Confinement effects on electrohydrodynamics of two-dimensional miscible liquid drops

The effect of domain confinement on the electrohydrodynamics of a two-dimensional miscible drop is investigated analytically, as a prototypical problem to explore confinement effect in two applications; namely, continuous flow electrophoresis and pattern formation in suspension of inhomogeneous colloidal dispersions. It is shown that the domain confinement may strengthen or weaken the electric field and leads to weakening of the flow field and change of the flow structure. A characteristic function is found to determine the sense of drop elongation and it is shown that below a critical domain size, the necessary condition for elongation in the direction normal to the field will be opposite to that for an unbounded domain.