Goranović, G.; Sørensen, M.P.; Bruus, H.; Brøns, M. Electrohydrodynamic (In)Stability of Microfluidic Channel Flows: Analytical Expressions in the Limit of Small Reynolds Number. Water2024, 16, 544.
Goranović, G.; Sørensen, M.P.; Bruus, H.; Brøns, M. Electrohydrodynamic (In)Stability of Microfluidic Channel Flows: Analytical Expressions in the Limit of Small Reynolds Number. Water 2024, 16, 544.
Goranović, G.; Sørensen, M.P.; Bruus, H.; Brøns, M. Electrohydrodynamic (In)Stability of Microfluidic Channel Flows: Analytical Expressions in the Limit of Small Reynolds Number. Water2024, 16, 544.
Goranović, G.; Sørensen, M.P.; Bruus, H.; Brøns, M. Electrohydrodynamic (In)Stability of Microfluidic Channel Flows: Analytical Expressions in the Limit of Small Reynolds Number. Water 2024, 16, 544.
Abstract
We study electrohydrodynamic (EHD) linear (in)stability of microfluidic channel flows, i.e. the stability of interface between two-shearing viscous (perfect) dielectrics exposed to an electric field in large aspect ratio microchannels. We then apply our results to particular microfluidic systems known as electroosmotic (EO) pumps. Our results are detailed analytical expressions for the growth rate of two-dimensional EHD modes in Couette-Poiseuille flows in the limit of small Reynolds number ($R$); the expansions to both zeroth- and first-order-$R$ are considered.
The growth rates are complicated functions of viscosity-, height-, density- and dielectric-constant ratio, as well as of wavenumbers and voltages, and to our knowledge have not been presented before in literature. To make the results more useful, e.g., for voltage-control EO pump operations, we also derive equations for the impending voltages of the neutral stability curves that divide stable from unstable regions in voltage-wavenumber stability diagrams. The voltage equations and the stability diagrams are given for all wavenumbers. We finally outline the flow regimes in which our first-order-$R$ voltage corrections could potentially be experimentally measured. Our work gives the insight into the coupling mechanism between electric field and shear flow in parallel-planes channel flows, correcting an erroneous attempt from literature. Our general analysis enables us also to refine the renowned instability mechanism due to viscosity stratification, i.e., the case of pure shear instability, when the first-order-$R$ voltage correction equals zero.
Keywords
Electrohydrodynamic (EHD) instability; microfluidic channel; electroosmotic pump; small Reynolds number regime
Subject
Physical Sciences, Fluids and Plasmas Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
