ON A HIERARCHY OF APPROXIMATE MODELS FOR FLOWS OF INCOMPRESSIBLE FLUIDS THROUGH POROUS SOLIDS

DOI10.1142/S0218202507001899zbMath1123.76066MaRDI QIDQ5293959

Kumbakonam R. Rajagopal

Publication date: 5 July 2007

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

zbMATH Keywords

Biot modelmixture theoryDarcy's equationBrinkman's equations

Mathematics Subject Classification ID

Flows in porous media; filtration; seepage (76S05) Research exposition (monographs, survey articles) pertaining to fluid mechanics (76-02)

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Cites Work

• Unnamed Item
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• Theories of immiscible and structured mixtures
• The diffusion of a fluid through a highly elastic spherical membrane
• Constitutive relations for the interaction force in multicomponent particulate flows
• On the propagation of waves through porous solids
• Combined extension and torsion of a swollen cylinder within the context of mixture theory
• On boundary conditions for a certain class of problems in mixture theory
• Some nonlinear diffusion problems within the context of the theory of interacting continua
• Flow of a fluid infused with solid particles through a pipe
• Wave propagation in elastic solids infused with fluids
• Diffusion through non-linear orthotropic cylinders
• On boundary conditions for fluid flow in porous media
• A variational theory of immiscible mixtures
• A contribution to the theory of non-linear diffusion
• Incompressible mixtures of Newtonian fluids
• A thermodynamic theory of mixtures of fluids
• Determination of the constitutive coefficients for a mixture of two solids
• Small motions superposed on large static deformations in porous media
• A multi-continuum theory for composite elastic materials
• Diffusion of fluids through transversely isotropic solids
• Fluid Film Lubrication
• Dissipation of Energy due to Solid Particles Suspended in a Viscous Liquid
• Fluid Dynamics / Strömungsmechanik
• The transverse force on a spinning sphere moving in a viscous fluid
• Mechanics of Deformation and Acoustic Propagation in Porous Media
• On a Problem in the Polymer Industry: Theoretical and Numerical Investigation of Swelling
• The lift force on a spherical body in a rotational flow
• Homogenization of the Navier-Stokes equations with a slip boundary condition
• Motion of aerosol particles in a temperature gradient
• CONTINUUM THEORIES OF MIXTURES: BASIC THEORY AND HISTORICAL DEVELOPMENT
• Brownian diffusion of particles with hydrodynamic interaction
• The mechanics of rubber elasticity
• Continuum Theories of Mixtures: Applications
• Shear behaviour of elastohydrodynamic oil films
• Plane Progressive Waves in a Binary Mixture of Linear Elastic Materials
• A BOUNDARY VALUE PROBLEM IN GROUNDWATER MOTION ANALYSIS — COMPARISON OF PREDICTIONS BASED ON DARCY’S LAW AND THE CONTINUUM THEORY OF MIXTURES
• A One-dimensional flow problem in porous media with hydrophile grains
• Substantiation of the Darcy law for a porous medium with condition of partial adhesion
• The viscosity of a fluid containing small drops of another fluid
• Unsaturated incompressible flows in adsorbing porous media
• Simple flows of fluids with pressure–dependent viscosities
• A Comprehensive Mathematical Model for a Multispecies Flow Through Ground Coffee
• Non-Linear Diffusion - Non-linear diffusion I. Diffusion and flow of mixtures of fluids
• ON BASIC EQUATIONS FOR MIXTURES
• A MIXTURE OF VISCOUS ELASTIC MATERIALS WITH DIFFERENT CONSTITUENT TEMPERATURES
• The lift on a small sphere in a slow shear flow
• The determination of the bulk stress in a suspension of spherical particles to order c 2
• Sedimentation in a dilute dispersion of spheres
• Behaviour of macroscopic rigid spheres in Poiseuille flow Part 1. Determination of local concentration by statistical analysis of particle passages through crossed light beams
• A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles
• The elastic and viscous properties of emulsions and suspensions