Effective hydrodynamic boundary conditions for microtextured surfaces

Abstract

We report measurements of the hydrodynamic drag force acting on a smooth sphere falling down under gravity to a plane decorated with microscopic periodic grooves. Both surfaces are lyophilic, so that a liquid (silicone oil) invades the surface texture being in the Wenzel state. A significant decrease in the hydrodynamic resistance force as compared with that predicted for two smooth surfaces is observed. To quantify the effect of roughness we use the effective no-slip boundary condition, which is applied at the imaginary smooth homogeneous isotropic surface located at an intermediate position between top and bottom of grooves. Such an effective condition fully characterizes the force reduction measured with the real surface, and the location of this effective plane is related to geometric parameters of the texture by a simple analytical formula.

4 pages, submitted to Phys. Rev. E

References in corpus (6)

• Effective slip in pressure-driven flow past super-hydrophobic stripes
• Wetting, roughness and flow boundary conditions
• Direct measurements of hydrophobic slippage using double-focus fluorescence cross-correlation
• Effective slip boundary conditions for arbitrary periodic surfaces: The surface mobility tensor
• Transverse flow in thin superhydrophobic channels
• Drag force on a sphere moving towards an anisotropic super-hydrophobic plane

Cited by in corpus (4)

• Influence of the enclosed fluid on the flow over a microstructured surface in the Cassie state
• Effective slip-length tensor for a flow over weakly slipping stripes
• Morphology of soft and slippery contact via fluid drainage
• Hydrodynamic radius approximation for spherical particles suspended in a viscous fluid: influence of particle internal structure and boundary