Numerical simulation of submicron multi-phase fluids (with Sanjoy Banerjee and Carlos Garcia-Cervera, Spring 2004 - Summer 2005)

The broad goal of this research project was to develop a numerical framework for simulating multi-phase fluid flow at the submicron scale, subject to long-range electrostatic and Van der Waals forces.  My contributions were to develop such a framework for two-phase flow in 2D.  To start with, I solved the two-phase incompressible Navier-Stokes' equations with sharp interface (Fedkiw, et.al., 2000).  I modified this method with a front-tracking algorithm (Ceniceros, Roma, 2004) to move the interface.  Although algorithmically more complex than level set methods, front-tracking has several key advantages: improved accuracy and stability in computing surface tension, better mass conservation, and the flexibility of modeling the film rupture event.  To model the presence of charges and dipoles, I seeded the fluid bulks and interface with particle clusters.  Finally, I summed the forces using a hierarchical tree code algorithm (Barnes and Hut, 1987) to help speed up this computational bottleneck.  This code was used to study a Van der Waals induced hydrodynamic instability during the coalescence of two flat liquid-air interfaces, as observed in experiments performed by Israelachvili, et.al., 2004.

Above: Coalescence of two approaching liquid films in air: slow approach (upper) and fast approach (lower).  Experiments performed by Israelachvili, et. al..

For a more detailed description of this problem and the numerical methods used, click here.

To see a movie of a numerical simulation of the above instability during coalescence, click here.