Multiscale modeling of a fluid saturated medium with double porosity: Relevance to the compact bone

Properties of water confined in hydroxyapatite nanopores as derived from molecular dynamics simulations

“…However, the role of nanopores on the fluid flow within the bone has been largely overlooked, most likely because the description of fluid flow has been so far restricted to a double-porosity approach involving vasculature (Haversian system) and submicrometer pores of canalicular network [8,9]. In the framework of porous media theory, the bone interstitial fluid flow is macroscopically described by a Darcy law obtained by upscaling a description of the flow at the pore scale to the macroscopic scale organ [10,11].…”

Towards Microstructure Based Tissue Perfusion Reconstruction From Ct Using Multiscale Modeling

“…[10,11], cf. [13], where the theory is explained in detail for a one compartment double-porosity medium.…”

Homogenization of a dual-permeability problem in two-component media with imperfect contact

“…Roughly speaking, it consists in the passage from microscopic scale to the macroscopic one by tending to zero a small parameter, usually denoted ε, which is the ratio between the two characteristic scales, see [6], [11]. We remark here that the fact that homogenization in double-porosity phases can lead to effective fluid flow behavior was observed by many authors in various problems [1], [2], [5], [9], [10]. For example, in [5], a microscopic model consisting of the usual equations describing Darcy flow in a reservoir with highly discontinuous porosity and permeability coefficients, was addressed.…”

“…Also for poroelastic heterogeneous media, various effective double porosity models of composites made of a mixture of two poroelastic solids saturated by a compressible Newtonian fluid have been derived. In [10], the homogenization of a compact bone poroelasticity model, describing interactions between deformation of the bone tissue and induced flow, is addressed. The double-porous structure consists of the Havers-Volkmann channels (the primary porosity) and the canaliculi (the dual porosity).…”