Geodesic
Two-Layer Flow with One Viscous Layer in Inclined Channels
O. K. Matar1 ; G. M. Sisoev2 ; C. J. Lawrence3
1 Department of Chemical Engineering, Imperial College London South Kensington Campus, SW7 2AZ, UK
2 School of Mathematics, University of Birmingham, Edgbaston Birmingham, B15 2TT, UK
3 Institutt for Energiteknikk, P.O. Box 40, 2027 Kjeller, Norway
Mathematical modelling of natural phenomena, Tome 3 (2008) no. 1, pp. 126-148

Voir la notice de l'article provenant de la source EDP Sciences

We study pressure-driven, two-layer flow in inclined channels with high density and viscosity contrasts. We use a combination of asymptotic reduction, boundary-layer theory and the Karman-Polhausen approximation to derive evolution equations that describe the interfacial dynamics. Two distinguished limits are considered: where the viscosity ratio is small with density ratios of order unity, and where both density and viscosity ratios are small. The evolution equations account for the presence of inertia, gravity, capillarity and viscous retardation; attention is restricted to situations in which the flow is laminar. The results of our linear stability analysis and numerical simulations indicate that the flow is destabilised by positive channel inclination in the stably stratified case. The dependence of the nonlinear wave dynamics on system parameters is also explored.
DOI : 10.1051/mmnp:2008037

O. K. Matar 1 ; G. M. Sisoev 2 ; C. J. Lawrence 3

1 Department of Chemical Engineering, Imperial College London South Kensington Campus, SW7 2AZ, UK
2 School of Mathematics, University of Birmingham, Edgbaston Birmingham, B15 2TT, UK
3 Institutt for Energiteknikk, P.O. Box 40, 2027 Kjeller, Norway 
@article{10_1051_mmnp:2008037,
     author = {O. K. Matar and G. M. Sisoev and C. J. Lawrence},
     title = {Two-Layer {Flow} with {One} {Viscous} {Layer} in {Inclined} {Channels}},
     journal = {Mathematical modelling of natural phenomena},
     pages = {126--148},
     publisher = {mathdoc},
     volume = {3},
     number = {1},
     year = {2008},
     doi = {10.1051/mmnp:2008037},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/mmnp:2008037/}
}
TY  - JOUR
AU  - O. K. Matar
AU  - G. M. Sisoev
AU  - C. J. Lawrence
TI  - Two-Layer Flow with One Viscous Layer in Inclined Channels
JO  - Mathematical modelling of natural phenomena
PY  - 2008
SP  - 126
EP  - 148
VL  - 3
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1051/mmnp:2008037/
DO  - 10.1051/mmnp:2008037
LA  - en
ID  - 10_1051_mmnp:2008037
ER  - 
%0 Journal Article
%A O. K. Matar
%A G. M. Sisoev
%A C. J. Lawrence
%T Two-Layer Flow with One Viscous Layer in Inclined Channels
%J Mathematical modelling of natural phenomena
%D 2008
%P 126-148
%V 3
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1051/mmnp:2008037/
%R 10.1051/mmnp:2008037
%G en
%F 10_1051_mmnp:2008037
O. K. Matar; G. M. Sisoev; C. J. Lawrence. Two-Layer Flow with One Viscous Layer in Inclined Channels. Mathematical modelling of natural phenomena, Tome 3 (2008) no. 1, pp. 126-148. doi: 10.1051/mmnp:2008037

Cité par Sources :