Enhanced Capillary Rise Model Incorporating Boundary Layer Effect and Wall Roughness

Abstract

An enhanced capillary rise model is introduced in this study, incorporating the momentum theorem of meniscus to determine the imbibition height. This model accounts for two significant micro-scale factors, viz. wall roughness and boundary layer. The resistance posed by wall roughness is analogized to fluid flow in porous media, while the impact of pressure variations within the boundary layer during imbibition is also considered. A comprehensive analysis compares the effects of wall roughness and boundary layer on capillary rise. Our findings are validated through comparisons with previously published models and experimental data. An analytical expression for the evolution of the height of capillary rise in a single capillary is obtained as functions of time, incorporating both wall roughness and the boundary layer. Our results indicate that the boundary layer enhances the nonlinear characteristic of imbibition although its influence on imbibition height is relatively minor due to the sluggish rate of fluid infiltration at the nanoscale. On the other hand, the wall roughness effect can be equivalent to that of a solid wall, which reduces the effective capillary radius. The uniqueness of our model lies in its application to understand capillary imbibition in porous media with nano-scale channels, offering insights into improved capillary rise comprehension.

Keywords: capillary rise, nano- to micro-channel, boundary layer effect, wall roughness