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Lattice Boltzmann investigation of droplet inertial spreading on various porous surfaces

Xavier Frank*

Patrick Perré

Huai-Zhi Li

  • IATE, INRA-CIRAD-UMII-SupAgro, 2 place Pierre Viala, 34060 Montpellier, France

  • École Centrale Paris, LGPM, Grande Voie des Vignes, 92290 Châtenay-Malabry, France

  • Laboratoire Réactions et Génie des Procédés, Université de Lorraine, CNRS, 1 rue Grandville, BP 20451, 54001 Nancy Cedex, France

  • *xavier.frank@supagro.inra.fr
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Phys. Rev. E 91, 052405 – Published 26 May, 2015

DOI: https://doi.org/10.1103/PhysRevE.91.052405

Abstract

The spreading of liquid drops on solid surfaces is a wide-spread phenomenon of both fundamental and industrial interest. In many applications, surfaces are porous and spreading patterns are very complex with respect to the case on smooth surfaces. Focusing on the inertial spreading just before the Tanner-like viscous regime, this work investigates the spreading of a low-viscosity droplet on a porous surface using lattice Boltzmann numerical simulations. The case of a flat surface is first considered, and it reveals a dependence on the solid equilibrium contact angle θseq, which is in good agreement with published experimental data. We conducted numerical experiments with various surfaces perforated by a regular pattern of holes of infinite length. The results show that the global spreading dynamics is independent of the porosity morphology. Through the assumption that, for wetting, the pores can be regarded as surface patches with a contact angle of θporeeq=180∘, we deduce an effective equilibrium contact angle θeffeq on the porous surface from the Cassie-Baxter law. A spreading model is then proposed to describe both a prefactor and an exponent that are similar to a flat surface whose equilibrium contact angle is θeffeq. This model compares satisfactorily with a large number of numerical experiments under varying conditions.

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Phys. Rev. E 91, 052405– Published 26 May, 2015
  • Received 12 June 2014

©2015 American Physical Society

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