Surface-tension-driven liquid-liquid displacement in a capillary

This paper presents theoretical and experimental studies of the surface-tension-driven, two-immiscible liquid-liquid displacement in a horizontal capillary. Using the dynamic contact angle approach, a one-dimensional mathematical model is developed to describe the capillary displacement of a fixed liquid column by another liquid that continuously flows into the capillary by surface tension. Experiments for a water column displaced by silicon oil were carried out to examine the effect of the water column length and capillary diameter on the displacement dynamics. It was found that a faster and longer displacement is achieved for a shorter water column in a larger capillary. The theoretical predictions agree reasonably well with the experimental studies conducted for the capillary displacement of the silicon oil-water interface. In addition, for a single liquid capillary flow, dimensionless Pi groups are derived using the similarity analysis. It is demonstrated that using the derived Pi groups, the experimental data for the displacement of silicon oil of various viscosities in capillaries of various diameters can collapse into one curve that is consistent with the Washburn equation.