A COMPREHENSIVE MODEL FOR CAPILLARY PRESSURE DIFFERENCE ACROSS A DROP/BUBBLE FLOWING THROUGH A CONSTRICTED CAPILLARY

Abstract

The capillary pressure is one of the crucial parameters in many science and engineering applications such as composite materials, interface science, chemical engineering, oil exploration, etc. The drop/bubble formation and its mechanisms that affect the permeability of porous media have steadily attracted much attention in the past. When a drop/bubble moves from a larger capillary to a smaller one, it is often obstructed by an additional pressure difference caused by the capillary force. In this paper, a comprehensive model is derived for the capillary pressure difference when a drop/bubble flows through a constricted capillary, i.e. a geometrically constricted passage with an abrupt change in radius. The proposed model is expressed as a function of the smaller capillary radius, pore-throat ratio, contact angle, surface tension and length of the drop/bubble in the smaller capillary. The model predictions are compared with the available experimental data, and good agreement is found between them.