Adaptive interface thickness based mobility—Phase-field method for incompressible fluids

Abstract

The ubiquity of two-phase systems has rendered them a subject of prime importance especially from numerical perspectives. Among several methods described in the literature, which are generally classified as sharp or diffuse interface methods, phase-field (diffuse interface) method has been at the paramount of several recent investigations owing to its several advantages, primarily to handle complex topological changes. Though several advancements have been made in the subject, one of the important challenges with this approach using Cahn-Hilliard equation lies in the determination of an appropriate value of mobility. Despite certain propositions in the literature in terms of non-dimensional numbers (Peclet and Cahn numbers), ambiguity in the velocity scale to be chosen for evaluating mobility poses a challenge for their straightforward extension to real systems. In addition it renders the system to be dependent on numerical parameters. In the current work, we address this problem using a new approach to calculate the mobility parameter in terms of local equilibrium interface thickness which in itself is evaluated from the phase-field parameter. Consequently, this helps to make the model independent of numerical parameters making it more reliable. We test this approach for several canonical and complex cases, such as the rise of lighter bubble in a heavier medium, bubble coalescence, Rayleigh-Taylor instability. The results are compared with those in literature or obtained using level set method. An excellent agreement is observed illustrating the potential of this approach to make phase-field model more prominent.