Numerical Approach of the Permeability of a Macroporous Bioceramic with Interconnected Spherical Pores

Abstract

Manufacturing a hybrid bone substitute requires a dynamic culture of the cells preliminarily seeded in a scaffold through a flow of physiological fluid. The velocity, pressure, and the distribution of fluid flow in this kind of macroporous medium are the important keys. Because of the difficulties in determining these parameters by experiment, a numerical approach has been chosen. One of the primary step of this study consists in the determination of permeability K. In this article, two types of structure of macroporous bioceramics are concerned. One is the interconnected pore spheres arranged either simple cubic, body-centered cubic or face-centered cubic systems. The other is the interconnected pore spheres randomly arranged. Based on Darcy’s law, the permeability K was calculated for many cases (type, porosity) by simulating the fluid flow through a small representative volume. These results are compared with some previous models such as Ergun, Carman–Kozeny, Rumpf–Gupte, and Du Plessis. The limits of Darcy’s law and the above-mentioned models have been determined using numerical simulation. The result showed that the porous media with spherical interconnected pores of BCC systems can be used to replace a complex random system in a range of porosity from 0.71 to 0.76 (i.e., porosity of our scaffolds). This assumption is validated for a pressure gradient lower the 1,000 Pa m–1 and a simple polynomial relation linking permeability and porosity (0.71–0.76) has been established.