An extended volume-of-fluid method for micro flows with short-range interactions between fluid interfaces

A formulation is developed allowing to take into account the interaction of fluid interfaces in computational methods for free-surface flow. The necessity for such an extension of the standard computational approaches is traced back to a large number of experimental and theoretical results showing that in the presence of surfactants, fluid interfaces often interact in such a way that coalescence of bubbles or droplets is slowed down or suppressed. The strategy pursued in this paper to incorporate such effects relies on a Debye-screened scalar field which develops steep gradients in the vicinity of an interface. The force density acting in a gap between two interfaces is computed using a function of the local field values and a cut off to eliminate those regions where no interaction takes place. It is shown that in such a way a power-law behavior of the force as a function of separation between the interfaces can be reproduced. The model is implemented into a standard volume-of-fluid scheme and it is exemplified that, compared to conventional approaches, completely different scenarios for micro flows of droplets can be reproduced. The important qualitative difference is that coalescence is avoided, so that the formation and transport of multibubble/multidroplet arrangements can be studied. (c) 2005 American Institute of Physics.