@Article{fdmp.2020.09265,
AUTHOR = {Lennon Ó Náraigh, Daniel R. Jansen van Vuuren},
TITLE = {Linear and Nonlinear Stability Analysis in Microfluidic Systems},
JOURNAL = {Fluid Dynamics \& Materials Processing},
VOLUME = {16},
YEAR = {2020},
NUMBER = {2},
PAGES = {383--410},
URL = {http://www.techscience.com/fdmp/v16n2/38666},
ISSN = {1555-2578},
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.},
DOI = {10.32604/fdmp.2020.09265}
}