Analysis of capillary flows in non-uniform cross-sectional capillaries

The capillary flow is widely applied recently in many modern processes such as underfilling of flip chip, crystal growth, flow in micro-fluidics, and a variety of other fields. In this study, a simple formulation of the interface progression in a non-uniform capillary was constructed based on analysis of the Lucas–Washburn equation. The effect of capillary geometry on the progress of the interface has been investigated using the formulation. A close form solution of the time required for interface advancement without gravity in a non-uniform capillary was developed. For capillary advancement along horizontal pipe without the effect of gravity, the wetting time was found to depend on some parameter of the capillary geometry. The developed formulation can be applied to evaluate the dynamic capillary flow of any other irregular capillaries with well-defined geometry.