Bilayer Flow Analysis of Immiscible Fluids in a Microchannel with Surface Heterogeneities

In the present work, the interfacial displacements and dynamics caused by the electro-osmotic flows of two immiscible and perfect dielectric fluid layers through a wavy microchannel are analytically investigated in the presence of an axially periodic surface potential, considering the small deformation of the liquid-liquid interface. Our ultimate objective is to convey various configurations of the evolved liquid-liquid interface and the electroosmotic flow (EOF) dynamics influenced by both the heterogeneous surface potential and the modulated channel topology and to enhance the disturbance along the liquid-liquid interface generating swirling flow dynamics, which may be used to design controlled superimposed flow systems with applications in various processes such as surface coating, molecular mixing and reaction along the interface, cleaning, and decontamination, as well as in a host of multipurpose microfluidic devices. The permittivity and viscosity jump along the liquid-liquid interface significantly change the velocity field in both the fluid layers, and therefore, to preserve a continuous interfacial velocity, the flow field needs to perform net work that leads to the deformation of the liquid-liquid interface. Closed-form solutions for the potential field, electroosmotic velocity field, and deformed liquid-liquid interface are obtained utilizing domain perturbation analysis. Based on our analysis, it is observed that the main factors influencing the deformation and subsequent flow features are the channel geometry, and our results show that the sinusoidal wavy charged surface leads to an increase of the interfacial contact area between the two fluids despite their reduced drag force, as well as higher interfacial tension values and enhanced pressure gradient with high-frequency fluctuations compared to straight channels.