Combined Pressure-Driven and Electroosmotic Slip Flow through Elliptic Cylindrical Microchannels: The Effect of the Eccentricity of the Channel Cross-Section

Abstract

Electroosmotic force has been used extensively to manipulate fluid flow in a microfluidic system with various channel shapes, especially an elliptic cylinder. However, developing a computational domain and simulating fluid flow for a system involving an elliptic channel consumes a large amount of time. Moreover, the mathematical expression for the fluid velocity of electroosmotic flow in an elliptic channel may be given in the form of the Mathieu functions that have difficulty in achieving the numerical result. In addition, there is clear scientific evidence that confirms the slippage of fluid at the solid-fluid interface in a microscale system. In this study, we present the mathematical model of combined pressure-driven and electroosmotic flow through elliptic microchannels under the slip-fluid condition. From the practical point of view in fluidics, the effect of the eccentricity of the channel cross-section is investigated on the volumetric flow rate to overcome the difficulty. The results show that the substitution of the equivalent circular channel for an elliptic channel provides a valid flow rate under the situation that the areas of both channel cross-sections are equal and the eccentricity of the elliptic cross-section is less than 0.5. Additionally, the flow rate obtained from the substitution is more accurate when the slip length increases or the pressure-gradient-to-external-electric-field ratio decreases.

Transforming Navier‐stokes equation to a fourth order nonlinear differential equation for the study of electrolyte flow in a circular microchannel

“…They verified their numerical solution and discussed the effect of various parameters on electroosmotic flow. Chuchard and Nunpamviwat [41] presented a mathematical model of combined pressure-driven and electroosmotic flow through elliptic microchannels under the slip-fluid condition. The effect of eccentricity of the channel cross-section on volumetric flow rate was investigated.…”

“…Equation (41) clearly show a relationship between injection velocity and external electric field parameter 𝜅. In practice, regulating parameters 𝑉 𝑖 and 𝜅, in such a way that Equation ( 41) is satisfied can result a stable (non-fluctuating) electrolyte flow in the microchannel.…”