Dynamics in closed and open capillaries

Abstract

Capillary rise of a liquid displacing gas is analysed for both open and closed capillaries. We include menisci mass and hysteresis, and show that oscillations due to inertia are muted by friction at the advancing meniscus. From single-phase numerical computations in a no-slip/slip capillary, we quantify losses due to entry, flow development, meniscus slip, exit and acceleration of fluid within the reservoir. For closed capillaries, determining viscous drag due to gas requires inclusion of compressibility, and solving a moving boundary problem. This solution is derived through perturbation expansion with respect to two different small parameters for obtaining pressure above the liquid meniscus. Our rise predictions spanning a large range of experimental conditions and fluids for both open and closed capillaries match the data. The experimental data confirm the adequacy of the theoretically constructed dimensionless groups for predicting oscillatory behaviour.