Spontaneous radial capillary impregnation across a bank of aligned micro-cylinders – Part I: Theory and model development

This paper presents an analytical and numerical approach to describe the capillary infusion of a liquid across an array of parallel micro-cylinders. Based on a series of simplifying assumptions, the model proposes a method to average the varying capillary pressure and introduces a technique to assess the inhibiting effects of the gas entrapped between the micro-cylinders as the liquid radially ingresses into the micro-cylinder array. The proposed averaging scheme of the capillary pressure is an improvement over previous analytical approaches, as it accounts for the physics of wetting at the micro-scale. The equations are non-dimensionalized and the role of various parameters such as gas entrapment and average capillary pressure is explored. The inclusion of the gas displacement phenomenon requires only one parameter to be determined empirically, in order to describe the impregnation behavior of the liquid. Two limiting cases when all gas is allowed to escape through the impregnating liquid and when all the gas is entrapped within are identified. This study should prove useful in understanding the role of entrained gas and capillarity on impregnation mechanics in micro-scale porous media.