J. Non-Newtonian Fluid Mech. 154 (2008) 13–21 Modelling capillary phenomena at a mesoscale: From simple to complex fluids  S. Merabia a,b,∗ , J. Bonet-Avalos a , I. Pagonabarraga b a Departament d’Enginyeria Quimica, Escola Tecnica Superior d’Enginyeria Quimica (ETSEQ), Universitat Rovira i Virgili, Avda. dels Paisos Catalans 26, 43007 Tarragona, Spain b Departament de Fisica Fonamental, Universitat de Barcelona, Marti i Franques 1, 08028 Barcelona, Spain Received 29 October 2006; received in revised form 2 July 2007; accepted 21 January 2008 Abstract A mesoscopic model for studying capillary phenomena is introduced. The fluid is represented by particles interacting through soft forces that allow condensation. A model for a solid wall is also presented whose affinity for the liquid can be tuned from hydrophilic to superhydrophobic. Regarding the dynamics, the validity of the model was assessed studying the classical drop spreading on a wetting substrate where good agreement was found with the scaling predicted theoretically. We show also how to extend the proposed model to deal with symmetrical binary mixtures. This model opens the way to model capillary phenomena involving complex fluids. © 2008 Elsevier B.V. All rights reserved. Keywords: Capillary phenomena; Mesoscopic drop model; Thin films; Binary mixtures 1. Introduction Capillary phenomena are ubiquitous in nature and in industry as well [1]. Numerical simulations may help in characterising and understanding such flows of fluid involving free boundaries. To this end, different strategies have been pursued: the most natural way seems to discretise Navier–Stokes equations treating interfaces as structureless. This route fails to describe situations where singularities occur such as drop break up [2] or the more common problem of the three phases contact line dynamics [3]. To remove such singularities, a more microscopic approach, e.g. molecular dynamics MD can be considered [4–7]. However, MD is limited to small time (10 ns) and length scales (10 nm), thus making the hydrodynamic regime hard to reach. Between molecular dynamics and continuum mechanics, an increasing effort has been devoted recently to the development of mesoscopic models. Examples of such models include Lat-  This paper was originally submitted at the PRATO conference. ∗ Corresponding author at: Laboratoire de Physique de la Mati` ere Condens´ ee et Nanostructures, Bˆ atiment L´ eon Brillouin, Universit´ e Lyon I, 43 Boulevard du 11 Novembre 1918, 69622 Villeurbanne, France. Tel.: +33 472431017; fax: +33 472432648. E-mail address: smerabia@gmail.com (S. Merabia). tice Boltzmann [8], dissipative particle dynamics DPD [9], Lowe Andersen thermostat [10] and smooth particle dynamics [11,12]. While in lattice Boltzmann the fluid is discretised on a lattice where a Boltzmann equation for the density is solved, the other quoted methods consider effective particles representing fluid elements and interacting through effective forces. In this respect, they are often called “particle-based methods” and can be con- sidered an extension of molecular dynamics. These methods have in common the use of a momentum conserving thermo- stat, allowing to recover Navier–Stokes equation in the large wavelength limit, contrary to Brownian dynamics simulations. Besides, the effective forces are taken to be soft, i.e. bounded potentials as opposed to interatomic potentials. Of course, there is the underlying idea that at a mesoscopic level interactions are softer than intermolecular interactions, but especially the soft- ness of the force is dictated by practical purposes as it allows the use of larger time steps than MD. As a consequence, the hydrodynamic regime is entered relatively fast. Although a body of work has been devoted to model complex fluids, e.g. colloidal suspensions [13], polymer solutions [14], copolymers [9] or surfactants [15] in the bulk, relatively few attention has been paid to capillary phenomena. It is nevertheless highly desirable to develop particle based models for interfaces that could in a later stage benefit from the simplicity and ver- 0377-0257/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jnnfm.2008.01.009