ABSTRACT
Capillarity-driven flows resulting from critical geometric wetting criterion are observed to yield significant shifts of the bulk fluid from one side of the container to the other during “zero gravity” experiments. For wetting fluids, such bulk shift flows consist of advancing and receding menisci sometimes separated by secondary capillary flows such as rivulet-like flows along gaps. Here we study the mean curvature of an advancing meniscus in hopes of approximating a critical boundary condition for fluid dynamics solutions. It is found that the bulk shift flows behave as if the bulk menisci are either “connected” or “disconnected.” For the connected case, an analytic method is developed to calculate the mean curvature of the advancing meniscus in an asymptotic sense. In contrast, for the disconnected case the method to calculate the mean curvature of the advancing and receding menisci uses a well-established procedure. Both disconnected and connected bulk shifts can occur as the first tier flow of more complex compound capillary flows. Preliminary comparisons between the analytic method and the results of drop tower experiments are encouraging.
ACKNOWLEDGMENTS
Support for this work is primarily provided by the National Aeronautics and Space Administration (NASA) under cooperative agreement NNX09AP66A managed by NASA's Glenn Research Center (GRC). Incremental contributions under previous funding sources such as NASA NNC05AA29A and National Science Foundation (NSF) CTS-0521890 are also acknowledged. The authors thank Y. Reichel for providing helpful comments.
