Numerical analysis of the effects of roughness on the electroosmotic laminar flow between two parallel plates

Abstract

In the present study, the effects of wall roughness on the dynamic of laminar electro-osmotic flow (EOF) between two parallel plates have been investigated numerically. The governing equations of the flow in a system of two-dimensional general coordinates are solved using the finite-volume numerical method in a non-uniform grid with the maximum orthogonality of the grid lines adjacent to the rough boundaries. In the first step, the surface ruggednesses of the wall are divided into two categories: ‘‘surface roughness’’ and ‘‘wall blocks’’. The wall surface ruggednesses haveprofilesin theformsof sinuses, saw teeth, and square teeth. Then, the distinction boundary ofsurface roughnessfrom wall blocksis determinedas h=Hjcr ¼ 0:078 by defining and applying two qualitative and quantitative criteria. Finally, the dynamic of EOF near the walls surface roughness with 0:001e=H0:05 is investigated. According to the results, unlike macro-scale pressure-driven flows, the effect of surface roughness is not only non-negligible on the laminar EOF through the microchannels but also disruptive for the ionic and dynamic development of the flow adjacent to the walls. Finally, based on the numerical results, a new correlation has been developed for variations of _m for laminar EOF between two parallel plates in the presence of the surface roughness and its maximum error is 2%.