5.3.1 Formulation of Unsteady EOF
Formulations of the equations of the motion of fluid flow in pulsed recirculation mixer is
similar to that provided in Section 4.2, except the addition of the temporal term due to the
application of a periodic electric field. The formulas include continuity equation, momentum
equation and Poisson equation. After the application of the effective slip boundary condition and
the normalization by
x* = TL
= FL/(70o)
t* = t/
P = /Po
The formulas become
V*. = 0 (5-1)
(Re.St) +Re f* (V*) = -4r2KV*p* +V*2r*
a9t (5-2)
v*2 = 0 (5-3)
In the formulas, x, V, t, p, q are the position vector, velocity vector, time, pressure, and
electric potential, and they are non-dimensionalized using P, L, r7, (g, r, which are the
characteristic applied pressure, the characteristic length scale of the ridged channel (the distance
between the periodic ridge), the electroosmotic mobility at the boundary (defined in Equation 1-
21), the characteristic applied electric potential, and the characteristic time scale (the period of
the applied pulsed electric field), respectively. The Laplacian and the gradient operators are also
normalized using L. K is the same dimensionless number defined in Equation 4-32, Re and St
are the Reynolds and Strouhal numbers respectively, and defined as
Re =r,/v (5-4)