In this paper, we investigate the effect of irrotational, viscous pressure on capillary instability of the interface between two viscous, incompressible, and thermally conducting fluids in a fully saturated porous medium when the phases are enclosed between two horizontal cylindrical surfaces coaxial with the interface and when there is mass and heat transfer across the interface. The analysis extends our earlier work in which the capillary instability of two viscous and thermally conducting fluids in a fully saturated porous medium was studied assuming that the motion and pressure are irrotational and the viscosity enters through the jump in the viscous normal stress in the normal stress balance at the interface. Here, we use another irrotational theory in which the discontinuities in the irrotational tangential velocity and shear stress are eliminated in the global energy balance by taking viscous contributions to the irrotational pressure. We use the Darcy's model, and a quadratic dispersion relation is obtained. It is observed that heat and mass transfer has a stabilizing effect on the stability of the system and this effect enhances in the presence of irrotational viscous pressure.

References

References
1.
Funada
,
T.
, and
Joseph
,
D. D.
,
2002
, “
Viscous Potential Flow Analysis of Capillary Instability
,”
Int. J. Multiphase Flow
,
28
, pp.
1459
1478
.10.1016/S0301-9322(02)00035-6
2.
Funada
,
T.
, and
Joseph
,
D. D.
,
2003
, “
Viscoelastic Potential Flow Analysis of Capillary Instability
,”
J. Non-Newtonian Fluid Mech.
,
111
, pp.
87
105
.10.1016/S0377-0257(03)00013-2
3.
Wang
,
J.
,
Joseph
,
D. D.
, and
Funada
,
T.
,
2005
, “
Pressure Corrections for Potential Flow Analysis of Capillary Instability of Viscous Fluids
,”
J. Fluid Mech.
,
522
, pp.
383
394
.10.1017/S0022112004002009
4.
Wang
,
J.
,
Joseph
,
D. D.
, and
Funada
,
T.
,
2005
, “
Viscous Contributions to the Pressure for Potential Flow Analysis of Capillary Instability of Viscous Fluids
,”
Phys. Fluids
,
17
, pp.
1
12
.
5.
Hsieh
,
D. Y.
,
1972
, “
Effect of Heat and Mass Transfer on Rayleigh–Taylor Instability
,”
J. Fluids Eng.
,
94
, pp.
156
162
.
6.
Hsieh
,
D. Y.
,
1978
, “
Interfacial Stability With Mass and Heat Transfer
,”
Phys. Fluids
,
21
, pp.
745
748
.10.1063/1.862292
7.
Nayak
,
A. R.
, and
Chakraborty
,
B. B.
,
1984
, “
Kelvin–Helmholtz Stability With Mass and Heat Transfer
,”
Phys. Fluids
,
27
, pp.
1937
1941
.10.1063/1.864849
8.
Asthana
,
R.
, and
Agrawal
,
G. S.
,
2007
, “
Viscous Potential Flow Analysis of Kelvin–Helmholtz Instability With Mass Transfer and Vaporization
,”
Physica A
,
382
, pp.
389
404
.10.1016/j.physa.2007.04.037
9.
Kim
,
H. J.
,
Kwon
,
S. J.
,
Padrino
,
J. C.
, and
Funada
,
T.
,
2008
, “
Viscous Potential Flow Analysis of Capillary Instability With Heat and Mass Transfer
,”
J. Phys. A: Math. Theor.
41
, pp.
1
10
.
10.
Awasthi
,
M. K.
, and
Agrawal
,
G. S.
,
2012
, “
Nonlinear Analysis of Capillary Instability With Heat and Mass Transfer
,”
Commun. Nonlinear Sci. Numer. Simulat.
,
17
, pp.
2463
2475
.10.1016/j.cnsns.2011.10.015
11.
Awasthi
,
M. K.
,
Asthana
,
R.
, and
Agrawal
,
G. S.
,
2012
, “
Pressure Corrections for the Potential Flow Analysis of Kelvin–Helmholtz Instability With Heat and Mass Transfer
,”
Int. J. Heat Mass Transfer
,
55
, pp.
2345
2352
.10.1016/j.ijheatmasstransfer.2012.01.032
12.
Awasthi
,
M. K.
,
Asthana
,
R.
, and
Agrawal
,
G. S.
,
2013
, “
Viscous Correction for the Viscous Potential Flow Analysis of Capillary Instability With Heat and Mass Transfer
,”
J. Eng. Math.
,
80
, pp.
75
89
.10.1007/s10665-012-9597-2
13.
Awasthi
,
M. K.
,
2013
, “
Viscous Corrections for the Viscous Potential Flow Analysis of Rayleigh–Taylor Instability With and Heat and Mass Transfer
,”
ASME J. Heat Transfer
,
135
(
7
), p.
071701
.10.1115/1.4023580
14.
Asthana
,
R.
,
Awasthi
,
M. K.
, and
Agrawal
,
G. S.
,
2012
, “
Kelvin–Helmholtz Instability of Two Viscous Fluids in Porous Media
Int. J. App. Math. Mech.
,
8
(
14
), pp.
1
10
.
15.
Allah
,
M. H. O.
,
2011
, “
Viscous Potential Flow Analysis of Interfacial Instability With Mass Transfer Through Porous Media
,”
Appl. Math. Comput.
,
217
, pp.
7920
7931
.10.1016/j.amc.2011.02.066
16.
Awasthi
,
M. K.
, and
Asthana
,
R.
,
2013
, “
Viscous Potential Flow Analysis of Capillary Instability With and Mass Transfer Through Porous Media
,”
Int. Commun. Heat Mass Trans.
,
41
, pp.
7
11
.10.1016/j.icheatmasstransfer.2012.10.026
17.
Awasthi
,
M. K.
,
2013
, “
Nonlinear Analysis of Rayleigh–Taylor Instability of Cylindrical Flow With Heat and Mass Transfer
,”
ASME J. Fluid Eng.
,
135
(
6
), p.
061205
.10.1115/1.4024001
18.
Moatimid
,
G. M.
, and
Hassan
,
M. A.
,
2013
, “
Three-Dimensional Viscous Potential Electrohydrodynamic Kelvin–Helmholtz Instability Through Vertical Cylindrical Porous Inclusions With Permeable Boundaries
,”
ASME J. Fluid Eng.
136
(
2
), p.
021203
.10.1115/1.4025681
You do not currently have access to this content.