Tensorial hydrodynamic slip
TL;DR: In this article, a tensor generalization of the Navier slip boundary condition is proposed to capture complicated effects of surface anisotropy, while preserving a simple fluid domain, and exact solutions for laminar shear flow and pressure-driven flow between parallel plates of arbitrary and different textures are provided.
Abstract: We describe a tensorial generalization of the Navier slip boundary condition and illustrate its use in solving for flows around anisotropic textured surfaces. Tensorial slip can be derived from molecular or microstructural theories or simply postulated as a constitutive relation, subject to certain general constraints on the interfacial mobility. The power of the tensor formalism is to capture complicated effects of surface anisotropy, while preserving a simple fluid domain. This is demonstrated by exact solutions for laminar shear flow and pressure-driven flow between parallel plates of arbitrary and different textures. From such solutions, the effects of rotating a texture follow from simple matrix algebra. Our results may be useful for extracting local slip tensors from global measurements, such as the permeability of a textured channel or the force required to move a patterned surface, in experiments or simulations.
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TL;DR: In this paper, it was shown that the "compact layer" and "shear plane" effectively advance into the liquid, due to the crowding of counterions, and that ionic crowding against a blocking surface expands the diffuse double layer and thus decreases its differential capacitance; each trend is enhanced by dielectric saturation.
800 citations
TL;DR: It is shown that the intensive current modes in electrodialysis are compatible with new trends in water treatment oriented towards Zero Liquid Discharge (ZLD) technologies.
324 citations
TL;DR: In this article, a review of the literature on overlimiting current density in electrodialysis (ED) is presented, where the authors focus on the specific knowledge and practice acquired in nano-and microfluidics into desalination.
315 citations
TL;DR: It is seen that hydrophobic slippage can be dramatically affected by the presence of roughness, and refined methods for setting very well controlled micro- or nanotextures on a solid are being exploited to induce novel hydrodynamic properties, such as giant interfacial slip, superfluidity, mixing and low hydrod dynamic drag.
Abstract: We discuss how the wettability and roughness of a solid impacts its hydrodynamic properties. We see in particular that hydrophobic slippage can be dramatically affected by the presence of roughness. Owing to the development of refined methods for setting very well controlled micro- or nanotextures on a solid, these effects are being exploited to induce novel hydrodynamic properties, such as giant interfacial slip, superfluidity, mixing and low hydrodynamic drag, that could not be achieved without roughness.
171 citations
TL;DR: This work considers the experimentally relevant limit of thin channels and obtains rigorous bounds on the effective slip length for any two-component texture with given area fractions, providing a framework for the rational design of superhydrophobic surfaces.
Abstract: Superhydrophobic surfaces reduce drag by combining hydrophobicity and roughness to trap gas bubbles in a microscopic texture. Recent work has focused on specific cases, such as arrays of pillars or grooves, with limited theoretical guidance. Here, we consider the experimentally relevant limit of thin channels and obtain rigorous bounds on the effective slip length for any two-component (e.g., low-slip and high-slip) texture with given area fractions. Among all anisotropic textures, parallel stripes attain the largest (or smallest) possible slip in a straight, thin channel for parallel (or perpendicular) orientation with respect to the mean flow. Tighter bounds for isotropic textures further constrain the effective slip. These results provide a framework for the rational design of superhydrophobic surfaces.
141 citations
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TL;DR: A review of the physics of small volumes (nanoliters) of fluids is presented, as parametrized by a series of dimensionless numbers expressing the relative importance of various physical phenomena as mentioned in this paper.
Abstract: Microfabricated integrated circuits revolutionized computation by vastly reducing the space, labor, and time required for calculations. Microfluidic systems hold similar promise for the large-scale automation of chemistry and biology, suggesting the possibility of numerous experiments performed rapidly and in parallel, while consuming little reagent. While it is too early to tell whether such a vision will be realized, significant progress has been achieved, and various applications of significant scientific and practical interest have been developed. Here a review of the physics of small volumes (nanoliters) of fluids is presented, as parametrized by a series of dimensionless numbers expressing the relative importance of various physical phenomena. Specifically, this review explores the Reynolds number Re, addressing inertial effects; the Peclet number Pe, which concerns convective and diffusive transport; the capillary number Ca expressing the importance of interfacial tension; the Deborah, Weissenberg, and elasticity numbers De, Wi, and El, describing elastic effects due to deformable microstructural elements like polymers; the Grashof and Rayleigh numbers Gr and Ra, describing density-driven flows; and the Knudsen number, describing the importance of noncontinuum molecular effects. Furthermore, the long-range nature of viscous flows and the small device dimensions inherent in microfluidics mean that the influence of boundaries is typically significant. A variety of strategies have been developed to manipulate fluids by exploiting boundary effects; among these are electrokinetic effects, acoustic streaming, and fluid-structure interactions. The goal is to describe the physics behind the rich variety of fluid phenomena occurring on the nanoliter scale using simple scaling arguments, with the hopes of developing an intuitive sense for this occasionally counterintuitive world.
4,044 citations
TL;DR: An overview of flows in microdevices with focus on electrokinetics, mixing and dispersion, and multiphase flows is provided, highlighting topics important for the description of the fluid dynamics: driving forces, geometry, and the chemical characteristics of surfaces.
Abstract: Microfluidic devices for manipulating fluids are widespread and finding uses in many scientific and industrial contexts. Their design often requires unusual geometries and the interplay of multiple physical effects such as pressure gradients, electrokinetics, and capillarity. These circumstances lead to interesting variants of well-studied fluid dynamical problems and some new fluid responses. We provide an overview of flows in microdevices with focus on electrokinetics, mixing and dispersion, and multiphase flows. We highlight topics important for the description of the fluid dynamics: driving forces, geometry, and the chemical characteristics of surfaces.
3,307 citations
TL;DR: This work presents a passive method for mixing streams of steady pressure-driven flows in microchannels at low Reynolds number, and uses bas-relief structures on the floor of the channel that are easily fabricated with commonly used methods of planar lithography.
Abstract: It is difficult to mix solutions in microchannels. Under typical operating conditions, flows in these channels are laminar—the spontaneous fluctuations of velocity that tend to homogenize fluids in turbulent flows are absent, and molecular diffusion across the channels is slow. We present a passive method for mixing streams of steady pressure-driven flows in microchannels at low Reynolds number. Using this method, the length of the channel required for mixing grows only logarithmically with the Pe «clet number, and hydrodynamic dispersion along the channel is reduced relative to that in a simple, smooth channel. This method uses bas-relief structures on the floor of the channel that are easily fabricated with commonly used methods of planar lithography.
3,269 citations
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TL;DR: In this paper, the authors describe how to make droplets stick to their substrates (even if they are inclined), which is a practical issue in many cases (windshields, window panes, greenhouses, or microfluidic devices).
Abstract: While the behaviour of large amounts of liquid is dictated by gravity, surface forces become dominant at small scales. They have for example the remarkable ability to make droplets stick to their substrates (even if they are inclined), which is a practical issue in many cases (windshields, window panes, greenhouses, or microfluidic devices). Here we describe how this problem can be overcome with super-hydrophobic materials. These materials are often developed thanks to micro-textures, which decorate a solid surface, and we describe the way such textures modify the wettability of that solid. We conclude by showing the unusual dynamics of drops in a super-hydrophobic situation.
1,176 citations
TL;DR: Results show for the first time that, in contrast to common belief, surface friction may be reduced by surface roughness, and open the possibility of a controlled realization of the 'nanobubbles' that have long been suspected to play a role in interfacial slippage.
Abstract: With the important development of microfluidic systems, miniaturization of flow devices has become a real challenge. Microchannels, however, are characterized by a large surface-to-volume ratio, so that surface properties strongly affect flow resistance in submicrometre devices. We present here results showing that the concerted effect of wetting properties and surface roughness may considerably reduce friction of the fluid past the boundaries. The slippage of the fluid at the channel boundaries is shown to be greatly increased by using surfaces that are patterned on the nanometre scale. This effect occurs in the regime where the surface pattern is partially dewetted, in the spirit of the 'superhydrophobic' effects that have been discovered at macroscopic scales1. Our results show for the first time that, in contrast to common belief, surface friction may be reduced by surface roughness. They also open the possibility of a controlled realization of the 'nanobubbles'2 that have long been suspected to play a role in interfacial slippage3,4.
554 citations