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Linear and Nonlinear Stability Analysis in Microfluidic Systems

Lennon Ó Náraigh1, *, Daniel R. Jansen van Vuuren2
1 School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland.
2 School of Engineering, University of Pretoria, Hatfield, Pretoria, South Africa.
* Corresponding Author: Lennon Ó Náraigh. Email: .
(This article belongs to this Special Issue: CFD Modeling and Multiphase Flows)

Fluid Dynamics & Materials Processing 2020, 16(2), 383-410.

Received 27 November 2019; Accepted 08 March 2020; Issue published 21 April 2020


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.


Multiphase flow, computational fluid dynamics, interfacial instability.

Cite This Article

Náraigh, L. ., R., D. (2020). Linear and Nonlinear Stability Analysis in Microfluidic Systems. FDMP-Fluid Dynamics & Materials Processing, 16(2), 383–410.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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