Calculation of meniscus height for Newtonian and non-Newtonian fluids in micro/nano channels

Abstract

Based on lubrication approximation, the governing equations for Newtonian and non-Newtonian fluid flow are built in terms of the action of a capillary force in micro/nano channel. The time-dependent contact angle is determined by fitting the experimental data. The change of the meniscus curvature is assumed to be governed by the ratio of meniscus curvature at the starting and ending points of the curve. The dynamic evolution of the meniscus is realized by the geometrical method with arc approximation. The algorithm is applied to solve the liquid height of the Newtonian fluid in micro/nano channel, in which a good agreement between predicted and experimental is achieved. This algorithm is further developed to solve fluid flow problem of Polycarbonate (PC) under the combined action of squeeze and capillary forces. Through simulation analysis, it is known that when non-Newtonian index n is 0.715, the material is easy to flow and the pillar rises quickly. When the Bond number is 0.1, the capillary force has stronger effect on the pillar’s meniscus, and the height of the meniscus is larger.