We present an experimental study of a low-Reynolds number shear flow between two surfaces, one of which has a regular grooved texture augmented with a superhydrophobic coating. The combination reduces the effective fluid-surface contact area, thereby appreciably decreasing the drag on the surface and effectively changing the macroscopic boundary condition on the surface from no slip to limited slip. We measure the force on the surface and the velocity field in the immediate vicinity on the surface (and thus the wall shear) simultaneously. The latter facilitates a direct assessment of the effective slip length associated with the drag reduction.

This study focuses on the demixing of neutrally buoyant suspensions of spheres during slow, pressure driven flows in circular conduits. Distributions of the solid fraction of particles, φ, and the suspension velocity, ν, are measured at different lengths from a static in-line mixer. Experiments were conducted over a range of volume average solids fractions, φbulk (0.10⩽φ⩽0.50), and at two different ratios of the particle radius, a, to the radius of the circular conduit, R (a/R=0.0256 and a/R=0.0625). At φbulk⩾0.20, the particles rapidly migrate to the low-shear-rate region in the center of the conduit. This migration results in a blunting of the ν profile, relative to the parabolic profile observed in homogeneous Newtonian fluids. For the flow geometry with the smaller ratio of a/R, the φ profile builds to a sharp maximum or cusp in the center. Particle structures are observed in the experiments with the higher a/R. The entrance lengths for the development of the φ and ν fields, Lφ and Lν, respectively, are strong functions of a/R and φbulk. Lφ and Lν rapidly decrease as φ and a/R increase. Over the range of our data, the ν profiles are observed to develop more rapidly than the φ profiles. The experimental results are compared with fully developed flow predictions from the shear-induced migration (SIM) model and the suspension balance (SB) model. At the smaller a/R, the SIM model more accurately predicts the experimental results. At larger a/R, some qualitative features of the experimental results are better predicted by the SB model, however, neither model provides good quantitative predictions, especially at low φbulk.

This report presents a study of electrokinetic transport in a series of integrated macro- to nano-fluidic chips that allow for controlled injection of molecular mixtures into high-density arrays of nanochannels. The high-aspect-ratio nanochannels were fabricated on a Si wafer using interferometric lithography and standard semiconductor industry processes, and are capped with a transparent Pyrex cover slip to allow for experimental observations. Confocal laser scanning microscopy was used to examine the electrokinetic transport of a negatively charged dye (Alexa 488) and a neutral dye (rhodamine B) within nanochannels that varied in width from 35 to 200 nm with electric field strengths equal to or below 2000 V m-1. In the negatively charged channels, nanoconfinement and interactions between the respective solutes and channel walls give rise to higher electroosmotic velocities for the negatively charged dye than for the neutral dye, towards the negative electrode, resulting in an anomalous separation that occurs over a relatively short distance (<1 mm). Increasing the channel widths leads to a switch in the electroosmotic transport behavior observed in microscale channels, where neutral molecules move faster because the negatively charged molecules are slowed by the electrophoretic drag. Thus a clear distinction between "nano-" and "microfluidic" regimes is established. We present an analytical model that accounts for the electrokinetic transport and adsorption (of the neutral dye) at the channel walls, and is in good agreement with the experimental data. The observed effects have potential for use in new nano-separation technologies.

We study fluid flow in the vicinity of textured and superhydrophobically coated surfaces with characteristic texture sizes on the order of 10μm. Both for droplets moving down an inclined surface and for an external flow near the surface (hydrofoil), there is evidence of appreciable drag reduction in the presence of surface texture combined with superhydrophobic coating. On textured inclined surfaces, the drops roll faster than on a coated untextured surface at the same angle. The highest drop velocities are achieved on surfaces with irregular textures with characteristic feature size ∼8μm. Application of the same texture and coating to the surface of a hydrofoil in a water tunnel results in drag reduction on the order of 10% or higher. This behavior is explained by the reduction of the contact area between the surface and the fluid, which can be interpreted in terms of changing the macroscopic boundary condition to allow nonzero slip velocity.

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This paper is NOT THE PUBLISHED VERSION; but the author's final, peer-reviewed manuscript. The published version may be accessed by following the link in th citation below.

SUMMARYIn many cases, boundary integral equations contain a domain integral. This can be evaluated by discretization of the domain into domain elements. Historically, this was seen as going against the spirit of boundary element methods, and several methods were developed to avoid this discretization, notably dual and multiple reciprocity methods and particular solution methods. These involved the representation of the interior function with a set of basis functions, generally of the radial type. In this study, meshless methods (dual reciprocity and particular solution) are compared to the direct domain integration methods. The domain integrals are evaluated using traditional methods and also with multipole acceleration. It is found that the direct integration always results in better accuracy, as well as smaller computation times. In addition, the multipole method further improves on the computation times, in particular where multiple evaluations of the integral are required, as when iterative solvers are used. The additional error produced by the multipole acceleration is negligible.

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