The distribution of fluids in irregular capillary tubes: a new capillary model based on the single-corner capillary

A new basic single-corner capillary model is presented. In this model, the distribution of immiscible fluids is determined by a particular threshold pressure. Additionally, we derive and analyze the interface curvature and profile of the fluid menisci in different tubes. Various polygonal cross sections are obtained by repeatedly superposing the basic single-corner capillary model. We study the relationship between the number of polygon edges and the distribution of fluids as well as the saturation of the wetting phase in equilateral polygon tubes. Furthermore, for the first time, we discuss the interaction of the corners to reveal the five stages of the fluid interfaces with various corner geometries. The dimensionless interface curvature and the radius of the circle are considered to extend our conclusions to similar cross-sectional capillary tubes of different sizes.