Linear and Nonlinear Stability Analysis in Microfluidic Systems

TL;DR

This paper combines analytical and numerical methods to analyze linear and nonlinear stability of two-phase microfluidic flows, validating models with CFD simulations and setting the stage for future 3D studies.

Contribution

It introduces a validated approach using Orr--Sommerfeld theory and CFD to study stability in microchannels, enabling future 3D flow analysis.

Findings

Excellent agreement between theory and CFD in small-amplitude regime

Demonstration of nonlinear wave generation and reverse entrainment

Validation of in-house CFD against commercial software

Abstract

In this article we use analytical and numerical modeling to describe parallel viscous two-phase flows in microchannels. The focus is on idealized two-dimensional geometries, with a view to validating the various methodologies for future work in three dimensions. In the first instance, we use analytical Orr--Sommerfeld theory to describe the linear instability which governs the formation of small-amplitude waves in such systems. We then compare the results of this analysis with an in-house Computational Fluid Dynamics (CFD) solver called TPLS. Excellent agreement between the theoretical analysis and TPLS is obtained in the regime of small-amplitude waves. We continue the numerical simulations beyond the point of validity of the Orr--Sommerfeld theory. In this way, we illustrate the generation of nonlinear interfacial waves and reverse entrainment of one fluid phase into the other. We justify our simulations further by comparing the numerical results with corresponding results from a commercial CFD code. This comparison is again extremely favourable -- this rigorous validation paves the way for future work using TPLS or commercial codes to perform extremely detailed three-dimensional simulations of flow in microchannels.