Electroosmosis with

1
Electroosmosis with
nonuniformly charged walls
2000. 11. 10. By S. J. Kim
2

• Electroosmosis is the flow which is the result of
  the electric field acting on
• the diffuse part of the double layer of charge
  at the pore wall

• By assuming l(the Debye length) is very small
  w.r.t. r(pore radius) and
• the surface is uniformly charged, the velocity
  profile is given by the Hel-
• mholtz equation and the slip velocity is
  applied at boundary.

3

• The zeta potential can be related to the charge
  density(s) of pore wall.

• After experimentally determining the fluid
  velocity and then calculating z
• from Helmholtz equation, one can estimate
  charge density by the Gouy-
• Chapman model.

• Above state is valid when the charge distribution
  is uniform. However,
• charged particles alter the local charge
  distribution, when they are absorb-
• ed to pore wall. Therefore it is reasonable to
  expect that z potential varies
• with position through the pore.

4

• Assuming the analysis is valid in the limits

• Governing equations

• As shown fig2., there is an apparent slip
  velocity at the pore wall.

And there must be no pressure difference btn
the ends of the capillary.
5

• A streaming function is defined for this
  axisymmetric problem.

• Then the boundary conditions are

6

• One obtain the following for the stream function.

• Then the velocity fields are

7
(No Transcript)