A continuous surface tension force formulation for diffuse-interface models Junseok Kim * Department of Mathematics, 103 Multipurpose Science and Technology Building, University of California, Irvine, CA 92697-3875, USA Received 25 March 2004; received in revised form 14 October 2004; accepted 19 October 2004 Available online 30 November 2004 Abstract We present a new surface tension force formulation for a diffuse-interface model, which is derived for incompress- ible, immiscible Navier–Stokes equations separated by free interfaces. The classical infinitely thin boundary of separa- tion between the two immiscible fluids is replaced by a transition region of small but finite width, across which the composition of the one of two fluids changes continuously. Various versions of diffuse-interface methods have been used successfully for the numerical simulations of two phase fluid flows. These methods are robust, efficient, and capa- ble of computing interface singularities such as merging and pinching off. But prior studies used modified surface ten- sion force formulations, therefore it is not straightforward to calculate pressure field because pressure includes the gradient terms resulting from the modified surface tension term. The new formulation allows us to calculate the pressure field directly from the governing equations. Computational results showing the accuracy and effectiveness of the method are given for a drop deformation and Rayleigh capillary instability. Ó 2004 Elsevier Inc. All rights reserved. Keywords: Continuum surface tension; Diffuse-interface; Phase field 1. Introduction In this paper, we derive a new surface tension force formulation for a diffuse-interface model of incom- pressible, immiscible two-phase flow. The basic idea underlying the new formulation is to replace level set based surface tension formulation [7] by an equivalent phase field form. The diffuse-interface method (see the review paper [2] for the development and application of this model for both single-component and 0021-9991/$ - see front matter Ó 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.jcp.2004.10.032 * Tel.: +1 949 250 8993. E-mail address: jskim@math.uci.edu. URL: http://www.math.uci.edu/~jskim. Journal of Computational Physics 204 (2005) 784–804 www.elsevier.com/locate/jcp