A Comprehensive Analysis of Capillary Penetration in Circular and Rectangular Microchannels

The current paper presents an analytical examination of the capillary penetration phenomenon. In this article, a laminar and incompressible flow in circular and rectangular ducts is considered. As a result, a differential equation is derived to describe the observed behavior. The study aims to provide a solid theoretical framework for understanding capillary penetration and its mathematical formulation in various duct geometries. This article investigates the governing equations, boundary conditions, and problem-solving approaches for capillary penetration, considering both dimensional and dimensionless formulations. In the dimensional mode, the influence of surface tension and viscous forces on the phenomenon of capillary penetration is thoroughly examined. The study reveals that an increase in surface tension force enhances the penetration flow, while an increase in viscous force leads to a decrease in the penetration flow. To facilitate a more accurate comparison of capillary penetration between circular and rectangular cross-sections, all equations are transformed and solved in a dimensionless framework. The findings indicate that flow penetration is greater in the rectangular cross-section compared to the circular cross-section for a given cross-sectional area. This approach enables a comprehensive understanding of the factors affecting capillary penetration while facilitating meaningful comparisons between different geometries.

Keywords:

capillary penetration , surface tension , viscous force , circular cross-section , rectangular cross-section