The dynamics of the annular liquid layer inside a cylindrical capillary

Abstract

When one fluid displaces another in a cylindrical capillary, a layer of the original fluid is often left behind on the capillary wall. We studied the dynamics of a cylindrical hexadecane layer deposited inside glass capillaries after the oil/air displacement experimentally and by a theoretical model prediction. Our experiments have shown that an annular oil layer is formed on the capillary wall after hexadecane is displaced by air. The oil layer subject to surface perturbation becomes unstable over time (Rayleigh instability), forming uniform, regularly spaced double concave meniscuses across the capillary that are bridged with dimples (collars). With time, the film between the meniscus and the dimple thins, but does not break, during the thinning process. The dynamics of the oil layer and the formation of the double concave meniscus with the dimple are more pronounced in a large capillary compared to those phenomena found in a small capillary. In order to reveal the phenomena of the film thinning and stability between the double concave meniscus and the dimple, we monitored an air bubble approaching a flat glass surface in hexadecane. We found that the oil film thinning in a cylindrical glass capillary and on a flat glass substrate was similar; the film did not break during the thinning process. The analysis also showed that the macroscopic contact angle (based on the Laplace solution-extrapolation to a solid substrate) was different from the microscopic contact angle (between the film and meniscus). We adapted the model proposed by Gauglitz and Radke [“An extended evolution equation for liquid film breakup in cylindrical capillaries,” Chem. Eng. Sci. 43, 1457 (1988)] for our system (oil-air displacement) and solved it numerically. The numerical result shows a stable film between the liquid bridge and the dimple, which is consistent with our experimental observations. We also estimated the meniscus-film-dimple thickness profile and found it was in fair agreement with the model prediction.