TY - JOUR
T1 - Large cells in nonlinear marangoni convection
AU - Sivashinsky, G. I.
N1 - Funding Information:
This researchw as supportedin part by the Israel Commissionf or Basic Researcha nd by the U S.-Israel BinationalS cienceFoundation Grant 1401.
PY - 1982/1
Y1 - 1982/1
N2 - The classical problem of surface-tension-driven convection in a liquid film is considered. If the film is nearly thermally insulated, the longitudinal dimension of the convective cells is significantly greater (near the critical Marangoni number) than the film thickness. As a result one can separate horizontal and vertical space variables and so lower the dimensionality of the problem. For example, in the two-dimensional problem the dynamics of the formation and stabilization of cells is described by the following one-dimensional equation for the average temperature perturbation of the film: ∂F ∂τ+ 1 ∂4F 15 ∂π4+ ∂ ∂ξ(1- 48 35( ∂F ∂ξ)2+ 13∂2F 10∂ξ2) ∂F ∂ξ+βF=0.
AB - The classical problem of surface-tension-driven convection in a liquid film is considered. If the film is nearly thermally insulated, the longitudinal dimension of the convective cells is significantly greater (near the critical Marangoni number) than the film thickness. As a result one can separate horizontal and vertical space variables and so lower the dimensionality of the problem. For example, in the two-dimensional problem the dynamics of the formation and stabilization of cells is described by the following one-dimensional equation for the average temperature perturbation of the film: ∂F ∂τ+ 1 ∂4F 15 ∂π4+ ∂ ∂ξ(1- 48 35( ∂F ∂ξ)2+ 13∂2F 10∂ξ2) ∂F ∂ξ+βF=0.
UR - http://www.scopus.com/inward/record.url?scp=49049133957&partnerID=8YFLogxK
U2 - 10.1016/0167-2789(82)90063-X
DO - 10.1016/0167-2789(82)90063-X
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AN - SCOPUS:49049133957
SN - 0167-2789
VL - 4
SP - 227
EP - 235
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
IS - 2
ER -