Slip on Superhydrophobic Surfaces

Rothstein, Jonathan P.

doi:10.1146/annurev-fluid-121108-145558

Cited by 1,026 publications

(767 citation statements)

References 93 publications

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“…Macroscopically, the effect of a superhydrophobic surface is usually parametrised by a Navier slip length boundary condition (Vinogradova 1999;Lockerby et al 2004;Min & Kim 2004;Rothstein 2010;Busse & Sandham 2012):…”

Section: Apparent Slip Lengthmentioning

confidence: 99%

“…Due to the lower dynamic viscosity of air compared to water the trapped air layer on a superhydrophobic surface has a lubricating effect on the flow over it. Drag reducing properties of superhydrophobic surfaces have been observed experimentally in microfluidic devices (Choi, Westin & Breuer 2003;Ou, Perot & Rothstein 2004;Ou & Rothstein 2005;Joseph et al 2006;Daniello, Waterhouse & Rothstein 2009;Govardhan et al 2009;Tsai et al 2009;Rothstein 2010) and for coated objects, such as hydrofoils (Gotge et al 2005), settling spheres (McHale et al 2009) and cylinders (Muralidhar et al 2011), covering flow regimes from laminar to turbulent. In a stable configuration, i.e.…”

Section: Introductionmentioning

confidence: 98%

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Change in drag, apparent slip and optimum air layer thickness for laminar flow over an idealised superhydrophobic surface

et al. 2013

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Analytic results are derived for the apparent slip length, the change in drag and the optimum air layer thickness of laminar channel and pipe flow over an idealised superhydrophobic surface, i.e. a gas layer of constant thickness retained on a wall. For a simple Couette flow the gas layer always has a drag reducing effect, and the apparent slip length is positive, assuming that there is a favourable viscosity contrast between liquid and gas. In pressure-driven pipe and channel flow blockage limits the drag reduction caused by the lubricating effects of the gas layer; thus an optimum gas layer thickness can be derived. The values for the change in drag and the apparent slip length are strongly affected by the assumptions made for the flow in the gas phase. The standard assumptions of a constant shear rate in the gas layer or an equal pressure gradient in the gas layer and liquid layer give considerably higher values for the drag reduction and the apparent slip length than an alternative assumption of a vanishing mass flow rate in the gas layer. Similarly, a minimum viscosity contrast of four must be exceeded to achieve drag reduction under the zero mass flow rate assumption whereas the drag can be reduced for a viscosity contrast greater than unity under the conventional assumptions. Thus, traditional formulae from lubrication theory lead to an overestimation of the optimum slip length and drag reduction when applied to superhydrophobic surfaces, where the gas is trapped.

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Section: Apparent Slip Lengthmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Change in drag, apparent slip and optimum air layer thickness for laminar flow over an idealised superhydrophobic surface

et al. 2013

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“…Superhydrophobic surfaces are typically no-slip surfaces endowed with additional microstructural features such as grooves, posts or holes and they can significantly reduce fluid drag in microchannels (Rothstein 2010). In many cases, in the Cassie state the microstructural surface features are occupied by pockets of gas rather than being liquid-filled (as in the Wenzel state).…”

Section: Introductionmentioning

confidence: 99%

Analytical formulae for longitudinal slip lengths over unidirectional superhydrophobic surfaces with curved menisci

Crowdy

2016

J. Fluid Mech.

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This paper reports new analytical formulae for the longitudinal slip lengths for simple shear over a superhydrophobic surface, or bubble mattress, comprising a periodic array of unidirectional circular menisci, or bubbles, protruding into, or out of, the fluid. The accuracy of the formulae is tested against results from full numerical simulations; they are found to give small relative errors even at large no-shear fractions. In the dilute limit the formulae reduce to an earlier result by Crowdy (Phys. Fluids, vol. 22, 2010, 121703). They also extend analytical results of Sbragaglia & Prosperetti (Phys. Fluids, vol. 19, 2007, 043603) beyond the limit of a small protrusion angle.

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“…Superhydrophobic surfaces are a special class of patterned surfaces on which the presence of free surface menisci spanning surface protrusions in the microstructure of the surface is presumed to supply close to no-shear regions that can enhance slip (Rothstein 2010). Over the last decade, there has been huge research effort in trying to understand the slip properties of such surfaces.…”

Section: Introductionmentioning

confidence: 99%

Effective slip lengths for immobilized superhydrophobic surfaces

Crowdy

2017

J. Fluid Mech.

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Analytical solutions are found for both longitudinal and transverse shear flow, at zero Reynolds number, over immobilized superhydrophobic surfaces comprising a periodic array of near-circular menisci penetrating into a no-slip surface and where the menisci are no longer shear-free but are taken to be no-slip zones. Explicit formulae for the associated longitudinal and transverse effective slip lengths are derived; these are then compared with analogous results for superhydrophobic surfaces of the same characteristic geometry but where the menisci are shear-free. The new formulae give results that are consistent with recent experimental observations that have prompted suggestions that menisci that are assumed to be free of shear have in fact been immobilized. Significantly, for transverse shear flow, it is found that at critical downward meniscus protrusion angles of around 47 • , for many surface geometries, it is impossible to distinguish, purely from the effective slip length, between a no-shear and a no-slip boundary condition. We also find that immobilized menisci bowing into the grooves at supercritical angles just below 90 • can be almost twice as slippery to transverse shear as no-shear menisci. The results are relevant to recent discussion as to whether surface immobilization, due to contamination by surfactants or other physical mechanisms, is compromising drag reduction properties expected from an assumed no-shear condition.

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Slip on Superhydrophobic Surfaces

Cited by 1,026 publications

References 93 publications

Change in drag, apparent slip and optimum air layer thickness for laminar flow over an idealised superhydrophobic surface

Change in drag, apparent slip and optimum air layer thickness for laminar flow over an idealised superhydrophobic surface

Analytical formulae for longitudinal slip lengths over unidirectional superhydrophobic surfaces with curved menisci

Effective slip lengths for immobilized superhydrophobic surfaces

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