Tensorial slip of super-hydrophobic channels

S.M.P. Schmieschek, A.V. Belyaev, J.D.R. Harting, O.I. Vinogradova

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    Abstract

    We describe a generalization of the tensorial slip boundary condition, originally justified for a thick (compared to texture period) channel, to any channel thickness. The eigenvalues of the effective slip-length tensor, however, in general case become dependent on the gap and cannot be viewed as a local property of the surface, being a global characteristic of the channel. To illustrate the use of the tensor formalism we develop a semianalytical theory of an effective slip in a parallel-plate channel with one superhydrophobic striped and one hydrophilic surface. Our approach is valid for any local slip at the gas sectors and an arbitrary distance between the plates, ranging from a thick to a thin channel. We then present results of lattice Boltzmann simulations to validate the analysis. Our results may be useful for extracting effective slip tensors from global measurements, such as the permeability of a channel, in experiments or simulations.
    Original languageEnglish
    Article number016324
    Number of pages11
    JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
    Volume85
    Issue number1
    DOIs
    Publication statusPublished - 2012

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