A dynamic model for the oscillatory regime of liquid rise in capillaries

Abstract

The oscillatory regime for liquid rise in vertical capillaries has been observed but the analytical solution that can be applied for this regime is still in shortage. Some lack terms in the existing analytical solutions make them show deviations when predicting the oscillatory behavior of liquid rise. An improved dynamic model is built in this work for the oscillatory regime. Two main contributions are made, concerning the non-equal pressure losses at the entrance for liquid rise and fall, and the receding dynamic contact angle for the regions with negative capillary numbers. Experiments are performed to correlate the empirical parameters in the submodels and to validate the combined dynamic model. Good accuracies of the present model are obtained by comparing with the experimental data both in literature and from the present study. Inclusion of the non-equal pressure loss equations for the end effect makes the model well capture the high asymmetry of oscillations, while the two-stage dynamic contact angle models correct the local bouncing of the meniscus. The dynamics of liquid in the oscillatory regime is discussed by comparing the contribution of each pressure force. Occurrence criteria of the oscillatory regime is obtained through a non-dimensional analysis. It is shown that the oscillatory regime is affected not only by the combined parameter (ω), but also by the immersed height of tube (H0) and the pressure head loss coefficients (ξ).