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On nonlinear doubly‐diffusive marangoni instability
Author(s) -
Ho KwokLun,
Chang HsuehChia
Publication year - 1988
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690340502
Subject(s) - marangoni effect , instability , marangoni number , mechanics , convection , bifurcation , amplitude , nonlinear system , mass flux , surface tension , physics , thermodynamics , optics , quantum mechanics
Enhancement of simultaneous heat and mass transfer due to surface tension gradient‐induced Marangoni convection is studied. The geometry considered is a thin liquid film between a solid phase and a gas phase. In regions where the two Marangoni numbers are of opposite signs (quadrants II and IV), Orr‐Sommerfeld analysis reveals the possibility of oscillatory roll cells. A nonlinear bifurcation study of the amplitude equations indicates that the finite‐amplitude oscillatory rolls are annihilated by steady rolls slightly beyond the oscillatory stability boundary in a heteroclinic bifurcation. Oscillatory rolls are hence restricted to quadrants II and IV. Finite‐amplitude instability due to subcritical bifurcation of the steady rolls is also shown to be limited to these quadrants. In addition to classifying the bifurcations, the numerical study also provides a useful correlation for single‐component flux enhancement, Nh * = 1 + 0.001324 Nu 0.23 Pr 0.16 ( N T − N T c ), which is compared to available experimental data.