Impregnation of liquids into a laminated porous material with a high permeability contrast

Abstract

This paper sets the physical basis for an efficient method designed to fill low permeable porous materials with liquids. Fast filling of these materials is achieved if one sandwiches a slightly permeable sample between highly permeable layers. We derived a useful engineering formula for the front speed as a function of the layer permeability and thickness. An asymptotic analysis of the two-dimensional liquid flow with moving front is performed assuming that the covering layers are much thinner than the sample thickness. It is shown that the front forms sawteeth with the tooth apexes moving along the highly permeable layers. If the surface layers are made of the same material, two sawteeth are mirror symmetric with respect to the sample midplane. The angle which they form drastically depends on the ratio of layer-to-sample permeabilities and on the ratio of skin-to-core thicknesses. The theory presented in this paper can be used to optimize the processes of impregnation of nanostructured materials.

Elastocapillarity: Stress transfer through fibrous probes in wicking experiments

“…The forced impregnation of nanofibrous preforms is used in composite applications [24,[36][37][38][39]. Using the estimates of the stress jump given in Table 1, one can appreciate the difficulty of impregnation of materials with nanometer pores: the tension might be comparable to the strength needed to break the porous material.…”

An asymptotic analysis of the steady process of saturation of a laminated porous material

“…The motion of the interface in the steady process of the saturation of a double-layer porous material is represented by the boundary-value problem 4 (1.1)…”

Evolution of the interface in a stratified anisotropic porous material

“…By the quantity p ± (x, y, t) is meant the relative pressure, i.e., the pressure reckoned from the value of P c . Then, the dynamic condition can be written as [1,2] BC ∪ CD:…”

“…The variant χ ± = 1, i.e., k ± xx = k ± yy = k ± , which corresponds to the case of a two-layer isotropic porous material, is considered in [2].…”

“…As in [2], we introduce two dimensionless parameters δ and ε, which characterize the relations between the thickness of the layers and their permeabilities:…”