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We study—through numerical simulations—a droplet sliding over a solid substrate as a result of a simple shear flow. We use a free-energy lattice Boltzmann (LB) scheme and compare its results with those of molecular dynamics (MD) simulations. According to the MD, at sufficiently low Reynolds and capillary numbers, the dimensionless sliding speed is a unique function of the equilibrium contact angle. Reproducing the MD results with LB simulations requires the use of a non-equilibrium boundary condition at the substrate and tuning a free parameter in the boundary condition.
Derksen, J. J., & Komrakova, A. E. (2019). Multiscale simulations of sliding droplets. Acta Mechanica, 230(2), 657–666. https://doi.org/10.1007/s00707-018-2264-6