edge of EDL is assumed a constant (denoted as or). Because the periodic channel geometry,
the flow is periodic in the x-direction.
The governing equations in this flow include the continuity equation, momentum
equations, and Poisson equation:
V- =0, (4-1)
(V.V)V VPP-
P P (4-2)
and
V2 = _Pe
E (4-3)
where V(x, y) is the velocity vector (with u as the x component and v as the y component),
p(x,y) is the pressure, pe(x,y) is the electric charge density and O(x,y) is the electric potential
in the fluid flow.
The boundary conditions are
V(x- L/2,y)= V(x + L/2, y) (4-4)
p(x-L/2,y)= p(x+L/2,y)+ P (45)
(x-L/2, y)= (x+L/2, y)- ), (4-6)
and
Swals (4-7)
In the bulk flow (also called as the outer flow region, relative to the double layer100), the
electric charge is neutral. As a result, the Lorentz force is dropped from the momentum Equation
4-2, which becomes the incompressible Navier-Stokes equation,
(V. V)V = v+ vV2V
P (4-8)
and the Poisson equation (Equation 4-3) becomes the Laplace equation by dropping the charge
density term,