scholarly journals Effective slip in pressure-driven flow past super-hydrophobic stripes

2010 ◽  
Vol 652 ◽  
pp. 489-499 ◽  
Author(s):  
A. V. BELYAEV ◽  
O. I. VINOGRADOVA
Keyword(s):  
Slip Length ◽  
Mean Flow ◽  
Flow Past ◽  
Relevant Situation ◽  
Effective Slip ◽  
Trapped Gas ◽  
Local Slip ◽  
Texture Size ◽  
Pressure Driven Flow ◽  
Pressure Driven

A super-hydrophobic array of grooves containing trapped gas (stripes) has the potential to greatly reduce drag and enhance mixing phenomena in microfluidic devices. Recent work has focused on idealized cases of stick-perfect slip stripes. Here, we analyse the experimentally more relevant situation of a pressure-driven flow past striped slip-stick surfaces with arbitrary local slip at the gas sectors. We derive approximate formulas for maximal (longitudinal) and minimal (transverse) directional effective slip lengths that are in a good agreement with the exact numerical solution for any surface slip fraction. By representing eigenvalues of the slip length tensor, we obtain the effective slip for any orientation of stripes with respect to the mean flow. Our results imply that flow past stripes is controlled by the ratio of the local slip length to texture size. In the case of a large (compared to the texture period) slip at the gas areas, surface anisotropy leads to a tensorial effective slip, by attaining the values predicted earlier for a perfect local slip. Both effective slip lengths and anisotropy of the flow decrease when local slip becomes of the order of texture period. In the case of a small slip, we predict simple surface-averaged isotropic flows (independent of orientation).

scholarly journals Influence of the enclosed fluid on the flow over a microstructured surface in the Cassie state

2014 ◽  
Vol 740 ◽  
pp. 168-195 ◽  
Author(s):  
Clarissa Schönecker ◽  
Tobias Baier ◽  
Steffen Hardt
Keyword(s):  
Flow Field ◽  
Slip Length ◽  
Two Fluids ◽  
Cassie State ◽  
Effective Slip Length ◽  
Primary Fluid ◽  
Effective Slip ◽  
Local Slip ◽  
Analytical Expressions ◽  
Secondary Fluid

AbstractAnalytical expressions for the flow field as well as for the effective slip length of a shear flow over a surface with periodic rectangular grooves are derived. The primary fluid is in the Cassie state with the grooves being filled with a secondary immiscible fluid. The coupling of the two fluids is reflected in a locally varying slip distribution along the fluid–fluid interface, which models the effect of the secondary fluid on the outer flow. The obtained closed-form analytical expressions for the flow field and effective slip length of the primary fluid explicitly contain the influence of the viscosities of the two fluids as well as the magnitude of the local slip, which is a function of the surface geometry. They agree well with results from numerical computations of the full geometry. The analytical expressions allow an investigation of the influence of the viscous stresses inside the secondary fluid for arbitrary geometries of the rectangular grooves. For classic superhydrophobic surfaces, the deviations in the effective slip length compared to the case of inviscid gas flow are pointed out. Another important finding with respect to an accurate modelling of flow over microstructured surfaces is that not only the effective slip length, but also the local slip length of a grooved surface, is anisotropic.

scholarly journals Flow past superhydrophobic surfaces with cosine variation in local slip length

2013 ◽  
Vol 87 (2) ◽  
Author(s):  
Evgeny S. Asmolov ◽  
Sebastian Schmieschek ◽  
Jens Harting ◽  
Olga I. Vinogradova
Keyword(s):  
Slip Length ◽  
Superhydrophobic Surfaces ◽  
Flow Past ◽  
Local Slip

scholarly journals Effective Slip Lengths for Stokes Flow over Rough, Mixed-Slip Surfaces

2021 ◽  
Author(s):  
◽  
Nathaniel Joseph Lund
Keyword(s):  
Shear Rate ◽  
Stokes Flow ◽  
Slip Velocity ◽  
Flat Surface ◽  
Slip Length ◽  
Simple Shear Flow ◽  
Slip Surfaces ◽  
Effective Slip Length ◽  
Effective Slip ◽  
Local Slip

<p>In this thesis, homogenization and perturbation methods are used to derive analytic expressions for effective slip lengths for Stokes flow over rough, mixed-slip surfaces, where the roughness is periodic, and the variation in slip length has the same period. If the classical no-slip boundary condition of fluid mechanics is relaxed, the slip velocity of the fluid at the surface is non-zero. For simple shear flow, the slip velocity is proportional to the shear rate. The constant of proportionality has dimensions of length and is known as the slip length. Any variation in the slip length over the surface will cause a perturbation to the flow adjacent to the surface. Due to the diffusion of momentum, at sufficient height above the surface, the flow perturbations have diminished, and flow is smooth and uniform. The velocity and shear rate at this height imply an effective slip length of the surface. The purpose of this thesis is to predict that effective slip length.  Homogenization is a technique for finding approximate solutions to partial differential equations. The essence of homogenization is to construct a mathematical model of a physical problem featuring some periodic heterogeneity, then generate a sequence of models such that the period in question reduces with each increment in the sequence. If the sequence is appropriately defined, it has a limit model in the limit of vanishing period, for which a solution can be found. The solution to the limit system is an approximation to the solutions of systems with a finite period.  We use homogenization to find the effective slip length of a system of Stokes flow over a periodically rough surface, described by periodic function h(x; y), with a local slip length b(x; y) varying with the same period. For systems where the period L is smaller than both the domain height P and typical slip lengths, the effective slip length bₑff is well-approximated by the harmonic mean of local slip lengths, weighted by area of contact between liquid and surface: [See 'Thesis' document below for equation.]  We further use a perturbation technique to verify the above expression in the special case of a flat surface, and to derive another effective slip length expression: For a flat surface with local slip lengths much smaller than the period and domain height, the effective slip length bₑff is well-approximated by the area-weighted average of local slip lengths: [See 'Thesis' document below for equation.]</p>

Benchmark Experimental Data for Fully Stalled Wide-Angled Diffusers

2008 ◽  
Vol 130 (10) ◽  
Author(s):  
K Kibicho ◽  
A. T. Sayers
Keyword(s):  
Fluid Dynamics ◽  
Flow Separation ◽  
Classical Case ◽  
Data Bank ◽  
Mean Flow ◽  
Mean Velocity ◽  
Validation Data ◽  
Flow Measurements ◽  
Pressure Driven Flow ◽  
Pressure Driven

Due to adverse pressure gradient along the diverging walls of wide-angled diffusers, the attached flow separates from one wall and remains attached permanently to the other wall in a process called stalling. Separated diffuser flows provide a classical case of pressure driven flow separation. Such flows present a very serious challenge to fluid dynamics modelers. This paper provides a data bank contribution for the streamwise mean velocity field and pressure recovery data in wide-angled diffusers. Turbulent mean flow measurements were carried out at Reynolds numbers between 1.07×105 and 2.14×105 based on inlet hydraulic diameter and centerline velocity for diffusers whose divergence angles were between 30 deg and 50 deg. The results presented provide a reliable validation data bank for computational fluid dynamics studies for pressure driven flow separation studies.

scholarly journals Effective slip boundary conditions for arbitrary one-dimensional surfaces

2012 ◽  
Vol 706 ◽  
pp. 108-117 ◽  
Author(s):  
Evgeny S. Asmolov ◽  
Olga I. Vinogradova
Keyword(s):  
Boundary Conditions ◽  
Slip Length ◽  
Longitudinal Component ◽  
Transverse Component ◽  
Slip Boundary Conditions ◽  
One Dimensional ◽  
Slip Boundary ◽  
Effective Slip Length ◽  
Effective Slip ◽  
Local Slip

AbstractIn many applications it is advantageous to construct effective slip boundary conditions, which could fully characterize flow over patterned surfaces. Here we focus on laminar shear flows over smooth anisotropic surfaces with arbitrary scalar slip $b(y)$, varying in only one direction. We derive general expressions for eigenvalues of the effective slip-length tensor, and show that the transverse component is equal to half of the longitudinal one, with a two times larger local slip, $2b(y)$. A remarkable corollary of this relation is that the flow along any direction of the one-dimensional surface can be easily determined, once the longitudinal component of the effective slip tensor is found from the known spatially non-uniform scalar slip.

scholarly journals Effective Slip Lengths for Stokes Flow over Rough, Mixed-Slip Surfaces

2021 ◽  
Author(s):  
◽  
Nathaniel Joseph Lund
Keyword(s):  
Shear Rate ◽  
Stokes Flow ◽  
Slip Velocity ◽  
Flat Surface ◽  
Slip Length ◽  
Simple Shear Flow ◽  
Slip Surfaces ◽  
Effective Slip Length ◽  
Effective Slip ◽  
Local Slip

<p>In this thesis, homogenization and perturbation methods are used to derive analytic expressions for effective slip lengths for Stokes flow over rough, mixed-slip surfaces, where the roughness is periodic, and the variation in slip length has the same period. If the classical no-slip boundary condition of fluid mechanics is relaxed, the slip velocity of the fluid at the surface is non-zero. For simple shear flow, the slip velocity is proportional to the shear rate. The constant of proportionality has dimensions of length and is known as the slip length. Any variation in the slip length over the surface will cause a perturbation to the flow adjacent to the surface. Due to the diffusion of momentum, at sufficient height above the surface, the flow perturbations have diminished, and flow is smooth and uniform. The velocity and shear rate at this height imply an effective slip length of the surface. The purpose of this thesis is to predict that effective slip length.  Homogenization is a technique for finding approximate solutions to partial differential equations. The essence of homogenization is to construct a mathematical model of a physical problem featuring some periodic heterogeneity, then generate a sequence of models such that the period in question reduces with each increment in the sequence. If the sequence is appropriately defined, it has a limit model in the limit of vanishing period, for which a solution can be found. The solution to the limit system is an approximation to the solutions of systems with a finite period.  We use homogenization to find the effective slip length of a system of Stokes flow over a periodically rough surface, described by periodic function h(x; y), with a local slip length b(x; y) varying with the same period. For systems where the period L is smaller than both the domain height P and typical slip lengths, the effective slip length bₑff is well-approximated by the harmonic mean of local slip lengths, weighted by area of contact between liquid and surface: [See 'Thesis' document below for equation.]  We further use a perturbation technique to verify the above expression in the special case of a flat surface, and to derive another effective slip length expression: For a flat surface with local slip lengths much smaller than the period and domain height, the effective slip length bₑff is well-approximated by the area-weighted average of local slip lengths: [See 'Thesis' document below for equation.]</p>

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