Abstract
Both micro electro mechanical systems (MEMS) based and lab-on-a chip (LoC) devices demand efficient micro-scale mixing mechanisms for its effective control which necessitates the quality research towards more efficient designs. A new venture is investigated in those direction with mixing micro-channel constricted with rectangular block under pressure-driven electro-osmotic flow and is numerically simulated by a modified immersed boundary method (IBM), an alternative technique in computational fluid dynamics (CFD). The electro-osmotic flow elucidated by electrical double layer theory when simultaneously considered with pressure driven flow in micro channels can be effectively figured out by the solution of Navier-Stokes equations linked with Nernst-Planck and Poisson equations for transportation of ion and electric field respectively. In this study, the effect of varying the height of rectangular block on the flow and mixing performance are analyzed. A hybrid method, which is a combination of active and passive techniques, is introduced simultaneously in the microchannel by the electro-osmotic effects and channel constriction. The approach is on the basis of finite volume methodology on a staggered mesh. The governing equations are solved by a time-integration technique based on a fractional step method. The velocity fields are corrected by a pseudo-pressure term to ensure the continuity in each computational time step. The extent of mixing in every cross section of the micro channel is assessed by a suitable mixing efficiency parameter. This study has shed light on the most predominant factors that influence mixing efficiency in a micro-channel, such as geometry of the block, non-dimensional numbers (Reynolds number, Re and Peclet number, Pe), zeta potential, external electric field strength and electrical double layer (EDL) thickness. The maximum efficiency in this micro mixer design is found to be 51.3% for Reynolds number of 0.05 and Peclet number of 450 with the rectangular block height of 0.75. It is clear that both electro osmotic effects and flow perturbations due to channel constriction caused a remarkable improvement in mixing efficiency. The outcomes of this investigation are widely applicable in cooling of microchips, heat sinks of MEMS based devices, drug delivery applications and Deoxyribonucleic acid (DNA) hybridization. The present IBM model is validated by experimental and numerical results from the literature.