2001' 5' 11' Kim Sung Jae

1
Electroosmosis with nonuniformly
charged walls Part II
2001. 5. 11. Kim Sung Jae
Pohang University of Science and
Technology Department of Chemical Engineering
and Division of Mechanical and Industrial
Engineering
2
Review

• Governing equations

• There is an apparent slip velocity at the pore
  wall and ?p is zero.

• Then the velocity fields are

Anderson, J. L., Chem. Eng. Commun, 38, 93 (1985)
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Governing Equation and nonuniform surface charge
conditions

• Governing equations.

• Surface charge densities modulated along x

• Due to linearity of governing equations, problem
  reduces to two geometry.

Ajdari, A., Phys. Rev. Lett. 75(4), 755 (1995)
4
Solution for electric potential and flow field

• Potential is given by Poission-Boltzmann equation.

• Stream functions
• in the limit of very thin Debye layer
  approximation and EextEx

• When EextE?y,

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Solution method for flow field

• Stream function satisfy the bi-harmonics..

• Trial solution is

• Reduced trial solution by following conditions

• Determine the unknown coefficient

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Equation for flow field
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Example of flow field (effect of surface charge)

• EextEx case

?1
Linear combination of ?v1(1- ?)v2. When ? is
0.5, only upper plate is charged with
?0
?.5
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Example of flow field (effect of electric field)

• Eext ? Ex ? E?y case

?.9, ?.46, only upper plate is charged and
initial point is (.1, -.9, .1)
z
x
z
y
y
x
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Bonus How can we determine the slip velocity?
fraction of molecules adsorbed
slippage is order of lf