Oscillatory Flow Through a Channel With Stick-Slip Walls: Complex Navier’s Slip Length

2011 ◽  
Vol 133 (1) ◽  
Author(s):  
Chiu-On Ng ◽  
C. Y. Wang
Keyword(s):  
Oscillation Frequency ◽  
Oscillatory Flow ◽  
Slip Length ◽  
Complex Nature ◽  
Channel Height ◽  
Boundary Slip ◽  
Stick Slip ◽  
Effective Slip ◽  
Flow Through ◽  
Shear Area

Effective slip lengths for pressure-driven oscillatory flow through a parallel-plate channel with boundary slip are deduced using a semi-analytic method of eigenfunction expansions and point matching. The channel walls are each a superhydrophobic surface micropatterned with no-shear alternating with no-slip stripes, which are aligned either parallel or normal to the flow. The slip lengths are complex quantities that are functions of the oscillation frequency, the channel height, and the no-shear area fraction of the wall. The dependence of the complex nature of the slip length on the oscillation frequency is investigated in particular.

Stokes Flow Through a Periodically Grooved Tube

2010 ◽  
Vol 132 (10) ◽  
Author(s):  
Chiu-On Ng ◽  
C. Y. Wang
Keyword(s):  
Stokes Flow ◽  
Slip Length ◽  
Geometrical Parameters ◽  
Slip Boundary ◽  
Effective Slip Length ◽  
Effective Slip ◽  
Flow Through ◽  
Transverse Grooves ◽  
Shear Area ◽  
Fluid Penetration

This is an analytical study on Stokes flow through a tube of which the wall is patterned with periodic transverse grooves filled with an inviscid gas. In one period of the pattern, the fluid flows through an annular groove and an annular rib subject to no-shear and no-slip boundary conditions, respectively. The fluid may penetrate the groove to a certain depth, so there is an abrupt change in the cross section of flow through the two regions. The problem is solved by the method of domain decomposition and eigenfunction expansions, where the coefficients of the expansion series are determined by matching velocities, stress, and pressure on the domain interface. The effective slip length and pressure distributions are examined as functions of the geometrical parameters (tube radius, depth of fluid penetration into grooves, and no-shear area fraction of the wall). Particular attention is paid to the limiting case of flow through annular fins on a no-shear wall. Results are generated for the streamlines, resistance, and pressure drop due to the fins. It is found that the wall condition, whether no-shear or no-slip, will be immaterial when the fin interval is smaller than a certain threshold depending on the orifice ratio.

scholarly journals Interface conditions of roughness-induced superoleophilic and superoleophobic surfaces immersed in hexadecane and ethylene glycol

2017 ◽  
Vol 8 ◽  
pp. 2504-2514 ◽  
Author(s):  
Yifan Li ◽  
Yunlu Pan ◽  
Xuezeng Zhao
Keyword(s):  
Surface Roughness ◽  
Slip Length ◽  
Theoretical Description ◽  
Interface Roughness ◽  
Real Surface ◽  
Interface Conditions ◽  
Boundary Slip ◽  
Effective Slip Length ◽  
Effective Slip ◽  
Underlying Mechanisms

Interface conditions are an important property that can affect the drag of fluid flow. For surfaces with different oleophobicity, the boundary slip at the solid–oil interface is mostly larger than that at the solid–water interface. Roughness is a key factor for the wettability of superoleophilic/superoleophobic surfaces, and it has been found to affect the effective value of slip length in measurements. Moreover, there are no studies on the effect of roughness on slip at interfaces between oil and superoleophilic/superoleophobic surfaces. A theoretical description of the real surface roughness is yet to be found. Results show that the effective slip length is negative and decreases with an increasing root mean squared (RMS) roughness of surfaces, as the increasing roughness enhances the area with discontinuous slip at the solid–liquid interface. The underlying mechanisms are analyzed. The amplitude parameters of surface roughness could significantly inhibit the degree of boundary slip on both superoleophilic surfaces in Wenzel state and superoleophobic surfaces in Cassie state immersed in oil. The oleic systems were likely to enhance boundary slip and resulted in a corresponding reduction in drag with decreasing roughness on the solid–oil interfaces.

scholarly journals Исследование гидродинамического сопротивления щелевого микроканала с текстурированной стенкой

2022 ◽  
Vol 48 (1) ◽  
pp. 15
Author(s):  
А.С. Лобасов ◽  
А.В. Минаков
Keyword(s):  
Reynolds Number ◽  
Pressure Drop ◽  
Friction Factor ◽  
Slip Length ◽  
Hydrodynamic Drag ◽  
Channel Height ◽  
Relative Pressure ◽  
Effective Slip Length ◽  
Effective Slip ◽  
Channel Lengths

The results of numerical investigation of the hydrodynamic drag of a slit microchannel with a textured wall surface, as well as the pressure drop in such a channel and the effective slip length on the wall for various Reynolds numbers, are presented. The channel height was 10 µm, and the length varied from 25 to 500 µm. It was found that the pressure drop in the textured microchannel was less than in a conventional channel for any of its lengths. The dependences of the relative pressure drop, the friction factor, and the effective slip length on the Reynolds number were obtained for various channel lengths. A correlation that describes the dependence of the relative pressure drop on the Reynolds number for small channel lengths was proposed. The friction factor is described by a correlation of form 20 / Re.

scholarly journals The investigation of the height effect of a slit microchannel with a textured wall on its hydrodynamic drag

2021 ◽  
Vol 2119 (1) ◽  
pp. 012050
Author(s):  
A S Lobasov ◽  
A V Minakov
Keyword(s):  
Reynolds Number ◽  
Pressure Drop ◽  
Drag Coefficient ◽  
Slip Length ◽  
Reynolds Numbers ◽  
Hydrodynamic Drag ◽  
Channel Height ◽  
Relative Pressure ◽  
Effective Slip Length ◽  
Effective Slip

Abstract The numerical investigation of the fluid flow in a slit microchannel with a textured wall was carried out. The effect of the channel height on the hydrodynamic drag coefficient, as well as on the pressure drop in such channel and the effective slip length on the wall for various Reynolds numbers, are presented in the paper. The channel length was 100 µm, and its height was varied from 25 µm to 500 µm. The Reynolds number was varied from 0.1 to 100. The main studied characteristics were compared to the similar ones obtained for a channel with normal walls (no-slip conditions). It was found that the pressure drop in such textured microchannel was lower as compared to a conventional channel for any of its heights and for any Reynolds numbers. The dependences of the relative pressure drop, effective slip length, and drag coefficient on the Reynolds number were obtained for different channel heights. The drag coefficient was described as 20/Re for the average values of the channel height. A correlation that describes the dependence of the friction factor on the Reynolds number for small and large heights of the channel was proposed. The accuracy of the proposed correlation was about 90%.

scholarly journals Effect of pH on Effective Slip Length and Surface Charge at Solid–Oil Interfaces of Roughness-Induced Surfaces

Micromachines ◽  
2021 ◽  
Vol 12 (7) ◽  
pp. 752
Author(s):  
Porui Tian ◽  
Yifan Li
Keyword(s):  
Charge Density ◽  
Surface Charge ◽  
Surface Charge Density ◽  
Ph Value ◽  
Slip Length ◽  
Boundary Slip ◽  
Effect Of Ph ◽  
Effective Boundary ◽  
Effective Slip Length ◽  
Effective Slip

In the development of micro/nano fluid control systems, fluid resistance has always been one of the key factors restricting its development. According to previous studies, it is found that the boundary slip effect of the solid-liquid interface can effectively reduce the resistance of the microfluid and improve the transport efficiency of the microfluid. The boundary slip length is mainly affected by surface wettability, roughness, and surface charge density. Among them, the influence mechanism of surface charge density on the boundary slip is the most complicated, and there is a lack of relevant research, and further investigation is needed. In this paper, we present research on quantification of effective slip length and surface charge density, where the roughness effect is considered. The electrostatic and hydrodynamic force data obtained from atomic force microscopy (AFM) measurements were fitted and processed for comparative analysis. We obtained the variation of surface charge density and effective slip length when different oleophobic surface samples were immersed in ethylene glycol with different pH values. The effect of pH on the surface charge density and effective slip length was investigated by their variations. The mechanism of the effect of pH on the surface charge density was discussed. The experimental results show that in the ethylene glycol solution, no matter whether the pH value of the solution increases or decreases, the charge density of the surface with the same properties decreases, and the effective boundary slip length also shows a downward trend. In deionized water, the surface charge density and effective boundary slip length decreases with the decrease of PH value.

Turbulent flow over superhydrophobic surfaces with streamwise grooves

2014 ◽  
Vol 747 ◽  
pp. 186-217 ◽  
Author(s):  
S. Türk ◽  
G. Daschiel ◽  
A. Stroh ◽  
Y. Hasegawa ◽  
B. Frohnapfel
Keyword(s):  
Boundary Conditions ◽  
Turbulent Flow ◽  
Drag Reduction ◽  
Secondary Flow ◽  
Slip Length ◽  
Laminar Flows ◽  
Superhydrophobic Surfaces ◽  
Mean Velocity ◽  
Effective Slip Length ◽  
Effective Slip

AbstractWe investigate the effects of superhydrophobic surfaces (SHS) carrying streamwise grooves on the flow dynamics and the resultant drag reduction in a fully developed turbulent channel flow. The SHS is modelled as a flat boundary with alternating no-slip and free-slip conditions, and a series of direct numerical simulations is performed with systematically changing the spanwise periodicity of the streamwise grooves. In all computations, a constant pressure gradient condition is employed, so that the drag reduction effect is manifested by an increase of the bulk mean velocity. To capture the flow properties that are induced by the non-homogeneous boundary conditions the instantaneous turbulent flow is decomposed into the spatial-mean, coherent and random components. It is observed that the alternating no-slip and free-slip boundary conditions lead to the generation of Prandtl’s second kind of secondary flow characterized by coherent streamwise vortices. A mathematical relationship between the bulk mean velocity and different dynamical contributions, i.e. the effective slip length and additional turbulent losses over slip surfaces, reveals that the increase of the bulk mean velocity is mainly governed by the effective slip length. For a small spanwise periodicity of the streamwise grooves, the effective slip length in a turbulent flow agrees well with the analytical solution for laminar flows. Once the spanwise width of the free-slip area becomes larger than approximately 20 wall units, however, the effective slip length is significantly reduced from the laminar value due to the mixing caused by the underlying turbulence and secondary flow. Based on these results, we develop a simple model that allows estimating the gain due to a SHS in turbulent flows at practically high Reynolds numbers.

Sign in / Sign up

Export Citation Format

Share Document