TY - JOUR
T1 - Effect of cross-diffusion on the gravitational instability in a ternary mixture
T2 - Asymptotic and linear analyses
AU - Kim, Min Chan
AU - Song, Kwang Ho
N1 - Funding Information:
Both authors contributed equally to this work. This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( NRF-2018R1D1A3A03000703 ).
Publisher Copyright:
© 2018 Elsevier Ltd
PY - 2018/12/14
Y1 - 2018/12/14
N2 - 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 (QSSAζ).
AB - 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 (QSSAζ).
KW - Asymptotic analysis
KW - Buoyancy-driven convection
KW - Cross diffusion
KW - Linear stability analysis
KW - Stability criteria
UR - http://www.scopus.com/inward/record.url?scp=85049357572&partnerID=8YFLogxK
U2 - 10.1016/j.ces.2018.06.071
DO - 10.1016/j.ces.2018.06.071
M3 - Article
AN - SCOPUS:85049357572
SN - 0009-2509
VL - 191
SP - 191
EP - 199
JO - Chemical Engineering Science
JF - Chemical Engineering Science
ER -