Microfluidic model of porous media wetting Application to a collagen network

A slightly deformable network may be considered as a particular porous media with a connected void phase. In this paper, a fluid flow through a collagen network is analyzed with applications in the area of restorative dentistry. Infiltration of a fluid into a network already saturated by another fluid is a complex issue especially when the fibers are so tightly distributed (10 to 100 nm between them in a dentinal collagen network) that capillary forces are significant (the bond and capillary number are small). In a general framework, the equation of the capillary membrane with variable curvature and the associated boundary condition at the contact line between the two fluids and the fiber wall are discussed. The resulting solution is approximated by the finite element method together with a level set technique to track the smeared front. The expected meniscus shape around a fiber and the capillary membrane advancing front in different networks are obtained. The influence of fiber orientation and interfibrillar space is discussed. This type of simulation is an essential step towards a refined understanding of the macroscopic behavior of a porous medium like the collagen network in order to estimate e. g. the equivalent capillary pressure or relative permeability.