Wetting and Navier-Stokes Equation — The Manufacture of Composite Materials

Abstract

It is well known that there are several processes to manufacture composite materials, a large part of which consist in the infiltration of a liquid (matrix) through a porous medium (reinforcement). To perform these processes, both thermodynamics (wetting) and kinetics (Navier-Stokes) must be considered if a good quality composite materialis sought. Although wetting and the laws that governithave been well known for over 200 years, dating back to the original works of Young and Laplace, this is not the case with the Navier-Stokes equation, which remains so far unsolved. Although the Navier-Stokes equation, which describes the motion of a fluid, has been solved for many particular cases, such as the motion of a fluid through a pipe, which has resulted in the well-known Poiseuille equation, or the motion of a fluid through a porous media, described by the Darcy’s law (empirical law obtained by Darcy), its general solution remains one of the greatestchallenges of mathematicians today. Therefore, the objective of this chapter is to present the resolution of the Navier-Stokes equation with the laws of wetting for different cases of interest in the manufacture of composite materials.