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Effect of cross-diffusion on the gravitational instability in a ternary mixture: Asymptotic and linear analyses

Authors
Kim, Min ChanSong, Kwang Ho
Issue Date
14-12월-2018
Publisher
PERGAMON-ELSEVIER SCIENCE LTD
Keywords
Cross diffusion; Buoyancy-driven convection; Stability criteria; Asymptotic analysis; Linear stability analysis
Citation
CHEMICAL ENGINEERING SCIENCE, v.191, pp.191 - 199
Indexed
SCIE
SCOPUS
Journal Title
CHEMICAL ENGINEERING SCIENCE
Volume
191
Start Page
191
End Page
199
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/71207
DOI
10.1016/j.ces.2018.06.071
ISSN
0009-2509
Abstract
To consider the effect of cross diffusion more rigorously, the onset and the growth of the gravitational instabilities in a Hele-Shaw cell saturated with ternary solution are analyzed by considering all cross diffusion coefficients. Through the asymptotic analysis, we identify the double-diffusive (DD)-, diffusive-layer convection (DLC)- and extended double diffusive (EDD)-type instability regimes. To support the asymptotic stability analysis, new linear stability equations are derived in the global domain and then transformed into the similar domain. In the similar domain, we prove that initially the system is unconditionally stable. For transient stability analysis, the linear stability equations are solved by employing quasi-steady state approximations (QSSA's). To avoid the limit of the conventional QSSAz, we obtain the critical time for the onset of instability motion using the QSSA in the similar domain (QSSA zeta). (C) 2018 Elsevier Ltd. All rights reserved.
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