Modeling of free surface motion during impregnation of a porous fiber bed.

Abstract

This work studies the free fluid surface shape and its motion through a porous fiber bed. The static free surface shape in a two-dimensional channel is numerically calculated. The results of the free surface shape are presented for different Bond numbers, contact angles and inclination angles. When analytical solution is available, numerical results are compared with the analytical results. Free surface shapes and locations are solved when the fluid is driven by capillary forces to flow through an anisotropic fiber bed. Such motion is simulated using the theory of creeping flow through a two-dimension channel. The results of free surface motion are presented for different fiber volume fraction, contact angle, and Bond numbers. It is found that gravity affects only the final stage of the impregnation process. Permeability of the fiber bed is obtained using Darcy's law and the fluid front velocity from the calculation. Anisotropic transverse permeability of a fiber bed due to different fiber arrangement pattern is discussed and compared with the longitudinal permeability. Permeability prediction using lubrication model is discussed. It is found that when fiber volume fraction reaches a certain level, the equation for the calculation of permeability needs to be reconsidered. An extension of the lubrication is suggested. Permeability for different fiber arrangement pattern is discussed and presented.