Flow of a Pressure-Dependent Viscosity Fluid in Porous Media

S. O. Arbilha, T. L. Alderson, M. H. Hamdan


Two-dimensional flow of a fluid with pressure-dependent viscosity through a variable permeability porous structure is considered. Exact solutions are obtained for a Riabouchinsky type flow using a procedure that is based on a method implemented by the late Professor Dr. R.K. Naeem of Karachi University in his study of Navier-Stokes flow with pressure-dependent viscosity.



Porous media, pressure-dependent viscosity, variable permeability

Full Text:



S. O. Alharbi, T. L. Alderson and M. H. Hamdan, “Flow of a Fluid with Pressure-Dependent Viscosity through

Porous Media”, Advances in Theoretical and Applied Mechanics, vol. 9, no. 1, pp. 1 – 9, 2016.

W.S. Almalki and M.H. Hamdan, “Investigations in effective viscosity of fluid in a porous medium”, Int. Journal

of Engineering Research and Applications, vol. 6, issue 4, no. 4, pp. 41-51, 2016.

M.M. Denn, Polymer Melt Processing, Cambridge University Press, Cambridge, 2008.

J.P. Du Plessis and J.H. Masliyah, “Mathematical modeling of flow through consolidated isotropic porous media”,

Transport in Porous Media, vol. 3, pp. 145-161, 1998.

A. Goubert, J. Vermant, P. Moldenaers, A. Gottfert and B. Ernst, “Comparison of measurement techniques for

evaluating the pressure dependence of the viscosity”, Applied Rheology, vol. 11, pp. 26–37, 2001.

J. Hron, J. Malek and K. R. Rajagopal, “Simple flows of fluids with pressure-dependent viscosities”, Proc. R. Soc.

Lond A, vol. 457, pp. 1-20, 2001.

K. Kannan and K.R. Rajagopal, “Flow through porous media due to high pressure gradients”, Applied

Mathematics and Computation, vol. 199, pp. 748–759, 2008.

K.D. Housiadas, G.C. Georgiou and R.I. Tanner, “A note on the unbounded creeping flow past a sphere for

Newtonian fluids with pressure-dependent viscosity”, International Journal of Engineering Science, vol. 86, pp. 1–

, 2015.

L. Fusi, A. Farina and F. Rosso, “Mathematical models for fluids with pressure-dependent viscosity flowing in

porous media”, International Journal of Engineering Science, vol. 87, pp. 110–118, 2015.

M.J. Martin-Alfonso, F.J. Martinez-Boza, F.J. Navarro, M. Fernandez and C. Gallegos, “Pressure-temperature-

viscosity relationship for heavy petroleum fractions”, Fuel, vol. 86, 227-233, 2007.

M.J. Martin-Alfonso, F.J. Martinez-Boza, P. Partal and C. Gallegos, “Influence of pressure and temperature on the

flow behaviour of heavy fluid oils”, Rheol. Acta, vol. 45, pp. 357-365, 2006.

R. K. Naeem, “Riabouchinsky type steady flows of an incompressible fluid of pressure-dependent viscosity”,

Journal of Basic and Applied Sciences, vol. 6, no. 2, pp. 99-105, 2010.

K.R. Rajagopal, “On implicit constitutive theories for fluids”, J. Fluid Mech., vol. 550, 243-249, 2006.

K.R. Rajagopal, “On a hierarchy of approximate models for flows of incompressible fluids through porous solids”,

Mathematical Models and Methods in Applied Sciences; vol. 17, no. 2, pp. 215-252, 2007.

K.R. Rajagopal and G. Saccomandi, “Unsteady exact solutions for flows of fluids with pressure-dependent

viscosities”, Mathematical Proceedings of the Royal Irish Academy, vol. 106A, no. 2, pp. 115-130, 2006.

M. Renardy, “Parallel shear flows of fluids with a pressure-dependent viscosity”, Journal of Non-Newtonian Fluid

Mechanics, vol. 114, pp. 229-236, 2003.


  • There are currently no refbacks.