Some exact properties of the effective slip over surfaces with hydrophobic patternings

Six, Pierre; Kamrin, Kenneth N

doi:10.1063/1.4790536

Cited by 7 publications

(1 citation statement)

References 21 publications

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“…Similarly, pressure-driven Hele-Shaw flows with varying wall slip lengths exhibit flow inhomogeneities. Walls of a microfluidic channel or Hele-Shaw cell with slip-length patterns produce specific flow patterns where the local flow direction differs from that of the globally applied pressure gradient (Hendy, Jasperse & Burnell 2005; Six & Kamrin 2013). The slip length can either originate from the molecular interactions between the liquid and the solid (Lei, Rigozzi & McKenzie 2016), or it can be an effective quantity reflecting the average effect due to a superhydrophobic or liquid-infused surface (Ybert et al.…”

Section: Introductionmentioning

confidence: 99%

Hydrodynamic dispersion in Hele-Shaw flows with inhomogeneous wall boundary conditions

2021

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Section: Introductionmentioning

confidence: 99%

Hydrodynamic dispersion in Hele-Shaw flows with inhomogeneous wall boundary conditions

2021

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Energy dissipation of the liquid in systems with a hydrophobic surface

2017

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Abstract:The work is divided into theoretical and experimental parts. In the theoretical part the viscous forces performance for both laminar as well as turbulent flow of compressible fluids are defined. It is split into the viscous forces useful power and the power corresponding to mechanical losses. This part is expressed by the dissipation function. It is shown that the dissipation function considering hydrophobic surfaces cannot be determined from the pressure difference. It is necessary to take into account the slip of the liquid over the hydrophobic surface which depends on the value of surface energy. The values of surface energy for different types of hydrophobic surfaces, obtained by experiment, are shown within this work. The new definition of the dissipation function for hydrophobic surfaces is presented depending on the adhesion coefficient, also determined by an experiment. The theoretical part of the work is complemented by experiment. The experiment is aimed at the differential pressure measurement in a circular cross section pipe. The results are processed for both laminar and turbulent stationary flow in relation to the flow. Both hydrophilic and hydrophobic surfaces and their mutual correlation are taken into consideration. On the basis of the new mathematical model for hydrophobic surfaces the value of dissipation function is determined depending on the slip velocity of the liquid along the hydrophobic surface.

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Permeability and effective slip in confined flows transverse to wall slippage patterns

2016

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The pressure-driven Stokes flow through a plane channel with arbitrary wall separation having a continuous pattern of sinusoidally varying slippage of arbitrary wavelength and amplitude on one/both walls is modelled semi-analytically. The patterning direction is transverse to the flow. In the special situations of thin and thick channels, respectively, the predictions of the model are found to be consistent with lubrication theory and results from the literature pertaining to free shear flow. For the same pattern-averaged slip length, the hydraulic permeability relative to a channel with no-slip walls increases as the pattern wave-number, amplitude, and channel size are decreased. Unlike discontinuous wall patterns of stick-slip zones studied elsewhere in the literature, the effective slip length of a sinusoidally patterned wall in a confined flow continues to scale with both channel size and the pattern-averaged slip length even in the limit of thin channel size to pattern wavelength ratio. As a consequence, for sufficiently small channel sizes, the permeability of a channel with sinusoidal wall slip patterns will always exceed that of an otherwise similar channel with discontinuous patterns on corresponding walls. For a channel with one no-slip wall and one patterned wall, the permeability relative to that of an unpatterned reference channel of same pattern-averaged slip length exhibits non-monotonic behaviour with channel size, with a minimum appearing at intermediate channel sizes. Approximate closed-form estimates for finding the location and size of this minimum are provided in the limit of large and small pattern wavelengths. For example, if the pattern wavelength is much larger than the channel thickness, exact results from lubrication theory indicate that a worst case permeability penalty relative to the reference channel of ∼23% arises when the average slip of the patterned wall is ∼2.7 times the channel size. The results from the current study should be applicable to microfluidic flows through channels with hydrophobized/super-hydrophobic surfaces.

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Some exact properties of the effective slip over surfaces with hydrophobic patternings

Cited by 7 publications

References 21 publications

Hydrodynamic dispersion in Hele-Shaw flows with inhomogeneous wall boundary conditions

Hydrodynamic dispersion in Hele-Shaw flows with inhomogeneous wall boundary conditions

Energy dissipation of the liquid in systems with a hydrophobic surface

Permeability and effective slip in confined flows transverse to wall slippage patterns

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