. A rigid film shows a large number of
interference fringes after formation. The rather slow drainage process
is found not to be uniform; and the mechanism which in films with mobile
surfaces affects the profile with an orderly increase of film thickness
from top to bottorn apparently is not operative in films with rigid
surfaces. In other words, a rigid film can have various thicknesses at
8
the same height. Mobile films drain relatively fast and nat too close to
the Plateau borders, the film thickness at a given height is uniform as
can be concluded from light interf erenee patterns. Rapid film motion
a long the Plateau borders (marginal regenerat ion) is visible. Mysels
explained the phenomenon of marginal regeneratien in the following way.
Thin film parts (with almast the same surface tension as the bulk
solution) will expand at the Plateau borders because they are nat
exposed to the border suction as much as thick film parts (see figure
2). Thick film parts therefore will disappear into the Plateau border.
An equation was derived with which the film thickness of expanding films
(with constant velocity) can be calculated (Frankel's law). Good
agreement was found between experiment 34 and Frankel's law, with regard
to the film thickness at a certain height near the bottorn film/bulk
salution transition, as a function of velocity of film draw-out.
However, Frankel already mentioned that disagreement with experiment was
found if their theory was applied in order to explain marginal
regeneratien near the vertical borders. The calculated thickness ratio
of film parts entering the film from the border, and film parts leaving
the film and flowing into the border (at the same height) did not agree
with experiment. The thickness ratio was calculated on the assumption
that the inflowing and outflowing film parts have the same surface
tension. Another complication with Mysels' theory is that in the
beginning of the drainage process (up to 60 s.), upward flows along the
Plateau borders are predominantly observed. This direction dependenee
can not be explained by the horizontal flows in fig.2 only.
An analogous theory is proposed by Stein35, where more realistic surface
velocity and liquid flows are assumed. Qualitatively, Stein35explains
the discrepancy between the experimentally observed and calculated
thickness ratio, by doubting the assumed equality in surface tension of
inflowing and outflowing regions. This aspect was already noticed by
Mysels, but no quantitative experimental data on this are available.
/ /
'- ~ r " ""' Fig.2 Marginal regeneratien as proposed by Mysels
Prins c. s ~ 6 showed that marginal regeneratien only occurs when the
surface elasticity does not exceed the value of 25 mN/m (this is an
order of magnitude). No quantitative data on the amount of exchanged
material between the film and the Plateau border could be obtained.
Bousfield37 found that low bulk elasticities (compared to high bulk
elasticities) increase the drainage rate of foam films. The effect of
relative low surface elasticities on the drainage mechanism will be
studied in this work {see chapter SI.
Observations by Hudales c.s~ 8 of particles flowing in the Plateau border
show that the Plateau region near the film flows upwards, and that the
more central part of the Plateau border descends. The reasen for the
upward flow given by Hudales c.s. is a Marangoni flow. This Marangoni
flow is due to an exchange of film parts with a higher surface tension
and liquid of the Plateau border with a lower surface tension. The
preesure drop in a Plateau border conduct was calculated by Leonard
c.s~ 9 as a function of the average velocity and the shape of the Plateau
border. Hudales c. s: 8 measured the shape of the Plateau border at
different heights, from which the preesure inside the borders can be
calculated.
Recently a new theory on marginal regeneratien was proposed by
Nierstrasz and Frens. Their work is not publ ished at the moment, and
therefore not all details of their theory are known to us. We will
however discues the main idea of their theory as communicated to us
personally. According to their theory, marginal regeneratien along the
10
vertical Plateau border only consists of outflowing film parts. This
assumption was made because mainly outflowing film parts are visible
during the drainage process. The outflowing film part a are exchanged
against inflowing parts only at the bottorn of the film. Qualitatively,
arguments of compression and expansion of film area in relation with
surface tension gradients are used in favour of this model. Nierstrasz
and Frens claim to be able to explain all experiments on the drainage of
mobile soap films performed by Mysels with respect to the dependenee of
film height. However, it is not clear to us how the model explains the
upflowing regions in the Plateau border observed by Hudales c.s.
By just looking at the phenomenon of marginal regeneratien at the bottorn
of the film, one can see some remarkable analogies with conveetien
streams. We will consider film parts which are not in contact with the
Plateau border at the bottorn of the film. The following consideration is
therefore a simplified case of the process of marginal regeneratien
which takes predominantly place at the vertical Plateau borders. The
thin film parts (compared to the average film thickness at the height
concerned) which rise in foam films, can be seen as the two dimensional
analogue of density differences. Low density bodies (in three
dimensions) will rise due to buoyancy forces, or in other words because
of pressure differences acting on the body surfaces. Flat foam films do
not have internal pressure differences, and therefore surface tension
differences will act as buoyancy forces (see tigure 3). The film part
will move up or down until the film part is at a place in the film,
where the weight is just compensated by the surface tension acting on
the circumference.
11
fig.3.The surface tension and gravity, acting on an inhomogeneity.
The circumference can be chosen arbitrarily large from the
center of the inhomogeneity, so that the surface tension
equals the surface tension of a vertical film in equilibrium.
The crigin of the density difference (in three dimensions) eeropared to
the thickness difference (in two dimensions) however is different. In
three dimensions heat/temperature, or concentratien differences will
cause the density difference. The crigin of thicker and thinner film
parts is however determined by surface tension gradients and pressure
gradients in the film, through surface and bulk rheology.
Influence of solid particles
Solid particles can have various effects on foam stability. Kruglyakov
c.s. 40 found a destabilizing effect because of adsorption of surfactant
molecules on particles (silicon dioxide, sulfite cellulose and carbon
black). Hudales c. s~ 1 also found that small particles promate film
rupture to a limited extend at low CTAB concentration, and explained
this effect by lowering of the CTAB concentratien through adsorption on
12
the glass particles. More experimental data on this effect are presented
in this thesis (see chapter 3) .
Most investigations showed that hydrapbobic particles have a
destabilizing effect on faam (Garrett 42), whereas hydrophilic particles
in general have a stahilizing effect, see Hudales c.s~ 1 Fang-Qiong Tang
c.s~ 3 however found that small hydrophobic particles could also have a
stahilizing effect, which was ascribed to the reduction of Ostwald
ripening in foam, by slowing down the diffusion process of gas from
small bubbles into larger bubbles.
A theoretica! discuesion on the destabilizing effect of hydrophobic
particles is given by Frye c.s~ 4 This effect was found to be due to
promotion of film rupture. Aronson 4 5 showed that hydrophobic draplets
stimulate rupture less than hydrapbobic particles, because of lower
surface roughness. Aronson also found that particles can be swept out of
a microscopie foam film into thicker regions of the film. Dippenaar 4 6
used high speed cinematography to study the behaviour of large glass and
silica particles in small horizontal films. These measurements showed
that particles moved in thin films in order to have the right contact
angle with the liquid. In the present thesis, the limited parameter area
as investigated by those authors is extended: experiments are described
with small particles differing in hydrophilic/hydrophobic character in
vertical films (see chapter 2), and it is shown that these particles can
be used to measure the film drainage.
Film rupture of horizontal films
Two reasans for film rupture have already briefly been mentioned, viz.
rupture by spreading, and rupture by hydrophobic particles.
The most common way for films to break, after drainage to the critical
film thickness, is rupture of the film by surface waves (see Vrij 2). We
do not intend to give a review on this subject, since film rupture
itself is a broad subject, we will only outline the major developments
in this area.
13
Repulsive electrastatic farces compensate the Van der Waals attraction
in equilibrium black films exactly. Two types of equilibrium black films
can be distinguished, the first black film (about 600 Ä) and the second
black film (about 50 Ä), see Overbeek~ 7 The electrastatic repulsion and
van der Waals attraction in these black films, or equilibrium films,
become important for film thicknesses of the order of magnitude of 600 Ä or smaller.
De Vries 48 calculated that spontaneous rupture of films due to thermal
motion, becomes highly improbable for films with a thickness higher than
100 Ä. However, the (critical) thickness at which films break is usually
higher.
The fact that a certain type of surface waves, in particular the
"squeezing mode" waves, may become self reinforcing and then lead to
film rupture, is due to the Gibbs free energy decrease when two close
surface parts become still closer because of Van der Waals attraction.
If the amplitude of such surface waves increases above the film
thickness, then rupture occurs. Vrij c.s:' 49 derived an equation for the
critical wavelength above which films rupture due to growing wave
amplitudes. A critical thickness can be calculated from this critica!
wavelength.
RHEOLOGICAL PROPERTIES
The rheological properties of soap solutions can be divided into two
classes, the surface rheological properties and the bulk rheology. We
will (in this chapter) only consider Newtonian liquida (with respect to
the bulk rheology) .
Apart from the bulk viscosity, the surface viscosity and surface
elasticity are thought to play an important role in foam stability. Two
surface viscosities have to be distinguished: the surface shear
viscosity and the surface dilational viscosity.
The surface shear viscosity is the two dimensional analogue of the bulk
viscosity (in three dimensionsJ and has the dimension (Ns/ml, this in
14
contrast with the bulk viscosity {Ns/m2). The order of magnitude of the
surface shear viscosity for surfactant solutions like CTAB, SOS and
Triton X-100 is about Se-8 Ns/m according to Jashnani c.s. 50 Similar
values were reported for Triton X-100 by Shih c.s: 1 and for SDS by
Shah c.s~ 2 Brown c.s: 3 and also Poskanzer c.s: 4 measured substantially
higher values for SDS solutions, being 2e-6 Ns/m. Mysels c.s7° found
surface viscosities of about 1e-8 Ns/m. Lauryl alcohol {which can be
present as an impurity in SDS) increases the surface viscosity of SDS
solutions significantly. This may both explain the large diEferences
between the surface shear viscosities found for SDS solutions, and the
time dependenee of the surface shear viscosity of a SDS salution as
reported by Bul as c. s 7 5 Some methods for measurements of the surface
shear viscosi.ty are summarized in Hühnerfuss 56and Weissberger c. s 7 7 If
we estimate the surface viscosity from the data above, then we obtain
the value se-8 Ns/m. The surface shear viscosity, gives information
about the mobility of complete film parts in the film. It does not give
information on thinning due to liquid flow between the two film
surfaces. In order to estimate the importance of the surface shear
viscosity compared to the bulk viscosity for the movability of complete
film parts, we consider a film with thickness d and shear rate T'=d7/dt,
where T represents the deformation (see figure 4).
15
d
~!'i 7'
fig.4 The role of the surface shear viscosity. The two reetangles repreaent the front and rear side of a .film with thickness d. This film is subject to a time and place dependent deformation as indicated with the arrows. 7' : Shear rate of deformation
The total force F per film height necessary to realize the shear rate 1'as shown in figure 4 will be the sum of the forces necessary to move the bulk liquid between the two surfaces, and the force per unit length along the height of the film,which causes the surface movement:
F (IJ. * d + 2 * IJ.s) * 7' [N/ml (3)
The contribut ion of the surface shear viscosity, compared to the bulk viscosity, can not be neglected for soap films with a thickness of 1 IJ.ffi,
if information is required about the shear stress of film parts rnaving with respect to adjacent film parts.
The importance of the dynamic surface tension for the drainage mechanism of foam films (determining mobile or rigid behaviour) has already been mentioned by Prins c.s: 6 We will discuss two different approaches to characterize these properties.
The surface elasticity and the surface dilational viscosity are both
16
correlated with gradients in surface tension. The dilation process is
drawn in figure 5.
" 1' 1' 1' 1'
"
~ -7
~ -7
~ -7
~ -7
"' -.v -.v -.v -.v "' !___ ..
fig. 5 Surface dilation. The surface tension increases due to
expansion of the surface area.
The system will still be close to equilibrium (and linearl for small
changes in surface area. Large changes in surface area will re sult in
surface properties far from equilibrium, where the surface tension
response on deformation is not linear. There are therefore two different
approaches to measure the surface behaviour, the approach by the
situation close to equilibrium and that by the situation far from
equilibrium. The surface of a situation close to equilibrium resembles
the surface of an already formed faam, and measurements in that case can
give indirectly information about the faam stability. The surface of the
situation far from equilibrium gives information about the surface
tension in the process of faam formation. Since we are interested in the
drainage of an already formed faam, we studied the close to equilibrium
situation in this thesis, with an apparatus similar to the one used
previously by Lucassen c. 8 The ring metbod which can also be used for
surface rheology was developed by Kakelaar c.s: 9
17
FOAH DESTRUCTION IN PRACTICE
A summary of defoaming techniques is given in Ferry c.s~ 0 Techniques which can be used are: thermal methods, mechanica! methods, preesure and acoustic vibrations, electrical methods and chemical defoamers. Here we will relate the more fundamental principles of foam stability/ destructien as described in this chapter to techniques used in practice.
Thermal methods affect the surface composition and surface rheological behaviour; drainage or Ostwald ripening may become faster in this way. Another effect of heating is gas expansion, and accordingly the films in between the gas bubbles will also expand. This results in an increase of surface tension and can destroy the force balance in the foam. Heating also enhances evaporation of liquid from foam films, which will cause thinning and eventually film rupture.
Foam films are deformed and can break by mechanica! action if stationary or rotating breakers are used. The deformation of the liquid/gas surface will result in a surface tension response determined by the surface rheology. The wettability of the foam/stirrer surface (whether moving or stationary) is frequently important.
Ferry c.s~ 0 does notmention any fundamental process responsible for the destructive effects of ultrasonic waves on foams. Experimental results (other than the work mentioned by Ferry c.s~ 0 ) were obtained by Isayev c.s~~ Sun~ 2 Ashley63 and Sandor c.s~ 4 We expect these waves to enhance the marginal regeneratien mechanism.
Foams can be broken by passage through devices similar to electrostatic precipitators for dust. Here the electrostatic double layer and the surface charge at the liquid/gas interface are used for foam destruction.
Chemical defoamers can act according to the spreading mechanism, or by replacement of surface active material by more surface active material
with poor film stability. A special case of chemical defoaming is formed by hydrophobic particles. The antifoaming capacity of FTFE particles, as
described by Garrett: 2 was found to be larger than the antifoaming
18
capacity of hydrophobic liquid particles (Aronson 45). Apart from the
'hydrophobic effect', particles can in principle destabilize the film by
adsorbing surfactant from it, and in this way deplete the film from
surfactant .Another way of chemica! defoaming is decreasing the
surfactant concentratien by reaction. The destabilizing effect by
adsorption is described in this thesis (see chapter 3).
REFERENCES
(1) Scheludko, Proc. K. Akad. Wetensch. B, 65, 87 (1962)
(2) Vrij, A., Disc. Faraday Soc., 42, 23-33 (1966)
(3) Gibbs, J.W., The Scientific Papers, 1, Dover publications, New York,
p. 244 (1961)
(4) Ronteltap, A.D., Damste, B.R., De Gee, M. and Prins, A., Colloids
Surfaces 47, 269-283 (1990)
(5) Ronteltap, A.D. and Prins, A., Colloids Surfaces 47, 285-298
(1990)
(6) Smith, C.S., Metal Interfaces (American Society of Metals,
Cleveland, Ohio, 1952), pp.65-108
(7) Aboav, D.A., Metallography, 13, 43-58 (1980)
(8) Glazier, J.A., Gross, S.P. and Stavans, J, Phys. Rev. A, 36-1,
306-312 (1987)
(9) Beenakker, C.W.J., Phys. Rev. A, 37-1, 1697-1702, (1988)
(10) Wejchert, J., Weaire, D. and Kermode, J.P., Philos. Mag. B, 53-1,
15-24 (1986)
(11) Weaire, D. and Kermode, J.P., Philos. Mag. B, 48-3, 245-259
(1983)
19
(12) weaire, D., Pbysica Scripta., T45, 29-33 (1992)
(13) Stavans, J. and Glazier, J.A., Phys. Rev. Letters, 62-11, 1318-1321
(1989)
(14) Neumann, J. von, Metal Interfaces (American Society of Metals,
(63) Ashley, M.J., The Chemical Engineer, 368-371 (1974)
(64) Sandor, N. and Stein, H.N., submitted for publication, J. Colloid
Int. Sc i.
23
CHAPTER 2 • DRAINAGE OF CTAB FILMS CONTAINING SOLID PARTICLES
ABSTRACT
In this chapter, marginal regeneratien in films drawn from CTAB
(=cetyltrimethylarnrnoniumbromide} solutions in a frame will be
discussed. The film thickness was measured as a function of time and
height, using interterenee colours which were evaluated by a computer
program, and a film thinning relation was derived for this type of
films. The program used for calculating film thicknesses is briefly
discussed.
Film thickness measurements were performed on polystyrene (PS)
dispersions in CTAB solutions up to 25 vol% PS. The thinning velocity
of the film was related to the viscosity of the dispersion.
PS particles in the film could be observed through their light
scattering. The particles were present in a film from the bottorn up to
a height where the film had a certain thickness. This thickness could
be correlated with the partiele diameter and the contact angle of the
PS particles with the CTAB film.
We also studied the influence of low volume fractions of glass
particles on the drainage of CTAB films. No partiele borderline could
be observed because of the polydispersity of the glass. Low volume
fractions of glass did not affect the drainage rate of the films. The
experiments performed with the glass particles confirm that the
drainage of the particles is determined by the hydrophobicity and the
film thickness.
•This chapter has been publisbed in Chem. Eng. Sci., 48-2, 351-365
(1993)
25
INTRODUCTION
Three phase systems are of ten used in industrial processes. In the
flotation process for example, particles are separated from the liquid
by creating a foam in which the particles disperse preferably. The
present investigation deals with the influence of solid particles on
foam.
Some particles lower the surfactant concentratien and therefore act as
a destabilizer (Kruglyakov1).
Most investigations showed that hydrophobic particles have a
destabilizing effect on foam (Garret 2), whereas hydrophilic particles
in general have a stahilizing effect (Hudales and Stein3). Fang-Qiong
Tang et al~, however found that small hydrophobic particles could also
have a stahilizing effect which was ascribed to the reduction of
Ostwald ripening in foam.
The destabilizing effect of hydrophobic particles has been
theoretically discussed (Frye and Berg5) and was found to be due to
promotion of film rupture. Aronson 6 showed that hydrophobic ( solid)
particles stimulate rupture more strongly than hydrophobic dropiets
because of higher surface roughness. Aronson also found that particles
can be swept out of a microscopie foam film into thicker regions of
the film. Dippenaar7 used high-speed cinematography to study the
behavior of large glass and silica particles (>160 ~m) in small films.
These measurements showed that particles moved in thin films in order
to have the right contact angle with the liquid.
The drainage of the type of films studied, is determined by marginal
regeneratien (Mysels 8, Hudales et al~).
In this work we used monodisperse PS particles (1900 nm, 1007 nm and
300 nm) in 20mmx15mm films drawn from CTAB (=cetyltrimethyl
ammoniumbromide) solutions. The maximum height that the particles
reach in the film is correlated with the film thickness measured with
a Fizeau interferometer. The influence of higher volume fractions of
PS on the drainage rate is studied.
26
THEORY
A film of thickness d reflects in normal direction an amount of light
I:
I=I sin2 (2nnd/A) 0
(1)
In this equation n is the refractive index of the liquid film (1.33),
and A is the wavelength of the light (546 nm). The absolute value of
the film thickness can be calculated at the top of the film as soon as
a black film bacomes visible. Equation (1) can be used for a film
region with no or only minor quantities of solid particles, because in
films containing solid particles the scattering of light makes
observation of interterenee fringes difficult, so that equation (1)
cannot be used for evaluating their thickness.
We observed a partiele borderline (above which there are no particles
in the film) as the films were draining. We will first show that this
effect is not directly caused by diffusion nor gravity (the particles
did nat fall down), but indirectly.
Ditfusion cannot cause the downward motion of the particles, because
this is in one direction only. Diffusion might counteract this
downward motion. However no distinct blurring of the transition
(part iele containing film) I (part iele free film) was observed.
Diffusion translates particles over a distance S:
S=v(2 (kT/(6rr~dll * t) (2)
The particles used can be displaced by diffusion in the drainage time
applied, here we see that this process can be neglected for the two PS
samples:
d=2 ~m;t=20 s; S=2 ~m
d=0.3~m;t=250s; S=20~m
The observed displacement of the partiele borderline was about 13 mm.
The effect of gravity on the partiele velocity in an infinite amount
of liquid or gas can be calculated with equation (3) (a balance
27
between gravity and viscous forces on a single particlel :
V= ~®~ *d2
(3)
The velocity in water and air according to this equation : Air :~=l.8x10- 5 Pas, àp=1000 kg/m3
, g=9.8l m/s 2, d=2x10- 6 m
Water:~=1.0xl0- 3 Pas, àp=70 kg/m3, 9=9.81 m/s 2
, d=2x10- 6 m The Reynolds number (Air) :p vd/~ = 1.2(kg/m3
) x 1.3e-5 = 1.6e-5
Calculated velocities:Vatr=0.12 nun/s;Vwater=0.00015 nun/s. The Reynolds number is small enough for neglecting turbulence (Cl i ft et al~ 0 l, equation 3 can be applied.
We can conclude from the fact that the particles would fall slower in air than they do in the foam film (measurements : 0.56 nun/s), that gravity indeed does play a minor role, and that there must be another reason for the separation of the particles from the liquid. This is
the contact angle phenomenon.
EXPERIHENTAL HETHODS
The apparatus
A film was drawn in a vertical brass frame (see figure 1), which was
held at a fixed position. The four legs of the frame formed four identical films. A fifth film in the middle of the former four mentioned, was a film with completely free Plateau-zones. The frame was positioned in a thermostatted tank in order to avoid evaporation of the liquid. The film could be observed from both the front as well as the back through two windows in the tank. From the front the film was illuminated by a 50 W super pressure mercury lamp (Osram HBO 50 Wl
(see figure 2) . Through the front window, the interterenee pattern of light reflected from the front and rear surfaces of the film was observed; through the rear window, light scattering information was obtained.
28
ALL ANGLES 120 DEOREES
,. .. ,."""'
;
' ,.)·----
20MM
Fig.l.The brass frame in which the films were drawn
Hg lamp Lens Semi reflecting Mirror
Filter
I
Thermostatted tank
Fig.2.The Fizeau interferometer
29
Frame
We placed a light filter (SFK21 Schott, 546 nml in the beam in order
to separate the (green) light from the other wavelengths.
Film thickness measurements
The film was observed with a Panasonic CCTV camera through the
semi-reflecting mirror (figure 2), and the pictures were analyzed
on-line with a computer. The program which calculated the film
thickness from the int erferenee pattern was as follows. First we
determined the exact position of a film in the picture and the
magnification (mm/byte) . After forming a new film in the frame,
pictures (384*288 byte, 256 grey levels) were taken with a variable
interval (0.5 s to 10 s). We masked every picture so that only film
information was visible. We added all bytes in horizontal direction
and put the result in a word (16 bit information) . It appeared that
the value (so calculated) never exceeded the maximum value of a word.
This array of words was stared in a file and processed afterwards. The
film thickness was determined by using equation (1). All films were
measured until the black or silver-black film was visible.
Light scattering measurements
The presence of the PS particles could be easily detected by their
light scattering causing a hazy aspect of the film (see figure 3).
30
Fig.3.The partiele borderline and marginal regeneratien
a 10 vol% dispersion of PS (sample 1, 1900 nm)
Therefore we measured the decrease of the height with time . For these
measurements we again reduced the pictures to an array of words. This
array was processed afterwards in order to calculate the height of the
partiele borderline.
The preparatien of the PS particles
We used for our experiments three PS samples. The preparatien of the
first sample is described below. The secend and the third samples were
kindly donated by H.Leendertse, and B.Krutzer respectively. The secend
and third samples were prepared surfactant-free.
We used a recipe similar to the one described by Almog et al~ 1 We used
PVP, ACPA and CTAB >99% (the recipe gives also good mono-disperse
particles if SOS is used instead of CTAB) The PVP
31
(polyvinylpyrrolidone, average MW 40000) was used for steric stabilization, and the ACPA (4,4'-Azo-bis(4-cyanopentanoic acid),
>98%) is the initiator for the emulsion polymerization. The styrene
{99%) was stabilized with 10-15 ppm p-tert-butyl-cathochol.
We prepared the particles in a batch reaction at 7o"c in 1000ml.
ethanol. The PVP (40 gram in 150 ml ethanol) was added with the CTAB
(12 gram in 50 ml ethanol) . We mixed 2. 8 gram of ACPA in 100 ml.
ethanol and after stirring (the ACPA did not dissolve completely), 300
ml of styrene was added to the ACPA. This was stirred for 5 seconds
and added to the reactor. The emulsion was slightly turbid after 10
minutes. The reaction stopped after 24 hours. The PS was centrifuged 4
times with water.
The characterization of the PS particles
The partiele diameter was determined both with the Coulter counter ZM and with the Coulter LS 130 (see table I). The (-potential of the
particles was determined with the Malvern (-sizer 3 (see table I) in a
0.002 M CTAB solution.
Table I. The partiele size and (-potential of the particles
In figure 3 we can see an interesting phenomenon. The process of
marginal regeneratien has been made visible by means of the PS
particles. Marginal regenerat ion creates thin film parts which rise
(rapidly) in the film. These parts again are essentially free of PS
particles. This indicates that neither gravity nor ditfusion is the
reason for the fact that the particles used can nat be present in a
film which is much thinner than the partiele diameter itself.
The place of the partiele borderline (above which there are no
particles in the film), can be explained similarly to the reasoning by
Dippenaar7 on the contact angle between glass particles in a film.
The film is expected to thin until it has reached a slightly smaller
thickness than the partiele diameter (see figure 8) . The particles
will create a contact angle and fall dry for a part. The film
continues thinning until it has no radius of curvature near the
particle. The partiele will be pushed downward in a thicker region. In
our case it is not clear whether the last drawing of figure 8 will be
reached in the thinning process, since the film is very large compared
38
to the particle. The film therefore has no significant radius of
curvature in all directions.
Fig.B.A partiele in a film,the drainageprocessof the partiele
in the film.
The hydrophilic particles (both 300 nm and 1007 nm) were pushed out of
the film when the film reached their own thickness. Hydrapbobic
particles could be present in a film which is thinner than the
partiele diameter. This can be explained by the larger contact angle
of the hydrapbobic particles, we calculated this angle to be 46
degrees. The small particles act the same as large particles (>160 ~m)
with which Dippenaar7 performed experiments. The contact angle causes
drainage of the particles which follow the drainage of the film
completely. If the particles stick to the surface, their Brownian
motion will be suppressed by the Marangoni effect and by contact angle
hysteresis. They will thus tend to follow the motion of the film. This
phenomenon appears to be strong enough to suppress even the Brownian
motion of the 300 nm spheres. We found a similar behaviour for glass
particles (1-2~.tm) which did not have a distinct effect on the film
thinning process of films drawn from CTAB solutions unless they lower
39
the CTAB concentratien by adsorption. Tbis bowever could not happen at
the volume fractions used ( <0. 5%) . The hydrophilic glass particles were not monodisperse, and the partiele borderline therefore was not
very sharp.
In table III we find within experimental accuracy a linear correlation between the thinning velocity (V) and the viscosity of the liquid:
(5)
The result of the present investigation indicates that marginal regeneratien is inversely proportional to the viscosity of the solution, since marginal regeneratien is the major mechanism of film drainage.
CONCWSIONS
The actual thickness of the film at the partiele borderline is determined by the hydrophobicity of the particles. This is in agreement with other investigations (Dippenaar 7
). The particles do not flow down because of gravity directly. Diffusion can be neglected.
The thinning rate from foam films of PS dispersions in CTAB (up to 25
vol% PS) is more or less linearly correlated with the viscosity. This suggests that marginal regeneratien is also linearly correlated with the viscosity, because marginal regeneratien is the major mechanism of film thinning in this type of films.
Low volume fractions of glass particles did not affect the drainage rate of CTAB films. The particles did not give a partiele borderline because of their polydispersity. The experiments with the glass particles confirm that the drainage of the particles is determined by the hydrophobicity and the film thickness.
40
REFERENCES
(1) Kruglyakov, P.M. and Taube, P.R., Colloid Journalof the USSR,
34, 194-196 (1972)
(2) Garret, P.R., J. Colloid Interface Sci., 69-1, 107-121 (1979)
(3) Hudales, J.B.M. and Stein, H.N., Colloid Interface Sci., 140-2,
307-313 (1990)
(4) Fang-Qiong Tang, Zheng Xiao, Ji-An Tang and Long Jiang, J. Colloid
Interface Sci., 131-2, 498-502 (1989)
(5) Frye, G.C. and Berg, J.C., J. Colloid Interface Sci., 127-1,
222-238 ( 1989)
(6) Aronson, M.P., Langmuir, 2, 653 659 (1986)
(7) Dippenaar, A., Int. J. Hiner. Process., 9, 1-14 (1982)
(8) Mysels, K.J., Soap films studies of their thinning and a
Bibliography, Pergamon Press, London (1959)
(9) Hudales, J.B.M. and Stein, H.N., J. Colloid Interface Sci., 138-2,
354-364 (1990)
(10) Clift, R., Grace, J.R. and Weber, M.E., Bubbles, Drops and
Particles, Academie Press (1978).
(11) Almog, Y., Reich, S. and Levy, M.,
(1982)
41
Polym. J., 14-4, 131-136
APPENDIX .ZA
We consider a film element with height Ah, width b and thickness d.
The volume V will therefore be V=b*d*Ah. The flow per unit of
height out of such an element will be:
Q = * v· =b*d' n
Hudales found Q to be equal to Q=k*d were k and n are arbitrary
constante. Separating thickness d from time t, and integration in time
leads to:
( 1-n) kt/b=d1-n
Here we assumed the film to be infinite thick at t=O, and n>1. A
double logarithmic plot gives information about k/b and n
lnld)=1/(1-n) * ln(t) + 1/(1-n) * ln(k(l-n)/b)
42
CHAPTER 3
THE INFLUENCE OF GLASS PARTICLES ON THE FOAM STABILITY
OF CTAB SOLUTIONS
INTRODUeTION
Solid particles can have many effects on the foam stability of
surfactant solutions. Both stahilizing and destabilizing effects have
been reported in literature~ 5 The stahilizing effect can be explained
by an increase in bulk viscosity (see chapters 2,4).
In this chapter, the destabilizing effect by adsorption of surfactant
on solid particles is investigated. The adsorption not only decreases
the surfactant concentration, but can also make the partiele surface
hydrophobic.
EXPERIMENT AL
Two kinds of experiments are described
experiment concerns the faam stability
in this chapter. The first
of a CTAB-solution/glass
mixture, and the second experiment is a direct adsorption maasurement
of CTAB on glass.
The foam stability was measured in a closed measuring cylinder. An
amount of surfactant salution to which glass was added, was mixed
rigorously in the measuring cylinder by shaking by hand for 10 s. A
foam was formed in the measuring cylinder. Af ter a certain time, a
rather well defined faam/pure liquid interface became visible. The
height in the measuring cylinder of this interface increased due to
drainage. It appeared that the foam/pure liquid interface was sharp
enough af ter 40% drainage of all liquid present. Two drainage times
were measured, going from 40% liquid drainage to 60% drainage (initial
drainage ra te), and from 60% to 80% drainage ( final drainage ra te) .
The experiments were performed in two measuring cylinders, 100 ml.
44
(filled with 25 ml. glass/surfactant solutionl and 250 ml. (filled with 50 ml. glass/surfactant solution) respectively. In this way, the drainage velocity {ml/s) could be calculated. Although this metbod cernprises shaking by hand and thus is subject to differences between different investigators, it is found that results obtained by one investigator aiming at reproducability of shaking, show a reasonable degree of reproducability.
The adsorption of CTAB on glass was measured directly by means of a potentiometric titration with the Orion 940/960 Autochemietry System, with an ion-selective electrode developed by Holten c.s~ Glass was added to a 0.01 M CTAB solution and stirred for 30 min. The glass was then separated by means of a centrifuge, and the CTAB concentratien was measured with the potentiometric titration. The separation of the glass was relatively easy because of the large density difference with the soap solution.
Materials
The adsorption and foam stability were measured with the following substances: CTAB (~ Sigma Chemica! Co.) and glass particles (<10 ~m Lauwers Glass, Hapert, The Netherlands). Twice distilled water was used toprepare the surfactant solutions. The particles were separated into fractions with different sizes by sedimentation~ The density of the glass particles was determined in a Quantachrome stereo-pycnometer SPY-3, and the partiele size distribution was measured with a Coulter Counter ZM (see table I).
Table I, The characterization of the glass particles Mean values and standard deviation
Two CTAB Concentratiens were used (0.02 M CTAB and 0.001 M CTAB). Bath
concentrations are above the cmc (9e-4 M). The results are presented
in figure 1 (0.02 M CTAB) and figure 2 (0.001 M CTAB).
We can only see an increase in foam stability, on the addition of
glass particles for the 0.02 M CTAB solution. The CTAB concentratien
will decrease due to the addition of the glass, but will not drop
under the cmc. For the 0.001 M salution (which is just above the cmc),
we see a decrease in foam stability due to adsorption of the CTAB on
the particles. In figure 2, the data for the 10 ww% 4-5 ~m glass and
20 ww% 5-10 ~m glass are not presented, because almast no foam was
formed after shaking.
The increase in foam stability of the 0. 02 M CTAB salution on the
addition of glass particles does not scale linearly with the increase
in bulk viscosity of the homogeneaus dispersion. The foam in
dispersion is however not a homogeneaus one, since the particles are
preferably present in the thicker Plateau borders. This gives rise to
an additional increase in bulk viscosity, and might explain the
apparent discrepancy with the results of chapter 2.
The very st rong decrease in foam stability of the 0. 001 M CTAB
salution on the actdition of glass particles can be explained by the
hydrophobic character of the glass in a CTAB salution with a
concentrat ion lower than the cmc. Hydrophobic surfaces destabilize
foam according to Garrett 4 and Frye c ..
From the adsorption measurements performed with the potentiometric
titration, we plotted the concentratien after the actdition of the
glass toa 0.01 M CTAB salution in figure 3. We can clearly see that
the glass decreases the CTAB concentratien in salution strongly.
46
1.00
0.80 .!e. :g til
0.60 I- -11- INITIAL RATE < ~ til 0 < 0.40
_._ FINAL RATE
z < ~ Q
0.20
0.00 0 10 20 30 40
WW% GLASS
Fig.1 The drainage rate [ml/sl - ww% Glass 4-5 ~m in a 0.02 M CTAB solution.
1.50 r-----.--r----..,...------.. I I ..
1.00
'I .. I' .I
'I .. I' •' I I •' '. .. 'I .. I' •' -11- INITIAL RATE I I ..
I .. .. 4-5 11m GLASS I • .. ,I
•' --- FINAL RATE .. .. •' Jl
4-Spm GLASS
•' •' •' -e- INITIAL RATE ,. 5-IOpm GLASS •: 0.50
-e- FINAL RATE 5-IOpm GLASS
0.00 ...._ _____ ......_ _____ __J
0 10 20
WW% GLASS
Fig.2 The drainage rate [ml/sl - ww\ Glass 4-5 ~m and 5-10 ~m
in a 0.001 M CTAB solution.
47
10
9
~ 8 0 ); 7 • ! :z 6 0 1= 5 < a: 4 .... z Q;l u 3
z 2 0
u
0 0 2 3 4 5 6 7 8 9 10
WW% GLASS 2-3 [f.lm)
Fig.3 The adsorption of CTAB on 2-3 ~m glass particles. Concentratien [rnMol/11 wwt glass.
CONCWSIONS
The results indicate that glass particles increase the faam stability if they do not decrease the surfactant concentratien to values below the cmc. Hudales c. s ~ found an increase in foam stability af ter addition of large glass particles, and a decrease in foam stability after actdition of small glass particles. This is in agreement with our work, since small particles have a much higher specific area. They will therefore decrease the CTAB concentratien and foam stability much more.
48
REFERENCES
(1) Schellinx, J., De Invloed van Vaste Deeltjes op de
Schuimstabiliteit van CTAB-oplossingen, afstudeerverslag T.U.E.,
Eindhoven ( 1990 l
(2) Hudales, J.B.M. and Stein, H.N., J.Colloid Interface Sci., 140-2,
307-313 (1990)
(3) Kruglyakov, P.M. and Taube, P.R., Colloid Journalof the USSR, 34,
Additional to the drainage times, information on marginal regeneration can be obtained by measuring the wavelength of the thin film spots at the bottorn of the film. The wavelength of these spots in the CTAB/water and the CTAB/water/50% (w/w) glycerol mixtures was measured near the horizontal film/bulk liquid transition at the lower side of the film. The results are given in Table III. Figure 5 is an example of an analyzed picture.
Table III, The wavelenght of marginal regeneration at the bottorn of a film
Water/CTAB 0.002 M glycerol/wateriCTAB 0.005 M
thickness wavelength thickness wavelength d[nm] À [mm] d[nml À [mmJ
1539 0.86 781 0.47 1232 0.79 391 0.35
513 0.62 293 0.31 410 0.62 195 0.32
DISCUSSION
The CTAB solutions below the critica! micelle concentration (cmc=9e-4 M) did not give rigid films and drained faster than solutions above
the cmc. The drainage time above the cmc was no langer a function of
60
the concentratien (except for a slight increase which can be ascribed
to the increase in viscosity} . The measurements below the cmc however
were very tedious and were performed with great care in order to
prevent dust from entering the solution. We found that sametimes rigid
films were formed below the cmc if this preeautien was not taken. This
gave rise to poor reproducibility. Rigidity was found to be due to
impurities by other researchers as well ':' 11
There is (as far as we know) no theory which describes the drainage of
mobile vertical films quantitatively. Seeking an easy way to campare
the measurements, we considered two possibilities: the drainage
velocity and the (extrapolated) drainage time. Although both options
are characteristic for the drainage process, we pref er to use the
drainage time because it is independent of height.
A significant effect but not a very strong
film thickness was found on the wavelength of
the bottorn film/Plateau border boundary.
horizontal (SDS + NaCl) film was measured
effect of viscosity and
marginal regeneratien at
The wavelength in a
by Radoev et al: The
diameter of the nonhomogenities was slightly larger than 0. 005 cm.
This is 1 order of magnitude smaller than the wavelength found in our
systems (about 0.07 cm). The influence of surface rheological
parameters on the decay of the amplitude of transveraal surface waves
is investigated in appendix 4A. The amplitude decay of the surface
waves was found to be negligible within the time scale of measurement
of the wavelength (see ref.2 appendix 4A).
The measurement of the glycerol/wateriCTAB mixture indicates that the
drainage-time scales (almost) proportional to the bulk viscosity, in
agreement with the theory of Ruckenstein and Sharma~' 7 The
proportionality can be used to estimate the effective shear rate and
shear stress, in the dominant process of film thinning as fellows. We
measured the CTAB/SA system in a Deer and a Bohlin viscosimeter and
found our results to be in agreement with the measurements of
Strivens~ At low shear rates, hysteresis was observed with the Bohlin
viscosimeter. For the CTAB/SA sample we found a drainage time of 231
s. This indicates that the viscosity of the salution is about 6. 4
mPas. The shear rate in this process therefore is (see figure 4) 100
61
/s. The shear stress therefore is 0.64 N/m2. This value is compared to
the shear stress as can be calculated with Mysels' theory on marginal
regeneration. Reasonable agreement was found (see Appendix 4B).
CONCLUSIONS
The drainage of thin liquid CTAB films does not depend on the film
height within the range 13 -17 mm. The drainage of a CTAB film above
the cmc is not a function of the concentratien (0. 001M-0.02Ml. The
drainage below the cmc shows a slight increase with a decrease of
concentration.
The drainage rate was found to be inversely proportional to the
viscosity. The shear stress causing the drainage was estimated to be
0. 64 N/m2• Reasonable agreement was found with calculated values on
the basis of Mysels' theory on marginal regeneration.
The wavelength of the film spots in marginal regeneratien was one
order of magnitude larger than the wavelength found in horizontal
films.
ACKNOiiLEDGEHENT
This work was made possible by financial support from Stichting
Technische Wetenschappen and Voorbij Beton b.v. We thank dr. N. van Os
for the donation of 3 SDBS samples, and A.J.G. van Diemen for placing
polystyrene particles at our proposal.
REFERENCES
(1) Brady, A.P. and Ross, S. J.Am.Chem.Soc. 66, 1348-1356, (1944)
(2) Rácz, Gy. Erdös, E. and Kocz6, K. Coll. Polym. Sci. 260,
720-725, (1982)
62
(3) Mysels, K.J. Shinoda, K. and Frankel, S., Soap films studies of
their thinning and a bibliography; Pergamon Press:London, 1959;
Chapter 2-1
(4) Hudales, J.B.M. and Stein, H.N. J. Colloid Interface Sci. 138,2,
354-364, (1990)
(5) Radoev, B.P. Scheludko, A.D. and Manev, E.D. Journal Colloid
Interface Sci. 95,1, 254-265, (1983)
(6) Ruckenstein, E. and Sharma, A.J., J.Colloid Interface Sci., 119,
1-13, {1987)
(7) Sharma, A. and Ruckenstein, E., Colloid Polym. Sci., 266, 60-69,
These equations are similar to the ones which were derived by Sharma and Ruckenstein 1 earlier. The change in film thickness is determined by this velocity profile, the mass balance [6], and the average
velocity u (formula [8]).
[61 a (HU)
+ ~- 0 ----ex- at -
The average velocity U can be calculated from:
Ho/2 [7] HoU= J u(x,z,t)dz
-Ho/2
[8] U(x,tl f(x,t) * ~/6 + Us(x,t)
A force balance at the film surface gives information about the surface tension gradient. This surface tension gradient is small, as can be verified with equation [13], but has to be calculated since it determines the surface velocity in time through the elasticity. The surface tension gradient is assumed to compensate the pressure gradient exactly.
[9) au au I ax = 11 az
Ho/2
Ho*f (x, t) *ll
The surface elasticity of the film relates the surface velocity with the surface tension behaviour in time, according to equation [10):
au aln A [10] at = c ---at c &A A at
c ( a (bus) A ) bAx ax x
au. c-ox
In this relation, c is considered to be a constant (c*f(t)), because the film is close to equilibrium. Now we have a set of 5 equations, which can be reduced to one differential equation. Formula [12] was
obtained from equation [6] were the assumption 8H/ax~O was used.
66
[ll] u (x, t) f(x,t) H~/6 + Us(x,t)
[12] Ho~ a x + BH 0 --at=
[13} 8f1' f (x, t) Ho 0 ax + 'Ij
[14] 8f1' aus(x,t) 0 at - e a x =
[15] f(x,t)
Differentiat:ion of [13] to t and [14] to x eliminatea the surface
tension as variable:
[16] = 0
Single integration of [16] gives (taking into consideration that the
derivatives for t~ go to zero):
[17] 0
Introducing forrnula [11] and [15] into [12] :
[18] 3 4
~f!o _2_!!4 + Ho 241J ax
BH + at 0
The surface velocity us can be eliminated with equation [17]. We then
obtain one differential equation [19] , which describes the drainage
behaviour in time.
[19] HofJ'o ~
1 BH +~at 0
It is useful to make this relation nondimensionless. We therefore
introduce the following parameters [20] into equation [19] and obtain
the dimensionless differential equation [21] :
[20) H=.lf*Ho X=~*Ho ; t= t*to where to 241JHo/fJ'o
[21]
67
I
We try the following solution, with the dimensionless parameters A, w ~ (W;W•* tol and k (k;k*Ho=2rrHo/À), for this equation:
[22] U = 1 + A*ei (wt-k)
and obtain the dispersion equation [231 for this problem.
Or, rewriting [23]:
[24] w
After resubstitution of the dimensionless parameters k,w as used in this Appendix, we obtain equation [25) . This relation has previously been derived by Vrij c.s~ as a special case of equation (5) in their paper, for the limiting case p~O and ~0.
1251 w• ( 24;Ho J = i (k Ho) 4
The assumption 8H/8x~o (which implies aujax~O according to equation [13]) is indeed valid for small amplitudes (A) as can be seen in formula [22). The neglected term in equation (2] contains A2
, and is smal! compared to the ether term which scales with A.
What we originally wanted to know is how fast ripples on a film surface fade away. If we start with the following film profile:
H(oc,O) = 1 +A cos (koc)
Then the evolution of the thickness u (a:, t) in time will be according to [221 :
The characteristic time (in [s]) for fade away of a ripple with wavelength À=2rr/k (m] on a film surface is therefore:
68
to * (1 + CTo(Hok) 2 /4c)/(Hok) 4 [s]
The wavelength of the waves in marginal regeneratien is for wateriCTAB
films 0.7 mm (see chapter 4). We take the following values:
Ho=1e-6 m, cro=37e-3 N/m, c=le-3 N/m, k=9e+3 /m, and l)=le-3 Pas. The
calculated characteristic time is r=100 s. This time will not decrease
significantly if the film elasticity is increased, because the term
cro(Hok) 2 /4c is small compared to unity already.
In the foregoing data obtained from measurements on vertical films has
been used (viz. the wavelengthof marginal regeneratien at the bottorn
film boundary) . It is not a priori clear on what bases these data can
be applied for calculations on the drainage of horizontal films. In
fact in the case of horizontal films as discussed here, Maraugani
flows are calculated which are formed spontaneously in order to
compensate for the pressure differences due to curvature of the film
surface. There are in this case no external influences on the film or
the film surface, since the contact with the Plateau border is
supposed to be absent in this calculation. It is reasonable to expect
that drainage by curvature also takes place in vertical films, as a
part of a much more complicated drainage process. It is therefore
useful to estimate the contribution of spontaueaus Marangoni flows in
combination with the Poiseuille flows on the drainage process.
If we look at the spots, formed at the bottorn of a vertical CTAB film,
we see that these spots rise in the film until they reach the height
were they have the same thickness as the film. The time necessary for
this process is much smaller than 100 s (the order of magnitude is 1
s). Therefore, spontaueaus Marangoni flows in the film do not have
enough time to affect the amplitude or the wavelength of the wave. The
wavelength will be the same at all times, according to equation [25].
We can therefore conclude that the wavelength measurements as
presented in Chapter 4, are not subject to significant errors due to
the process mentioned above. The large characteristic fade away time
also gives an explanation for the persistenee of the marginal
regeneratien spots in vertical films.
69
REFERENCES
(1) Ruckenstein, E. and Sharma, A., J. Colloid Interface Sci., 119-1
1-13 (1987)
(2) Vrij, A., Hesselink, F.Th., Lucassen, J. and Van Den Tempel, M.,
Proc. Kon. Ned. Akad. Wetensch., 873, 124-135 (1970)
70
APPENDIX 48
COHPARISON WITH HYSELS' THEORY OF MARGINAL REGENERATION
The shear stress far the process determining film thinning in a
CTAB/SA salution (0.001M) as calculated in the present work fram the
drainage time is 0. 64 N/m". We will naw calculate the shear stress
according to the theory of marginal regeneratien of Mysels et al~
The shear stress ~ will be equal to the gradient in surface tension,
and thatwill compensate the pressure gradient exactly, because there
is no net force acting on film elements. The symbols used are defined
as in Mysels' work, were r is the shear stress, ~ the viscasity, 7 the
surface tension, x the direction of flow, T the film thickness, P the
pressure, and y the direction perpendicular to the direction of flow.
The value of the shear stress calculated from this relation is a
maximum value, since both the parameters v and d 3Y/dX 3 were given
their maximum value. The order of magnitude of the measured shear
stress in the CTAB/SA system is in agreement with the theory of Mysels
on marginal regeneration, and Hudales, who fellows this theory in this
respect. The shear stress is calculated for the out-flow of the
Plateau border. The experimental agreement indicates that out-flow is
the rate determining step.
REFERENCES
(1) Mysels, K.J., Shinoda, K. and Franke!, S., Soap films studies of
their thinning and a bibliography; Pergamon Press: Londen, 1959;
Chapter 5
72
CHAPTER 5
SURFACE RHEOLOGY OF SURFACTANT SOLUTIONS CLOSE TO EQUILIBRIUM
ABSTRACT
In this chapter we present surface rheological measurements of various
surfactant solutions close to equilibrium in a Langmuir trough. We
found that the starage modulus is, in the systems investigated, higher
than the loss modulus. The rheological behaviour depends strongly on
the surfactant concentration, even at concentrations exceeding the
cmc. Films with quite different surface rheological properties were
found to show similar drainage rates. This supports earlier work! in
which the velocity of film drainage was found to be determined by bulk
viscosity effects.
A number of possible explanations are examined for the cause of the
surface rheological effects found in our solutions. The rheological
effects at concentrations exceeding the cmc can best be ascribed to
2-dimensional ordering of surfactant molecules at the surface combined
with interaction of these molecules with micelles in the nearby
solution.
INTRODUCTION
It is generally accepted that knowledge of surface rheology is
indispensable for a good understanding of foam production and faam
stabilization or destruction. Two major types of surface rheology for
liquid surfaces can be distinguished: the surface rheology far from
equilibrium and the surface rheology close to equilibrium. Each type
has its own field of interest. The situation far from equilibrium is
interesting to obtain information about foam production, since this
process is usually accompanied with expanding liquid surfaces due to
bubble formation. The situation close to equilibrium resembles an
already formed foam during drainage. The latter gives therefore
74
information about the foam stability once it is formed.
Measurements at the situation far from equilibrium give information about the diffusion coefficient of soluble surfactants, as reported by Rillaerts c.s~ and Fang c.s: Measurements in the situation close to equilibrium can give information about the diEfusion coefficient and can also be used to determine the surface elasticity and surface dilational viscosity due to other processas than diffusion.
Our research was focused on the situation close to equilibrium. There are a number of ways to create such a situation, a.o. the methad used by Kakelaar c.s~ In our experiments, a Langmuir trough was used to measure the surface dilational and elastic behaviour, similar to its use in measuring monolayers (see Lucassen c.s~l.
The foams in which we are interested, are foams made from solutions with a surfactant concentratien exceeding the cmc. Recent experimental and theoretica! work on surface rheology of surfactant solutions above the cmc has been done by Dushkin c. s ~, Fainerman 7 and Fang c. s ~ Lucassen 8 investigated the surface rheology of surfactant solutions above the cmc, subject to periodical oscillations. This theory was generalized by taking into account the effect of polydispersity of diffusing micelles by Dushkin c.s:
EXPERIMENT AL
The apparatus
The experiments were performed in a PTFE trough (see fig.1), with PTFE barriers. The effective length of the trough (L) could be varied in between 76 and 510 mm. The width (160 mml was fixed, and the trough was filled up with liquid to the rim (depth 12 mm) . Overflow was prevented by the finite value of the contact angle. The solutions were measured within one hour. One of the barriers was driven by an excentric (angular frequency varying from 0.003 to 1 s- 1
), the other barrier was fixed. The displacement of the harriers was measured with
75
a Sangamo Schlumberger DFS displacement transducer. The signal
produced by the displacement transducer had a sinusoidal character
with a r.m.s. deviation of 0.006 mm (for an amplitude of 2.96 mml.
Deviations Erom sinusoidal deformation were about 0.2% of the
deformation at the time concerned. The surface tension was measured as
close to the stationary barrier as possible, with the maximum distance
between the edge of the plate and the barrier being 5 mm. This was
done in order to minimize the disturbing influence of the oscillating
bulk liquid on the Wilhelmy plate, by means of drag forces. These
farces might be important for solutions with low elasticities.
Solutions with higher elastic moduli can best be measured at a
di stance of 0. 423*L from the moving barrier as reported by
Lucassen:'· 10 The surface tension was measured as a function of time
with a Cahn 2000 balance and a Pt Wilhelmy plate with a circumference
of 40.0 mm (see fig 1).
STATIONARY BARRIER
MOVING BARRIER
~ I
·;;- 160 MM
j L
WILHELMY PLATE fig.l The Langmuir trough.
Two signals in time were obtained from the trough measurements, one
from the Cahn balance (the surface tension), and one from the
76
displacement transducer {the barrier movementl . Bath signals were
stared and processed in a computer. The phase angle and the amplitude
or the signals were calculated from these data.
Data processing
The methad of data processing, as reported below, is an easy to use
and fast algorithm to calculate the relative phase angle and amplitude
of the surface tension response on deformation. Attention is paid to
this process, in order to eliminate the disturbing influence of signal
noise as much as possible.
For a calculation of surface rheological properties, we need
values of the surface tension amplitude, the barrier position
amplitude, the angular frequency and the relative phase angle.
The angular frequency {w) of bath signals is the same. Bath the
angular frequency and the barrier position amplitude are well known
(determined by the excentric) . The phase angle ~ {compared to a pure
sinus with arbitrarily chosen time of passage through zero
displacement) was calculated for bath signals; and the angles were
subtracted from each other in order to calculate the relative phase
angle e (8=~1-~2) . The average value of the surface tension was
estimated manually, from a plot of the surface tension against time,
because a numerical summatien of the data might introduce errors due
to 'incomplete' waves. A sample timeT was chosen for bath the surface
tension signal (consisting of N points at times [O,T,2T, .. , (N-l)T])
and the signal from the barrier movement (consisting of N points
measured at the same times) . The constant sample time T was chosen
arbitrarily but subject to the condition that T<O .ln/w. This means
that during one barrier movement at least 20 measurements were
performed. The total nuffiber of measurements N was chosen as N>60.
The surface tension signal for example was treated as fellows.
The average surface tension value was subtracted from every point,
77
g1v1ng N points y1
• The obtained values were then used for calculating
the following two summations ( [1], [2]) which are regarded as the
numerical approximations of the integrals ( [3], [4]), for which also
analytica! expressions are available.
N-1 L y1sin (wiT) * T M [1]
1=0
N-1 L y1cos (wiT) * T Q [2]
l=O
Two equations ([3), [4)) with two unknown parameters, ~ and A
The measurements reported in this chapter exclude the possibility that
differences in surface elasticity affect the drainage of the soap
films investigated previously! since a relatively large difference in
surface elasticity does not significantly affect the drainage of the
films concerned. The drainage time is related much more closely to the
bulk viscosi ty, as suggested in chapter 4. We also see (fig . 3) that
the elastici ty increases when glycerol is added i however we do not
expect a large effect on film drainage by this increase of elasticity,
since similar surface rheological differences were found to have only
a small effect on the drainage time in the case of CTAB solutions
(0.002M and 0 . 02M).
Both octanol as weIl as pentanol were added to the CTAB solution. In
the case of pentanol we found very different values for the phase
angle. Addition of oetanol results in sueh low IEl values as to make
them very diffieult to measure preeisely by our apparatus. However,
the drainage times of the CTAB solutions with or without the added
aleohols were almost the same (32.7, 33.3 and 36.8 5) .
A number of SDBS solutions differing in the place of attaehment of the
benzene ring to the alkyl ehain were measured, and all of them gave
low IEl moduli and low phase angles. The Na 2-(3-dodecyl)-4,5 dimethyl
benzenesulfonate gave moduli with too much signal
interpretation.
86
noise for
An attempt to explain the surface rheological behaviour in terms of molecular struct\.lr& (see Appendix 5A) was ba.mp&red by Uw high dependenee of the data on concentration, even at concentrations exceeding the cmc. In the case of CTAB, which was investigated at concentrations 2*cmc and 20*cmc, the solutions showed only minor differences in bulk viscosity (see table I). This excludes the formation of liquid crystals.
The observed surface rheological behaviour can not be explained by diffusional exchange of surfactant molecules to the surface. Arguments for this are given below. In order to explain the surface rheological behaviour and the influence of concentratien on this, we consider apart from the diffusional exchange mechanism three other possibilities.
A) Diffusion of surfactant to the surface
It is interesting to know whether diffusion plays a role in the measurements close to equilibrium. A model which describes the surface rheology determined by diffusion, was presented by Lucassen c.s: This theory is valid for solutions with a concentratien up to the cmc. We apply the theory for a salution at the cmc, starting with the calculation of the parameter ( = {F v (ID/2w) for a CTAB sol ut ion. In this relation, c is the concentratien of surfactant, r the surface excess, ID the diffusion coefficient and w the angular frequency. For the diffusion coefficient, a value of 5.6e-10 m2 /s (Rillaerts and Joos 2
) was employed.
For dc/dï we derive from the Langmuir equation, dc/dr=(2a/rool (c/a+ll~
Using the experimentally obtained rro and a values, we obtain for ((w),
((w) 15.4/vw. If diffusion is rate determining, then the phase angle e and modulus IEl will be:
B = atn((/(1+())
-(d~/dlnï)/v(1+2(+2(2)=RTÏ00 (c/a)/v(l+2Ç+2Ç2 )
0.0618/11'(1+2(+2( 2)
87
[12]
[13)
[14)
From this result it is clear that values calculated for the phase
angle e are in between 44.8 and 43 . 2 degrees for w=O.Ol/s to 1/5. The
curve plotted in Eig.3 , represents the modulus IEl calculated with
equation [14).
A more sophisticated model was described by Lucassen~ taking into
account micellization . Both the phase angle and the slopes of the
log I EI-log w plot were expected to increase due to the presence of
micelles. Lucassen 8 also concluded that the elasticity IEl decreases
for solutions exceeding the cmc . However, we found substantially lower
phase angles than 43 degrees and the slopes of the log/EI-log w plot
were lower than 0.5. Moreover, the measured elasticities IEl were
higher than the values calculated according to the diffusion mechanism
at the cmc, whereas lower elasticities were expected.
These observations exclude an explanation of the difference between
surf ace rheological data at concentrations 2*cmc and 20*cmc by
diffusion .
B) Electrostatic repuls ion between the head groups
An explanation for the large differences in surf ace rheological
properties found between the two CTAB solutions above the cmc might be
a difference in electrostatic repulsion between the he ad groups. The
effective free ion concentration however, is not expected to change
above the cmc for a surfactant solution.
The double layer (l/k) calculated on the basis of surEactant molecules
not bound in micelles is in both cases (0.002M and 0 . 02M CTAB) 10 nm .
This is much larger than the average di stance between adjacent
adsorbed CTA' ions, calculated Erom r oo and a (0 . 70 nm, on the
assumption oE cubic close packing) .
The electrostatic repulsion between micel les may be important iE the
average distance bet ween micelles becomes smaller than twice the
electrical double layer, al though we expect also a more pronounced
diEEerence in viscosity tor the two samples it this interaction would
88
be important. The number of surfactant molecules per micelle as given
by Roelants C.S~4 for CTAB is 104. This means that the average
distance bet ween micelles varies from 55 nm in the 0.002M solution to
20 nm in the 0.0 2M solut ion . lntermicellar interact ion can only j ust
explain the differences bet ween the two concentrations (since the
intermicellar distance equals twice the double layer), but not the
existence of the surface rheology of the systems.
This conclusion was corroborated by data for Triton X-IOO solutions .
In this case, the cmc as determined by the break point of the surf ace
tension curve with log (concentration) is 0 . 16 gr i l. Solutions of
Triton X-IOO were measured at two concentrations above the cmc (0.3
gril and 3 gril). The signal noise was too large in the lat ter case.
This confirms our view that electrostatic repulsion does not dominate
the rheological behaviour of the surface, since Triton is a nonionic
surfactant. Moreover we would not have had any response in surf ace
tension from the Triton sample if electrostatic interactions would
determine the surface rheology.
Cl Impurities
A common way for testing the purity of a surfactant is measuring the
1/log(cl curve . The 1/log(c) curve for CTAB does not show a minimum
(see fig.7).
89
80
a 70 Z-a z S2 60 Vl Z IJ.! i- SO IJ.! U « u.
'" 40 ::> Vl
30 -5 -4 -3 -2
LOG(CONCENTRATION (gr CTAB/gr WATER]
fig.7 Surface tension CTAB - log(concentration)
The absence of a minimum is astrong indication that the surfactant is
pure, but does not prove that the surfactant is pure enough . Only
surface a c tive impurities are expected to be able to influence the
measurements significantly.
Another indication of the purity of the CTAB can be found by comparing
the parameters of the Szyszkowski equation to the ones obtained by
Prins C.S~2 earlier. The value obtained for r W was 20% lower than the
one calculated by Prins c. s ~ 2 The presence of impurity reported by
Prins, as could be concluded from the rigidity of the surface af ter
standing for hours, was not observed in our experiments.
The concentration dependenee of the surf ace rheological properties of
CTAB solutions above the cmc might be explained through impurities
which are adsorbed into micelles to a larger extent in 0 . 02M than in
0.002M CTAB solutions, and are not readily released from the micelles
on deformation of the surface.
A theory is presented (see appendix 5B), in which the influence of a
90
single surface active impurity on the surface rheology of a surfactant salution below the cmc was derived, analogous to the theory of Lucassen c.s~ However, large amounts of data (relations between r,7
and cl are required if the theory is to be applied. Unfortunately, these data are only available (as far as we know) for the system
SDS/dodecanol.
We will now investigate the influence of dodecanol on the surface rheology of SOS, making use of the equations derived in Appendix SB. Data for the BOS/Dodecanol mixture can be obtained from Fang c.s7; 15
were the following 5 relations are applied: Csds
Cd oh
rsds
asds rsas/(rm rsds rdoh)
adoh rdoh/(r~ rsds - rdoh)
rm (Csds/asds)/(1 + Cdoh/adoh + Csds/asds)
rdob rm (Cdoh/adoh)/(1 + Cdoh/adoh + Csds/asds)
n = -RTr00 ln (1 - rsds/r
00- rdoh/r
00)
[15] [16] [17] [18]
[19] The partial derivatives of equation [15] and [16] are order to calculate (J:
required in
ac,;arJ = aJ * (r00
- rk)/(r00
r, - rk)2
[20]
The partial derivatives of equation [19] are equal to: EJ =- 87/olnrJ - RTr"" rJ/{r~ rsds rdoh) [21]
Figures · 8 and 9 were constructed, using the following parameters as reported by Fang c.s~ 5 :
De door Kale et al. gerapporteerde oplosbaarheden van CTAB en de verklaringen voor de gevonden lage hellingen in de E(mV)-log(c) curve zijn ongeloofwaardig.
Bij het construeren van een adsorptie-isotherm uit adsorptiemetingen van ionogene surfactants aan vaste stoffen dient rekening te worden gehouden met de mogelijkheid dat er ionen worden afgegeven door de vaste stoffen.
(6)
De conclusies van Hühnerfuss omtrent de oppervlakte shear viscositeit
van surfactant oplossingen zijn onvoldoende gefundeerd.