Flow past superhydrophobic surfaces with cosine variation in local slip length

Inelastic non-Newtonian flow over heterogeneously slippery surfaces

In this study, we investigated inelastic non-Newtonian fluid flow over heterogeneously slippery surfaces. First, we simulated the flow of aqueous xanthan gum solutions over a bubble mattress, which is a superhydrophobic surface consisting of transversely positioned no-slip walls and no-shear gas bubbles. The results reveal that for shear-thinning fluids wall slip can be increased significantly, provided that the system is operated in the shear-thinning regime. For a 0.2 wt% xanthan gum solution with a power-law index of n=0.4, the numerical results indicate that wall slip can be enhanced 3.2 times when compared to a Newtonian liquid. This enhancement factor was also predicted from a theoretical analysis, which gave an expression for the maximum slip length that can be attained over flat, heterogeneously slippery surfaces. Although this equation was derived for a no-slip/no-shear unit length that is much larger than the typical size of the system, we found that it can also be used to predict the enhancement in the regime where the slip length is proportional to the size of the no-shear region or the bubble width. The results could be coupled to the hydrodynamic development or entrance length of the system, as maximum wall slip is only reached when the fluid flow can fully adapt to the no-slip and no-shear conditions at the wall.

Local Flow Field and Slip Length of Superhydrophobic Surfaces

While the global slippage of water past superhydrophobic surfaces has attracted wide interest, the local distribution of slip still remains unclear. Using fluorescence correlation spectroscopy, we performed detailed measurements of the local flow field and slip length for water in the Cassie state on a microstructured superhydrophobic surface. We revealed that the local slip length is finite, nonconstant, anisotropic, and sensitive to the presence of surfactants. In combination with numerical calculations of the flow, we can explain all these properties by the local hydrodynamics.

Interfacial slip on rough, patterned and soft surfaces: a review of experiments and simulations

Advancements in the fabrication of microfluidic and nanofluidic devices and the study of liquids in confined geometries rely on understanding the boundary conditions for the flow of liquids at solid surfaces. Over the past ten years, a large number of research groups have turned to investigating flow boundary conditions, and the occurrence of interfacial slip has become increasingly well-accepted and understood. While the dependence of slip on surface wettability is fairly well understood, the effect of other surface modifications that affect surface roughness, structure and compliance, on interfacial slip is still under intense investigation. In this paper we review investigations published in the past ten years on boundary conditions for flow on complex surfaces, by which we mean rough and structured surfaces, surfaces decorated with chemical patterns, grafted with polymer layers, with adsorbed nanobubbles, and superhydrophobic surfaces. The review is divided in two interconnected parts, the first dedicated to physical experiments and the second to computational experiments on interfacial slip of simple (Newtonian) liquids on these complex surfaces. Our work is intended as an entry-level review for researchers moving into the field of interfacial slip, and as an indication of outstanding problems that need to be addressed for the field to reach full maturity.

Electrokinetics over charge-modulated surfaces in the presence of patterned wettability: role of the anisotropic streaming potential

In the present study, we focus on evaluating the induced streaming electric field along the orthogonal directions in a narrow fluidic confinement in the presence of patterned surface wettability and modulated surface charges. We attempt to assess the implications of such modulations on the related important quantities and pinpoint the regimes of improved induced streaming potential field and the resulting anisotropy in the induced potential. Our results reveal that for certain combinations of the parameters characterizing the modulated slip, a significant amount of augmentation in the streaming electric field might be obtained, whereas in other cases the effects may lead to adverse consequences. We further demonstrate that the presence of anisotropic modulations on the channel walls give rise to considerable off-diagonal effects, which makes the streaming potential "disoriented" with the applied pressure gradient, when the same is not applied along one of the orthogonal directions. Our analysis also shows that one can remove such "mis-orientations" by finely tuning several relevant flow and geometric parameters, which may bear immense scientific and technological consequences towards an improved design of miniaturized energy conversion devices.

Effective slip-length tensor for a flow over weakly slipping stripes

We discuss the flow past a flat heterogeneous solid surface decorated by slipping stripes. The spatially varying slip length, b(y), is assumed to be small compared to the scale of the heterogeneities, L, but finite. For such weakly slipping surfaces, earlier analyses have predicted that the effective slip length is simply given by the surface-averaged slip length, which implies that the effective slip-length tensor becomes isotropic. Here we show that a different scenario is expected if the local slip length has steplike jumps at the edges of slipping heterogeneities. In this case, the next-to-leading term in an expansion of the effective slip-length tensor in powers of max[b(y)/L] becomes comparable to the leading-order term, but anisotropic, even at very small b(y)/L. This leads to an anisotropy of the effective slip and to its significant reduction compared to the surface-averaged value. The asymptotic formulas are tested by numerical solutions and are in agreement with results of dissipative particle dynamics simulations.