PRINCIPLES OF MIXING FOR INDUSTRIAL BIOPROCESSING Hari Venkitachalam
PRINCIPLES OF MIXINGFOR
INDUSTRIAL BIOPROCESSING
Hari Venkitachalam
Purposes of mixing (in industrial bio-processes)
Homogenizephysical properties of a mixture of fluids
Create a dispersion in a liquid of a solid, gas or another immiscible liquid
Improve mass transfer effectivenesse.g. rate of dissolution of a solid or gas into a liquid
Methods of mixing
Air liftLiquid circulation due to the drag effect of a rising
column of air bubbles
Static mixersUsed mainly for mixing one liquid with anotherConsist of a pipe or tube with stationary dividers
(baffles) positioned in the interior
Mechanical agitationNeeded where a high mixing intensity is called for e.g. when the components separate relatively easily (as
in gas/liquid or liquid/solid mixing)
Energy for mixing
Energy transferFrom mixing equipment to the fluid causes fluid circulation
The transferred energyAccelerates the liquid and increases its kinetic energy level (called the velocity head, H) Gets transferred through smaller and smaller scales of turbulent eddiesIs eventually dissipated as heat due to fluid friction
Without continuous energy transferFluid movements will eventually die down
Characterizing mixing equipment
Liquid flow patternsLiquid pumping rate
Rate and intensity of liquid circulationHigher pumping rate means more rapid homogenization
Distribution of shear rate in the vesselFluid velocity differentials and fluctuations (due to fluid friction)Higher shear rates mean higher mass transfer effectiveness
Power absorption (i.e. energy transferred to the fluid)the greater the energy transferred, the greater the mixing effectiveness
Flow patterns of different impellers
Axial flow and hydrofoil produce large flows at low powerProduce a single circulating loope.g. marine propeller, PBT and Prochem-Maxflo
Radial flowFlow radiates out from the impellerTwo circulating loops are generatede.g. Rushton turbine
Close clearancefor highly viscous substancese.g. anchor and helical ribbon impellers
Liquid flow induced by mixing
The primary liquid flowIs liquid flow directly induced by the impeller rotation
Secondary (or entrained) flows Is due to the flowing liquid dragging adjacent liquid and entraining it Secondary flows allow the entire contents of vessel to circulate even when a small impeller is inducing the primary flowSecondary flow component is smaller relative to primary flow for larger impellers
Liquid pumping rate
Depends on impeller typeAxial flow turbines produce high flow rates (but low shear rates) at a given power consumption
Radial flow turbines produce higher shear rates (but lower flow)
For a particular type of impeller,Q = Nq.ND3
where Nq = is an impeller-dependent constantN = rotation speed (s-1)D = impeller diameter (m)Q = induced liquid flow (m3s-1)
The velocity head (H)Is the energy transferred to the liquid in accelerating it to its flow velocityIs proportional to the square of the liquid velocity
Liquid velocity induced by the impeller is proportional to impeller tip speed (ND)
ThereforeH N2D2
Velocity head
Energy transfer from impellersPower (Energy per unit time)
transferred by a mixing impeller to the fluid is given by
P Q.H (ND3).(N2D2)or
P = Np.. N3D5where P = power absorbed (J/s)
Np = power number (an impeller-dependentconstant)
= liquid density (kg/m3)
Power no. (NP) vs Reynolds no. (Re)Re = (.N.D2)/
where = liquid viscosity
Tank baffle and impeller spacing
Power absorption from the turbine to the liquid is maximized when the width of the vertical baffles at the tank wall is one-tenth the tank diameter
The spacing of impellersin multi-impeller vessels also impacts on the power absorption. Normal spacing of multiple impellers is at least one impeller diameter apart
Shear rate and shear stress
Shear rate is the velocity gradient in the liquid at a given
location (variation in liquid velocity with distance)is proportional to both the impeller speed and
diameter Shear stress in the liquid
increases proportionately with shear rate Shear stress is responsible for
causing fluid intermixingshearing and dispersion of solids, liquid droplets and gas bubblesand therefore also for enhancing mass transfer
Distribution of shear rates
Maximum shear rate occurs near the tip of the impeller (proportional to tip speed)
Shear rate within the impeller regionis typically an order of magnitude larger than the average shear rate in the whole vessel
Minimum shear rate in the vessel is around 25% of the average shear rateoccurs in regions well away from the impeller zone
Macro-mixing and micro-mixing
Macro-mixingis largely the general circulation of liquid through various zones in the vessel controls effectiveness of homogenization dependent on the pumping capacity of impeller
Micro-mixingrefers to the intensity of turbulence (rapid velocity fluctuations)characterized by the root mean square velocity at a pointThe greater the velocity fluctuations, the greater the shear stressesvery important for enhancing dispersion and mass transfer
For equal power consumption,the relationship between the diameters (D1 and D2) and speeds (N1 and N2) of two geometrically similar impellers is:
Np..N13.D15 = Np..N23.D25i.e., (D1/D2)5 = (N2/N1)3
e.g., when D2/D1 = 0.5, (N2/N1) = 3.2, at equal power;i.e., an impeller half the size of another will need to run at 3.2 times the speedThe larger impeller will give rise to higher flow but the smaller impeller will result in greater shear
Impeller size vs speed trade-off
Impeller application
Large diameter impellers at low speed are best suited for homogenization
Small diameter impellers at higher speed achieve better phase dispersion and mass transfer outcomes (e.g. oxygen mass transfer)
Mixing and oxygen transfer
In bio-processes mechanical agitators (turbines)are often needed to effect high rates of oxygen transfer to the liquid (i.e., high kLa)
Oxygen transfer rate is determined bythe mass transfer resistance at the gas/liquid interfacethe gas-liquid interfacial area, a (e.g., surface area of gas bubbles dispersed in the liquid medium)average gas hold-up in the liquid, (the volume of gas bubbles in a unit volume of the liquid medium)the mean residence time of gas bubbles, R
Effect of shear rate
Increased shear rate in the liquid Tears up large bubbles into smaller onesdecreases the mass transfer resistance at the gas/liquid interface due to increased turbulence intensity and reduced liquid boundary layer thickness around gas bubbles
Bubble generation in impeller zone
Sparged air is drawn into vortex threads and vortex sheets in the wake of the impeller blades
Small bubbles shear off the tips of the the vortex threads/sheets
The sheared bubbles are dispersed radially out from the impeller zone and rise up the liquid column
Some of the bubbles are recycled back through the impeller zone in a downdraught with the liquid drawn down into it.
Effect of bubble size
With smaller bubbles,Gas/liquid interfacial area of a given volume of dispersed air bubbles will increase (e.g. halving the Bubble size will double as/liquid interfacial area)Rise rate of the bubbles will be slower, so
the gas bubbles will remain in the liquid longer, bubbles will be recirculated more frequently by the liquid circulationgas hold up in the medium will increasethe time that individual bubbles are able to transfer oxygen into the liquid is extended
So, O2 transfer is greatly enhanced
For a given power absorption: A smaller impeller will have to run at a much higher
speeed (when D2/D1 = 0.5, (N2/N1) = 3.2)The shear rate in the liquid (both maximum and average)
being proportional to ND, a smaller impeller will give rise to greater shear rate in the liquid (halving the impeller diameter, will increase shear rate by 0.5x3.2 = 1.6 times)
Smaller impellerstherefore better suited to providing high oxygen mass
transfer rates
Impeller selection for O2 transfer
Impeller selection for O2 transfer
Radial flow turbines Transfer more power and generate greater shear in the liquid than the axial flow designs of the same diameter and speed.
They are therefore preferred for oxygen mass transfer applications
The Rushton turbine design is among the most popular for fermenter applications
Aeration rate and oxygen transfer
Increasing air flow rate improves O2 transfer only to a limited extent
Excessive air flow rate will cause flooding of the impeller
At low impeller speeds, flooding will occur at relatively low air flow rates
Increasing mixer speed will allow higher aeration rate without flooding
Recommended Reading:
M. Howe Grant (Editor) Encyclopedia of Chemical Technology (4th Edition) Vol. 16J. I. Kroschwitz (Executive Editor)John Wiley & Sons, N.Y. (1995)pp. 844-857; 866-869R660.03 E56 2 V.16(in the Librarys reserve collection)