3220f343-badf-4fa8-b8e7-ea4681a7746f20210811030958071wseas:wseasmdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON APPLIED AND THEORETICAL MECHANICS2224-34291991-874710.37394/232011http://wseas.org/wseas/cms.action?id=40063420213420211610.37394/232011.2021.16https://wseas.org/wseas/cms.action?id=23298Two-Pressure Model of Particle-Fluid Mixture Flow with Pressure-Dependent Viscosity in a Porous MediumS. JayyousiDajaniDepartment of Mathematics and Computer Science Lake Forest College Lake Forest, IL 60045, USAM. S. AbuZaytoonDepartment of Mathematics University of Petra, Amman, JORDANM. H.HamdanDepartment of Mathematics and Statistics University of New Brunswick Saint John, N.B., E2L 4L5, CANADAEquations governing the flow of a fluid-particle mixture with variable viscosity through a porous structure are developed. Method of intrinsic volume averaging is used to average Saffman’s dusty gas equations. A modelling flexibility is offered in this work by introducing a dust-phase partial pressure in the governing equations, interpreted as the pressure necessary to maintain a uniform particle distribution in the flow field. Viscosity of the fluid-particle mixture is assumed to be variable, with variations in viscosity being due to fluid pressure. Particles are assumed spherical and Stokes’ coefficient of resistance is expressed in terms of the pressure-dependent fluid viscosity. Both Darcy resistance and the Forchheimer micro-inertial effects are accounted for in the developed model8112021811202185939https://wseas.com/journals/mechanics/2021/a185111-004(2021).pdf10.37394/232011.2021.16.9https://wseas.com/journals/mechanics/2021/a185111-004(2021).pdf10.1016/j.ijengsci.2014.11.007Fusi, L., Farina, A. and Rosso, F., Mathematical Models for Fluids with Pressure Dependent Viscosity Flowing in Porous Media. International Journal of Engineering Science, Vol. 87, 2015, pp. 110-118. 10.1016/j.ijengsci.2014.09.004Housiadas, K.D., Georgiou, G.C. and Tanner, R.I., A Note on the Unbounded Creeping Flow Past a Sphere for Newtonian Fluids with PressureDependent Viscosity. Int. Journal of Engineering Science, Vol. 86, 2015, pp. 1–9. 10.1002/fld.2358Nakshatrala, K.B. and Rajagopal, K.R. (2011). A Numerical Study of Fluids with Pressure-Dependent Viscosity Flowing through a Rigid Porous Medium. Int. J. Numer. Meth. Fluids, Vol. 67, 2011, pp. 342- 368. 10.1615/jpormedia.v20.i3.60Chang, J., Nakashatrala, K.B. and Reddy, J.N., Modification to Darcy-Forchheimer Model Due to Pressure-Dependent Viscosity: Consequences and Numerical Solutions. J. Porous Media, Vol. 20, No. 3, 2017, pp. 263-285. Abu Zaytoon, M.S., Allan, F.M., Alderson, T.L. and Hamdan, M.H., Averaged Equations of Flow of Fluid with Pressure-Dependent Viscosity through Porous Media. Elixir Appl. Math., Vol. 96, 2016, pp. 41336-41340. 10.12988/atam.2016.51212Alharbi, S.O., Alderson, T.L. and Hamdan, M.H., Flow of a Fluid with Pressure-Dependent Viscosity through Porous Media”, Advances in Theoretical and Applied Mechanics, vol. 9(1), 2016, pp. 1-9. Abu Zaytoon, M.S. and Hamdan, M.H., The Flow of a Saffman’s Dusty Gas with Pressure-Dependent Viscosity through Porous Media Elixir Appl. Math., Vol. 98, 2016, pp. 42550-42554 Roach, D.C., Abu Zaytoon, M.S. and Hamdan, M.H., On the Flow of Dusty Gases with Pressure - Dependent Viscosities through Porous Structures, Int. J. Enhanced Research in Science, Technology & Engineering, Vol. 5, No. 9, 2016, pp. 46-54. 10.1017/s0022112062000555Saffman, P.G., On the Stability of Laminar Flow of a Dusty Gas, J. Fluid Mechanics, Vol. 13, No. 1, 1962, pp. 120-128. Marble, F. E., Dynamics of Dusty Gases, Annual Review of Fluid Mechanics, Vol. 2, 1970, pp. 397-446. 10.1016/0096-3003(93)90033-bHamdan, M.H. and Barron, R.M., On the DarcyLapwood-Brinkman-Saffman Dusty Fluid Flow Models in Porous Media. Part I: Models Development, Applied Mathematics and Computation, 54, No. 1, 1993, pp. 65-79. 10.1016/0096-3003(93)90034-cHamdan, M.H. and Barron, R.M., On the DarcyLapwood-Brinkman-Saffman Dusty Fluid Flow Models in Porous Media. Part II: Applications to Flow into a Two-Dimensional Sink, Applied Mathematics and Computation, 54, No.1, 1993, pp. 81-97. Alzahrani, S.M. and Hamdan, M.H., GasParticulate Models of Flow through Porous Structures, Int. J. Engineering Research and Applications, Vol. 6, No.2(3), 2016, pp.54-59. Alzahrani, S.M. and Hamdan, M.H., Mathematical Modelling of Dusty Gas Flow through Isotropic Porous Media with Forchheimer Effects, Int. J. of Enhanced Research in Science, Technology & Engineering, Vol. 5, No. 5, 2016, pp. 116-124. Barus, C.J., Note on Dependence of Viscosity on Pressure and Temperature. Proceedings of the American Academy, Vol. 27, 1891, pp. 13-19. 10.2475/ajs.s3-45.266.87Barus, C.J., Isothermals, Isopiestics and Isometrics Relative to Viscosity. American Journal of Science, Vol. 45, 1893, pp. 87–96. 10.1007/bf00820342Du Plessis, J.P. and Masliyah, J.H., Mathematical Modeling of Flow through Consolidated Isotropic Porous Media, Transport in Porous Media, Vol. 3, 1988, pp. 145-161. 10.1007/bf00208950Du Plessis, J.P. and Masliyah, J.H., Flow through Isotropic Granular Porous Media, Transport in Porous Media, Vol. 6, 1991, pp. 207-221.