Forced Phase Separation in a Closed Cell

Phase separation of oil-water mixtures is of interest as water recovery becomes more pertinent. It is therefore of interest to find ways to accelerate this process to make applications such as graywater recycling more efficient. Preliminary work carried out by the group of Manor at Technion suggests that a MHz Rayleigh surface acoustic wave (SAW) propagating through the underlying substrate has the ability to accelerate spinodal decomposition in the mixture sitting atop. Experiments are performed using a lithium-niobate substrate and a drop of silicon oil and water mixture. In this study, we present a simplified model derived from first principles that describes a binary mixture undergoing spinodal decomposition due to a substrate vibration in a closed cell. Enforcing conservation of mass for the mixture and requiring the model to be consistent with the second law of thermodynamics provides the governing equations of the system. The model is then closed with an appropriate free energy functional, which we do in accordance with the Cahn-Hilliard theory. Numerical results carried out in 3D are presented with parameter values estimated from experimental observations. Simulations show that phase separation is accelerated by such a force in agreement with experimental results.