Tensorial slip of superhydrophobic channels

Schmieschek, Sebastian; Belyaev, Aleksey V.; Harting, Jens; Vinogradova, Olga I.

doi:10.1103/physreve.85.016324

Cited by 58 publications

(84 citation statements)

References 53 publications

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“…Hydrophobic microstructures containing trapped gas bubbles have been shown to be advantageous for drag reduction (5)(6)(7)(8)(9)(10)(11). Their orientation with respect to the flow direction (12)(13)(14)(15)(16) and the geometry of gas-liquid menisci (11)(12)(13)(14)17) has been demonstrated to affect the slippage. In particular, microscale bubbles transverse to the flow direction can alter the flow resistance, depending on the protrusion of the bubbles into the flow.…”

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confidence: 99%

Control of slippage with tunable bubble mattresses

Karatay

Haase

Visser

et al. 2013

Proc. Natl. Acad. Sci. U.S.A.

163

139

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Tailoring the hydrodynamic boundary condition is essential for both applied and fundamental aspects of drag reduction. Hydrodynamic friction on superhydrophobic substrates providing gasliquid interfaces can potentially be optimized by controlling the interface geometry. Therefore, establishing stable and optimal interfaces is crucial but rather challenging. Here we present unique superhydrophobic microfluidic devices that allow the presence of stable and controllable microbubbles at the boundary of microchannels. We experimentally and numerically examine the effect of microbubble geometry on the slippage at high resolution. The effective slip length is obtained for a wide range of protrusion angles, θ, of the microbubbles into the flow, using a microparticle image velocimetry technique. Our numerical results reveal a maximum effective slip length, corresponding to a 23% drag reduction at an optimal θ ≈ 10°. In agreement with the simulation results, our measurements correspond to up to 21% drag reduction when θ is in the range of −2°to 12°. The experimental and numerical results reveal a decrease in slip length with increasing protrusion angles when θ ≳ 10°. Such microfluidic devices with tunable slippage are essential for the amplified interfacial transport of fluids and particles. D espite more than two decades of intense research on hydrodynamic slippage on substrates with various physicochemical properties (1-4), tuning the hydrodynamic slippage remains a challenge, especially for microfluidic laminar flow. The slip length-quantifying the slippage-ranges from a few nanometers for flat hydrophobic substrates to several micrometers for superhydrophobic substrates with hybrid (liquid-gas and liquidsolid) interfaces (4). Hydrophobic microstructures containing trapped gas bubbles have been shown to be advantageous for drag reduction (5-11). Their orientation with respect to the flow direction (12-16) and the geometry of gas-liquid menisci (11)(12)(13)(14)17) has been demonstrated to affect the slippage. In particular, microscale bubbles transverse to the flow direction can alter the flow resistance, depending on the protrusion of the bubbles into the flow. Moreover, transition from slippage to friction has been predicted for trapped bubbles perpendicular to the flow in theoretical (14, 18) and numerical studies (12,13,19,20). The presence of such a critical protrusion angle highlights the feasibility of manipulating the flow resistance via bubble geometry. One recent experimental study suggests that for flow over a hydrophobic surface with trapped passive microbubbles, there is a transition from an enhanced slippage state to the frictional state at a large protrusion angle, in an estimated range of 30°-60°(20). However, there has been no experimental investigation of flow past a hydrophobic surface with transversely embedded microbubbles for a wide range of protrusion angles at high resolution. In this paper, we report on integrated microfluidic devices that permit the presence of stable and controllable microbubb...

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mentioning

confidence: 99%

Control of slippage with tunable bubble mattresses

Karatay

Haase

Visser

et al. 2013

Proc. Natl. Acad. Sci. U.S.A.

163

139

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“…Moreover, the code has been used to study for example the self-assembly of cubic mesophases [33], micromixing [34], flow through porous media [10] and fluid surface interactions [35,36]. A refactored version of the code with limited functionality that focuses mainly on multiphase fluid simulation functionalities, has recently been released under the LGPL [37].…”

Section: Methodsmentioning

confidence: 99%

Multi Relaxation Time Lattice Boltzmann Simulations of Multiple Component Fluid Flows in Porous Media

Schmieschek

Narváez

Harting

2012

High Performance Computing in Science and Engineering ‘12

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The flow of fluid mixtures in complex geometries is of practical interest in many fields, ranging from oil recovery to freeze-dried food products. Due to its inherent locality the lattice Boltzmann method allows for straightforward implementation of complex boundaries and excellently scaling parallel computations. The widely applied Bhatnagar Gross Krook (BGK) scheme, used to model the contribution of particle collisions to the velocity field, does however suffer from limitiations in precision that become more prominent with increasing surface to volume ratio. To increase the accuracy of simulations of mixtures in porous media, we integrated a so-called multi relaxation time (MRT) collision scheme with a pseudo-potential method for fluids with multiple components. We describe some optimisation details of the implementation and present test results verifying the physical accuracy as well as benchmarks obtained on the XC2 Opteron cluster at the Scientific Supercomputing Centre Karlsruhe (SSCK).

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“…1). As in most previous publications [7,12,15,20,29,[35][36][37], we model the superhydrophobic plate as a flat heterogeneous interface. In such a description, we neglect an additional mechanism for a dissipation connected with the meniscus curvature [15,38,39].…”

Section: Model and Governing Equationsmentioning

confidence: 99%

“…The concept of an effective slip length tensor is general and can be applied for arbitrary channel thickness [12]. It is a global characteristic of a channel [9], and the eigenvalues usually depend not only on the parameters of the heterogeneous surfaces, but also on the channel thickness.…”

Section: Introductionmentioning

confidence: 99%

“…The main task is to find the connection between the eigenvalues of the slip-length tensor and the parameters of such one-dimensional surface textures. Up to now analytical results for the effective slip length have only been obtained for the simplest geometry of rectangular grooves [12,[20][21][22][23][24]. We are unaware of any prior work that has obtained analytical results for other types of one-dimensional textures.…”

Section: Introductionmentioning

confidence: 99%

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Effective slippage on superhydrophobic trapezoidal grooves

Zhou

Asmolov

Schmid

et al. 2013

The Journal of Chemical Physics

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We study the effective slippage on superhydrophobic grooves with trapezoidal cross-sections of various geometries (including the limiting cases of triangles and rectangular stripes), by using two complementary approaches. First, dissipative particle dynamics (DPD) simulations of a flow past such surfaces have been performed to validate an expression [E. S. Asmolov and O. I. Vinogradova, J. Fluid Mech. 706, 108 (2012)] that relates the eigenvalues of the effective slip-length tensor for one-dimensional textures. Second, we propose theoretical estimates for the effective slip length and calculate it numerically by solving the Stokes equation based on a collocation method. The comparison between the two approaches shows that they are in excellent agreement. Our results demonstrate that the effective slippage depends strongly on the area-averaged slip, the amplitude of the roughness, and on the fraction of solid in contact with the liquid. To interpret these results, we analyze flow singularities near slipping heterogeneities, and demonstrate that they inhibit the effective slip and enhance the anisotropy of the flow. Finally, we propose some guidelines to design optimal one-dimensional superhydrophobic surfaces, motivated by potential applications in microfluidics.

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Tensorial slip of superhydrophobic channels

Cited by 58 publications

References 53 publications

Control of slippage with tunable bubble mattresses

Control of slippage with tunable bubble mattresses

Multi Relaxation Time Lattice Boltzmann Simulations of Multiple Component Fluid Flows in Porous Media

Effective slippage on superhydrophobic trapezoidal grooves

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