Friction and the Continuum Limit – Where is the Boundary?

2000 ◽  
Vol 651 ◽  
Author(s):  
Yingxi Zhu ◽  
Steve Granick
Keyword(s):  
Continuum Limit ◽  
Fluid Transport ◽  
Liquid Surface ◽  
Microfluidic Devices ◽  
Slip Boundary Condition ◽  
Surface Interactions ◽  
Slip Boundary ◽  
Low Viscosity ◽  
Solid Liquid ◽  
The Continuum

AbstractThe no-slip boundary condition, believed to describe macroscopic flow of low-viscosity fluids, overestimates hydrodynamic forces starting at lengths corresponding to hundreds of molecular dimensions when water or tetradecane is placed between smooth nonwetting surfaces whose spacing varies dynamically. When hydrodynamic pressures exceed 0.1-1 atmospheres (this occurs at spacings that depend on the rate of spacing change), flow becomes easier than expected. Therefore solid-liquid surface interactions influence not just molecularly-thin confined liquids but also flow at larger length scales. This points the way to strategies for energy-saving during fluid transport and may be relevant to filtration, colloidal dynamics, and microfluidic devices, and shows a hitherto-unappreciated dependence of slip on velocity.

On Stability Analysis of a Flexible Cylinder in an Array of Rigid Cylinders

1992 ◽  
Vol 114 (1) ◽  
pp. 12-19 ◽  
Author(s):  
J. Marn ◽  
I. Catton
Keyword(s):  
Experimental Data ◽  
Boundary Condition ◽  
First Principles ◽  
Control Volume ◽  
Slip Boundary Condition ◽  
Flexible Cylinder ◽  
Slip Boundary ◽  
Advantages And Disadvantages ◽  
Solid Liquid Interface ◽  
Solid Liquid

The concept of an unsteady control volume is used to predict the onset of instability for a simple array of cylinders. The array consists of a flexible cylinder placed amidst rigid cylinders. The fluid is assumed to be incompressible with a “slip” boundary condition used on the solid/liquid interface. The equations derived for the model from first principles are solved in the complex plane. The results are compared to experimental data. The paper is concluded with a discussion of the advantages and disadvantages of the model and an assessment of the accuracy of the predictions.

No-Slip Boundary Condition for Weak Solid−Liquid Interactions

2011 ◽  
Vol 115 (17) ◽  
pp. 8613-8621 ◽  
Author(s):  
Adam P. Bowles ◽  
Christopher D. F. Honig ◽  
William A. Ducker
Keyword(s):  
Boundary Condition ◽  
Slip Boundary Condition ◽  
Slip Boundary ◽  
Solid Liquid

scholarly journals Scale effect of slip boundary condition at solid–liquid interface

2017 ◽  
Vol 7 (1) ◽  
Author(s):  
Gyoko Nagayama ◽  
Takenori Matsumoto ◽  
Kohei Fukushima ◽  
Takaharu Tsuruta
Keyword(s):  
Boundary Condition ◽  
Scale Effect ◽  
Slip Boundary Condition ◽  
Liquid Interface ◽  
Slip Boundary ◽  
Solid Liquid Interface ◽  
Solid Liquid

scholarly journals Isotropic-turbulence-induced mass transfer across a severely contaminated water surface

2016 ◽  
Vol 797 ◽  
pp. 665-682 ◽  
Author(s):  
H. Herlina ◽  
J. G. Wissink
Keyword(s):  
Mass Transfer ◽  
Schmidt Number ◽  
Isotropic Turbulence ◽  
Slip Boundary Condition ◽  
Gas Transfer ◽  
Transfer Velocity ◽  
Slip Conditions ◽  
Slip Boundary ◽  
Turbulent Reynolds Number ◽  
Solid Liquid

Direct numerical simulations were performed to investigate the effect of severe contamination on interfacial gas transfer in the presence of isotropic turbulence diffusing from below. A no-slip boundary condition was employed at the interface to model the severe contamination effect. The influence of both Schmidt number ($Sc$) and turbulent Reynolds number ($R_{T}$) on the transfer velocity ($K_{L}$) was studied. In the range from $Sc=2$ up to $Sc=500$ it was found that $K_{L}\propto Sc^{-2/3}$, which is in agreement with predictions based on solid–liquid transport models, see e.g. Davies (1972, Turbulence Phenomena, Academic). For similar $R_{T}$, the transfer velocity was observed to reduce significantly compared with the free-slip conditions. The reduction becomes more pronounced with increasing Schmidt number. Similar to the observation for free-slip conditions made by Theofanous et al. (Intl J. Heat Mass Transfer, vol. 19 (6), 1976, pp. 613–624), the normalized $K_{L}$ in the present no-slip case was also found to depend on $R_{T}^{-1/2}$ and $R_{T}^{-1/4}$ for small and large turbulent Reynolds numbers, respectively.

Detailed Investigation of Thermal and Hydrodynamic Flow Behaviour in Micro/Nano Cavity Using DSMC and NSF Equations

2011 ◽  
Author(s):  
Alireza Mohammadzadeh ◽  
Ehsan Roohi ◽  
Hamid Niazmand ◽  
Stefan Kanchev Stefanov
Keyword(s):  
Boundary Conditions ◽  
Direct Simulation Monte Carlo ◽  
Velocity Slip ◽  
Slip Boundary Condition ◽  
Second Order ◽  
Driven Cavity ◽  
Slip Boundary ◽  
Slip Regime ◽  
Simulation Monte Carlo ◽  
The Continuum

We utilized direct simulation Monte Carlo (DSMC) method to investigate the effectiveness of the NSF equations in the slip and transition regimes. Monatomic argon confined in a micro/nano lid-driven cavity is considered in this study. Full NSF equations accompanied by the first and second order velocity slip and temperature jump boundary conditions are used to investigate non-equilibrium phenomena. It is seen that although velocity profiles are predicted quite accurately by means of proper slip boundary conditions, the NSF equations fail to predict correct shear stress distribution and heat flux direction even in the middle slip regime. It is also seen that applying the second order velocity slip boundary condition in the transition regime reduces the accuracy of the continuum approach. Fourier law, which assumes the heat always fluxes from hotter to colder region, loses its validity in the slip regime and beyond.

Theory of the Oscillating Viscometer for Slip Flow

1971 ◽  
Vol 38 (3) ◽  
pp. 659-664 ◽  
Author(s):  
V. L. Shah
Keyword(s):  
Boundary Condition ◽  
Slip Flow ◽  
Slip Boundary Condition ◽  
New Method ◽  
Infinite Cylinder ◽  
Slip Boundary ◽  
The Continuum ◽  
Oscillating Viscometer ◽  
The Way

The theory of the oscillating viscometer has been extended for a slip boundary condition. The cases considered here are: an infinite disk, an infinite cylinder, a sphere, and a pile of infinite disks. This study has prepared the way for the formulation of a new method for measuring the amount of slip experienced by bodies moving in gases outside the continuum regime. The theory of Kestin and Wang [11] has been extended to include slip at the boundary.

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