INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS Int. J. Numer. Meth. Fluids (2016) Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/fld.4226 Modeling of static contact angles with curved boundaries using a multiphase lattice Boltzmann method with variable density and viscosity ratios Sébastien Leclaire 1,2 , Kamilia Abahri 1 , Rafik Belarbi 2 and Rachid Bennacer 1, * ,† 1 Ecole Normale Superieure de Cachan, LMT 61 avenue du Président Wilson, 94230 Cachan, France 2 LaSIE UMR 7356, Université de La Rochelle, Av. Michel Crépeau 17042 Cedex 1, La Rochelle, France SUMMARY Numerical modeling of multiphase flow generally requires a special procedure at the solid wall in order to be consistent with Young’s law for static contact angles. The standard approach in the lattice Boltzmann method, which consists of imposing fictive densities at the solid lattice sites, is shown to be deficient for this task. Indeed, fictive mass transfer along the boundary could happen and potentially spoil the numerical results. In particular, when the contact angle is less than 90 degrees, the deficiencies of the standard model are major. Various videos that demonstrate this behavior are provided (Supporting Information). A new approach is proposed and consists of directly imposing the contact angle at the boundaries in much the same way as Dirichlet boundary conditions are generally imposed. The proposed method is able to retrieve analytical solutions for static contact angles in the case of straight and curved boundaries even when variable density and viscosity ratios between the phases are considered. Although the proposed wetting boundary condition is shown to significantly improve the numerical results for one particular class of lattice Boltzmann model, it is believed that other lattice Boltzmann multiphase schemes could also benefit from the underlying ideas of the proposed method. The proposed algorithm is two-dimensional, and the D2Q9 lattice is used. Copyright © 2016 John Wiley & Sons, Ltd. Received 23 November 2015; Revised 26 January 2016; Accepted 5 February 2016 KEY WORDS: lattice Boltzmann method; multiphase flow; immiscible fluid; wetting boundary condition; contact angle; curved boundary 1. INTRODUCTION Recent developments on the lattice Boltzmann method show a clear potential for solving scientific problems related to numerical modeling of multiphase flow in complex geometries. In this regard, the review article by Liu et al. [1] is a good summary in which four types of lattice Boltzmann model are discussed:  RK (Rothman and Keller) [2, 3];  Shan and Chen [4];  Free-Energy from Swift et al. [5]; and  Mean-Field from He et al. [6]. For the interested reader, general reviews concerning the lattice Boltzmann method can be found in Refs. [7, 8] while a recent book on multiphase lattice Boltzmann method may be found in Ref. [9]. For simulating multiphase flows with solid boundaries, a numerical scheme for modeling the contact angle at the solid boundary must be introduced in order to capture Young’s law. Indeed, it has been shown experimentally that the contact angle at the contact line is extremely dependent on *Correspondence to: Rachid Bennacer, Ecole Normale Superieure de Cachan, LMT, 61 Avenue du Président Wilson, 94230 Cachan, France. † E-mail: rachid.bennacer@ens-cachan.fr Copyright © 2016 John Wiley & Sons, Ltd.