Flow past superhydrophobic surfaces with cosine variation in local slip length

Anisotropic superhydrophobic surfaces have the potential to greatly reduce drag and enhance mixing phenomena in microfluidic devices. Recent work has focused mostly on cases of superhydrophobic stripes. Here, we analyze a relevant situation of cosine variation of the local slip length.We derive approximate formulas for maximal (longitudinal) and minimal (transverse) directional effective slip lengths that are in good agreement with the exact numerical solution and lattice-Boltzmann simulations. Compared to the case of superhydrophobic stripes, the cosine texture can provide a very large effective slip. However, the difference between eigenvalues of the slip-length tensor is smaller, indicating that the flow is less anisotropic

Lattice-Boltzmann simulations of the drag force on a sphere approaching a superhydrophobic striped plane

By means of lattice-Boltzmann simulations the drag force on a sphere of radius R approaching a superhydrophobic striped wall has been investigated as a function of arbitrary separation h. Superhydrophobic (perfect-slip vs. no-slip) stripes are characterized by a texture period L and a fraction of the gas area ¿. For very large values of h/R, we recover the macroscopic formulae for a sphere moving towards a hydrophilic no-slip plane. For h/R = O(1), the drag force is smaller than predicted by classical theories for hydrophilic no-slip surfaces, but larger than expected for a sphere interacting with a uniform perfectly slipping wall. At a thinner gap, h « R the force reduction compared to a classical result becomes more pronounced, and is maximized by increasing ¿. In the limit of very small separations, our simulation data are in quantitative agreement with an asymptotic equation, which relates a correction to a force for superhydrophobic slip to texture parameters. In addition, we examine the flow and pressure field and observe their oscillatory character in the transverse direction in the vicinity of the wall, which reflects the influence of the heterogeneity and anisotropy of the striped texture. Finally, we investigate the lateral force on the sphere, which is detectable in case of very small separations and is maximized by stripes with ¿ = 0.5