# Two-Layer Flow with One Viscous Layer in Inclined Channels

O. K. Matar; G. M. Sisoev; C. J. Lawrence

Mathematical Modelling of Natural Phenomena (2008)

- Volume: 3, Issue: 1, page 126-148
- ISSN: 0973-5348

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topMatar, O. K., Sisoev, G. M., and Lawrence, C. J.. "Two-Layer Flow with One Viscous Layer in Inclined Channels." Mathematical Modelling of Natural Phenomena 3.1 (2008): 126-148. <http://eudml.org/doc/222281>.

@article{Matar2008,

abstract = {
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.},

author = {Matar, O. K., Sisoev, G. M., Lawrence, C. J.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {slug flows; interfacial instability; two-layer flow; channel flow; modelling},

language = {eng},

month = {7},

number = {1},

pages = {126-148},

publisher = {EDP Sciences},

title = {Two-Layer Flow with One Viscous Layer in Inclined Channels},

url = {http://eudml.org/doc/222281},

volume = {3},

year = {2008},

}

TY - JOUR

AU - Matar, O. K.

AU - Sisoev, G. M.

AU - Lawrence, C. J.

TI - Two-Layer Flow with One Viscous Layer in Inclined Channels

JO - Mathematical Modelling of Natural Phenomena

DA - 2008/7//

PB - EDP Sciences

VL - 3

IS - 1

SP - 126

EP - 148

AB -
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.

LA - eng

KW - slug flows; interfacial instability; two-layer flow; channel flow; modelling

UR - http://eudml.org/doc/222281

ER -

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