Dynamics of a Viscous Drag Pump for Maxwell Immiscible Fluids Under Interfacial Electroosmotic and Hydrophobic Effects in a Microannulus

Abstract

Abstract The present study analyzes the flow dynamics of two immiscible viscoelastic fluids through a cylindrical microannulus with hydrophobic walls. The pumping technique is produced by electroosmotic effects that act on the conducting fluid dragging the non-conducting fluid by viscous forces. The dimensionless mathematical model considers the linearized Poisson Boltzmann equation, the Cauchy momentum equation, and the rheological Maxwell model, which is solved semi-analytically by the Laplace transform method. The results of the transient flow field are presented in terms of velocity profiles, velocity tracking, and flow rate. Due to the elastic properties of fluids, oscillatory behavior of the flow is produced, whose frequency, amplitude, and duration depend on the relaxation times of fluids. Also, other dimensionless parameters are investigated, such as the electrokinetic parameter of the conducting fluid, the viscosity ratios in both fluids, as well as the hydrodynamic slip length in the walls, and the liquid-liquid interface position, showing its influence on the velocity magnitude, flow rate, and time in which the flow reaches the steady-state regime. The present investigation extends the knowledge about the transport methods of non-Newtonian and non-conducting fluids in microfluidic devices.