Effects of interfaces on dynamics in micro-fluidic devices: slip-boundaries' impact on rotation characteristics of polar liquid film motors

Abstract

Slip-boundary effects on the polar liquid film motor (PLFM) -- a novel micro-fluidic device with important implications for advancing knowledge on liquid micro-film's structure, dynamics, modeling and technology -- are studied. We develop a mathematical model, under slip boundary conditions, describing electro-hydro-dynamical rotations in the PLFMs induced either by direct current (DC) or alternating current (AC) fields. Our main results are: (i) rotation characteristics depend on the ratio $k=l_{s}/D$ ($l_{s}$ denotes the slip length, resulting from the interface's impact on the structure of the liquid and $D$ denotes the film's diameter). (ii) As $k$ ($k>-1/2$) increases: (a) PLFMs subsequently exhibit rotation characteristics under "negative-", "no-", "partial-" and "perfect-" slip boundary conditions; (b) the maximum value of the linear velocity of the steady rotating liquid film increases and its location approaches the film's border; (c) the decay of the angular velocities' dependency on the distance from the center of the film slows down, resulting in a macroscopic flow near the boundary. (iii) In addition to $k$, the rotation characteristics of the AC PLFM depend on the magnitudes, the frequencies, and the phase difference of the AC fields. (iv) Our analytical derived rotation speed distributions are consistent with the existing experimental ones.