Local volume-conservation-improved diffuse interface model for simulation of Rayleigh–Plateau fluid instability

Abstract

The Rayleigh–Plateau instability is a typical multi-phase fluid interface problem which is driven by the surface tension. After the break-up of a liquid thread, the satellites droplets will appear. To prevent the disappearance of small droplets due to interfacial length minimization, we present a new Cahn–Hilliard-type diffuse interface model to improve the conservation of local volume. By coupling with the incompressible Navier–Stokes equations, the fluid flow-coupled binary system and its axisymmetric form are derived. The pressure projection method and the semi-implicit time-marching method are used to discretize the fluid equations and the diffuse interface equations in time. In the axisymmetric domain, the finite difference method is used to perform the spatial discretization. The fully discrete solution algorithm is introduced in detail. The numerical experiments show that the proposed model has better local volume conservation than the classical Cahn–Hilliard model. The qualitative comparison with a real experiment indicates that the proposed model has a good potential to simulate the coating problem of a cylindrical fibre with a liquid film.