Controlling bubble coalescence in metallic foams: A simple phase field-based approach

The phase-field method is used as a basis to develop a strictly mass conserving, yet simple, model for simulation of two-phase flow. The model is aimed to be applied for the study of structure evolution in metallic foams. In this regard, the critical issue is to control the rate of bubble coalescence compared to concurrent processes such as their rearrangement due to fluid motion. In the present model, this is achieved by tuning the interface energy as a free parameter. The model is validated by a number of benchmark tests. First, stability of a two dimensional bubble is investigated by the Young-Laplace law for different values of the interface energy. Then, the coalescence of two bubbles is simulated until the system reaches equilibrium with a circular shape. To address the major capability of the present model for the formation of foam structure, the bubble coalescence is simulated for various values of interface energy in order to slow down the merging process. These simulations are repeated in the presence of a rotational flow to highlight the fact that the model allows to suppress the coalescence process compared to the motion of bubbles relative to each other. Moreover, since density is treated as an auxiliary variable slaved to the volume occupied by a given phase, the present model allows realization of arbitrarily large liquid-gas density ratios. This property is demonstrated by simulation of a system with rho(l)/rho g = 10, 000.