Title: Phase-field-based simulation of axisymmetric binary fluids by using vorticity-streamfunction formulation

Authors: Jun-Jie Huang; Haibo Huang; Shi-Long Wang

Addresses: Department of Engineering Mechanics, Chongqing University, Chongqing 400044, China; Chongqing Key Laboratory of Heterogeneous Material Mechanics (Chongqing University), Chongqing 400044, China; State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400044, China ' Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China ' State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400044, China

Abstract: We propose a numerical method for the simulation of axisymmetric binary fluids based on the phase-field theory and vorticity-streamfunction formulation. Unlike most existing methods that solve the incompressible Navier-Stokes equations in the velocity-pressure form, we recast the equations into the vorticity-streamfunction form, which only need to treat one evolution equation of the vorticity for two-dimensional (2-D) or axisymmetric (pseudo 2-D) problems. Besides, this formulation enforces the continuity equation more easily. This method is verified through a series of benchmark problems under axisymmetric conditions, including the Laplace relation for a quiescent drop, coalescence of two drops, and the contact angle of a drop on a smooth wall with given wettability. Good agreements with theoretical relations or another numerical method are achieved for all these problems.

Keywords: numerical simulation; axisymmetric two phase flow; phase field; vorticity streamfunction; drop dynamics; fluid flow; interface dynamics; interfacial tension; modelling; binary fluids; incompressible flow.

DOI: 10.1504/PCFD.2015.072776

Progress in Computational Fluid Dynamics, An International Journal, 2015 Vol.15 No.6, pp.352 - 371

Received: 08 May 2021
Accepted: 12 May 2021

Published online: 27 Oct 2015 *

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