1 distance Potential - - - - + + + + + + - - + - - + - + + - - - - Diffuse Layer Bulk Solution + d IHP OHP The electrical double layer + + + - i
1
distance
Pote
nti
al
-
-
-
-+
+
+
++
+-
-
+
--
+-
+
+
-
-
-
-
Diffuse Layer
Bulk Solution
+d
IHP OHP
The electrical double layer
+
+
+
-
i
2
ζ =κ με ΔP
φs
ζ: zeta potentialκ : liquid conductivityμ: viscosityε : liquid permittivityΔP: pressure difference from inlet to outlets: measured streaming potential
3
ζ: zeta potentialκ : liquid conductivity: kinematic viscosityε: liquid permittivitya: disk radiusz: distance of reference electrode from sample: rotation rates: measured streaming potential
ζ ≅1.96κ ν 1/2
ε aΩ3/2
1
2 1−z
a−
1
2z2
a2 +1⎛⎝⎜
⎞⎠⎟
1/2
⎛
⎝
⎜⎜⎜⎜
⎞
⎠
⎟⎟⎟⎟
φs
4
distancePlane of
shear(possibly)
Pote
nti
al
ζ-
-
-
-+
+
+
++
+-
-
+
-
-
-+
-
+
++
-
-
-
-
Diffuse Layer
Bulk Solution
+d
IHP OHP
++
The plane of shear
5
voltmeter
Sample solid
Liquid
Reference electrode (e.g. Ag/AgCl)piston/pump
A schematic of the parallel plate capillary system.
receptacle
6
voltmeter
LiquidReference electrodeSample solid
Schematic of the rotating disk system
7
8
ζ =2RT
zFsinh−1 −zFλ q2
2εRT⎛⎝⎜
⎞⎠⎟
ζzeta potentialR: gas law constantT: temperaturez: 1, for a 1:1 saltF: faraday’s constant: Debye lengthq2:charge density of the diffuse layerε: permittivity of water
9
10
11
12
13
14
15