Journal ArticleDOI
Unsteady diffusion of fluids through a non-linearly elastic cylindrical annulus
L. Tao,Kumbakonam R. Rajagopal +1 more
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In this paper, the unsteady radial diffusion motions of an incompressible fluid through a cylindrical annulus are studied by using the theory developed by Tao et al. [Mathematical Models and Methods in Applied Sciences 1 (1991)].Abstract:
The unsteady radial diffusion motions of an incompressible fluid through an isotropic and transversely isotropic non-linearly elastic cylindrical annulus are studied by using the recent theory developed by Tao et al. [Mathematical Models and Methods in Applied Sciences 1 (1991)]. As the fluid diffuses through the solid, ahead of it there is a pure solid while behind the diffusing front there is a mixture of a fluid and a solid. Governing equations for both the constituents, within the content of the theory of mixture, are used in the mixture region. On the diffusing front, the evolution equations are used based on the previous work of Tao et al. [Mathematical Models and Methods in Applied Sciences 1 (1991)]. The problems are solved numerically using a finite difference method.read more
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Diffusion through polymeric solids undergoing large deformations
TL;DR: In this paper, the authors review the literature on the diffusion of liquids through polymers that are undergoing large deformations, and discuss the difficulties associated with modelling such a process, the inadequacy of simple equations such as Fick's equation or Darcy's equation to describe the problem with regard to characterising the stresses and strains in the polymer through which the liquid is diffusing, and the change in its material properties during swelling and the need for an alternate approach.
Journal ArticleDOI
Structure of the dependence of Darcy and Forchheimer coefficients on porosity
TL;DR: In this paper, the coefficients of the Darcy and Forchheimer terms are analyzed as functions of the porosity of a saturated porous medium and it is proved that the solution to flow in a Forchheimen porous material depends continuously on changes in the porosities.
Journal ArticleDOI
A multiple-network poroelastic model for biological systems and application to subject-specific modelling of cerebral fluid transport
TL;DR: Numerical results of smoking and non-smoking subjects show hypoperfusion in the brains of smoking subjects, which demonstrate that the numerical model is capable of capturing spatio-temporal fluid transport in biological systems across different scales.
Book ChapterDOI
Deformable Porous Media and Composites Manufacturing
Angiolo Farina,Luigi Preziosi +1 more
TL;DR: In this paper, a mathematical model of deformable porous media and their application to composite materials manufacturing is presented, as a first step toward the understanding of the complex process of this complex process.
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Mathematical modeling of flows through inelastic porous solids
Angiolo Farina,Lorenzo Fusi +1 more
TL;DR: In this article, the authors propose a framework based on classical mixture theory to describe the isothermal flow of an incompressible fluid through a deformable inelastic porous solid.
References
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Journal ArticleDOI
Continuum theories of mixtures: basic theory and historical development
R. J. Atkin,R. E. Craine +1 more
Book ChapterDOI
Classical Field Theories
TL;DR: In this article, the Coriolis acceleration at every point inside a rotating body is considered to be a vector field, and it is not regarded as a real field because it can be transformed away by choosing a reference frame rotating with the body.
Journal ArticleDOI
Incompressible mixtures of newtonian fluids
TL;DR: In this paper, the constitutive equations for an incompressible mixture of Newtonian fluids using an entropy production inequality are derived, which involve the introduction of an arbitrary hydrostatic pressure.
Journal ArticleDOI
On boundary conditions for a certain class of problems in mixture theory
TL;DR: In this article, an additional boundary condition for solid-fluid mixtures is proposed for the situation in which a mixture boundary is in a saturated state, derived from a thermodynamic characterization of the state and taking the form of a relationship between the total stress tensor, the stretch tensor and the volume fraction of the solid.
Journal ArticleDOI
Applications of the theory of interacting continua to the diffusion of a fluid through a non-linear elastic media
TL;DR: In this article, the theory of interacting continua is applied to the problem of diffusiion of a fluid through a non-linear elastic layer and a hollow sphere, and restrictions are derived from a thermodynamic standpoint for the partial stresses for the fluid and solid and the diffusive body force.