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