Slip over rough and coated surfaces

1994 ◽  
Vol 273 ◽  
pp. 125-139 ◽  
Author(s):  
Michael J. Miksis ◽  
Stephen H. Davis
Keyword(s):  
Slip Boundary Condition ◽  
Slip Condition ◽  
Slip Coefficient ◽  
Outer Flow ◽  
Navier Slip ◽  
Two Fluids ◽  
Slip Boundary ◽  
Lubricating Film ◽  
Effective Slip ◽  
Coated Surfaces

We study the effect of surface roughness and coatings on fluid flow over a solid surface. In the limit of small-amplitude roughness and thin lubricating films we are able to derive asymptotically an effective slip boundary condition to replace the no-slip condition over the surface. When the film is absent, the result is a Navier slip condition in which the slip coefficient equals the average amplitude of the roughness. When a layer of a second fluid covers the surface and acts as a lubricating film, the slip coefficient contains a term which is proportional to the viscosity ratio of the two fluids and which depends on the dynamic interaction between the film and the fluid. Limiting cases are identified in which the film dynamics can be decoupled from the outer flow.

A moving fluid interface on a rough surface

1976 ◽  
Vol 76 (4) ◽  
pp. 801-817 ◽  
Author(s):  
L. M. Hocking
Keyword(s):  
Rough Surface ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Solid Boundary ◽  
Simple Type ◽  
Slip Coefficient ◽  
Two Fluids ◽  
Slip Boundary ◽  
Effective Slip

When an interface between two fluids moves in contact with a solid boundary, the Navier-Stokes equations and the no-slip boundary condition provide an unsatisfactory theoretical model, because they predict an undefined velocity at the contact line and a non-integrable stress on the solid boundary. If the surface irregularities are included in the model, the flow on a length scale large compared with their size can be calculated, using a slip coefficient and treating the surface as smooth.A simple type of corrugated surface is examined, and the effective slip coefficient calculated, for grooves of finite and infinite depth. The slip coefficient when the grooves are filled with one fluid and another fluid flows over them is also calculated. It is suggested that, when a fluid displaces another on a rough surface, the displaced fluid remains in the hollows on the surface, thus providing a partly fluid boundary for the displacing fluid and leading to a slip coefficient for the flow.Fluid contained between two vertical plates and rising between them provides a simple example of a flow for which the solution can be found with and without a slip coefficient. With slip present, the force on the plates is finite and its value is calculated.

Numerical Investigation of the Drag and Lift Forces Acting on Impenetrable Rotating Spherical Nano-Particle

2008 ◽  
Author(s):  
M. R. Meigounpoory ◽  
A. Rahi ◽  
A. Mirbozorgi
Keyword(s):  
Lift Coefficient ◽  
Three Dimensional ◽  
Slip Boundary Condition ◽  
Slip Condition ◽  
Nano Particle ◽  
Slip Coefficient ◽  
Slip Boundary ◽  
Lift Forces ◽  
Drag And Lift ◽  
Drag And Lift Coefficient

The drag and lift forces acting on a rotating impenetrable spherical suspended nano-particle in a homogeneous uniform flow are numerically studied by means of a three-dimensional numerical simulation with slip boundary condition. The effects of both the slip coefficient and rotational speed of the nanosphere on the drag and lift forces are investigated for Reynolds numbers in the range of 0.1 < Re < 100. Increase of rotation increases the drag and lift force exerted by flow at the surface of nano-sphere. By increasing slip coefficient the values of drag and lift coefficients decreases. At full slip condition, rotation of the nano-sphere has not significant effects on the drag and lift coefficient values moreover the lift coefficient of flow around the rotating spherical particle will be vanished. Present numerical results at no-slip condition are in good agreements with certain results of flow around of rotating sphere.

A moving fluid interface. Part 2. The removal of the force singularity by a slip flow

1977 ◽  
Vol 79 (2) ◽  
pp. 209-229 ◽  
Author(s):  
L. M. Hocking
Keyword(s):  
Contact Line ◽  
Slip Flow ◽  
Slip Condition ◽  
Solid Boundary ◽  
Parallel Plates ◽  
Fluid Interface ◽  
Slip Coefficient ◽  
Outer Flow ◽  
Normal Contact ◽  
Two Fluids

If the no-slip condition is used to determine the flow produced when a fluid interface moves along a solid boundary, a non-integrable stress is obtained. In part 1 of this study (Hocking 1976), it was argued that, when allowance was made for the presence of irregularities on the solid boundary, an effective slip coefficient could be found, which might remove the difficulty.This paper examines the effect of a slip coefficient on the flow in the neighbourhood of the contact line. Particular cases which are solved in detail are liquid–gas interfaces at an arbitrary angle, and normal contact of fluids of arbitrary viscosity. The contribution of the vicinity of the contact line to the force on the boundary is obtained.The inner region, near the contact line, must be matched with an outer flow, in which the no-slip condition can be applied, in order to obtain the total value of the force on the boundary. This force is determined for the flow of two fluids between parallel plates and in a pipe, with a plane interface. The enhanced resistance produced by the presence of the interface is calculated, and it is shown to be equivalent to an increase in the length of the column of fluid by a small multiple of the pipe radius.

scholarly journals Generalized slip condition over rough surfaces

2018 ◽  
Vol 858 ◽  
pp. 407-436 ◽  
Author(s):  
Giuseppe A. Zampogna ◽  
Jacques Magnaudet ◽  
Alessandro Bottaro
Keyword(s):  
Boundary Condition ◽  
Rough Surface ◽  
Hexagonal Lattice ◽  
Fluid Flows ◽  
Reynolds Numbers ◽  
Slip Condition ◽  
Strain Rate Tensor ◽  
Outer Flow ◽  
Navier Slip ◽  
Roughness Amplitude

A macroscopic boundary condition to be used when a fluid flows over a rough surface is derived. It provides the slip velocity $\boldsymbol{u}_{S}$ on an equivalent (smooth) surface in the form $\boldsymbol{u}_{S}=\unicode[STIX]{x1D716}{\mathcal{L}}\boldsymbol{ : }{\mathcal{E}}$, where the dimensionless parameter $\unicode[STIX]{x1D716}$ is a measure of the roughness amplitude, ${\mathcal{E}}$ denotes the strain-rate tensor associated with the outer flow in the vicinity of the surface and ${\mathcal{L}}$ is a third-order slip tensor arising from the microscopic geometry characterizing the rough surface. This boundary condition represents the tensorial generalization of the classical Navier slip condition. We derive this condition, in the limit of small microscopic Reynolds numbers, using a multi-scale technique that yields a closed system of equations, the solution of which allows the slip tensor to be univocally calculated, once the roughness geometry is specified. We validate this generalized slip condition by considering the flow about a rough sphere, the surface of which is covered with a hexagonal lattice of cylindrical protrusions. Comparisons with direct numerical simulations performed in both laminar and turbulent regimes allow us to assess the validity and limitations of this condition and of the mathematical model underlying the determination of the slip tensor ${\mathcal{L}}$.

scholarly journals Morphological evolution of microscopic dewetting droplets with slip

2017 ◽  
Vol 828 ◽  
pp. 271-288 ◽  
Author(s):  
Tak Shing Chan ◽  
Joshua D. McGraw ◽  
Thomas Salez ◽  
Ralf Seemann ◽  
Martin Brinkmann
Keyword(s):  
Slip Length ◽  
Morphological Evolution ◽  
Early Time ◽  
Slip Boundary Condition ◽  
Similarity Solutions ◽  
Contact Angles ◽  
Equilibrium Contact Angle ◽  
Navier Slip ◽  
Slip Boundary ◽  
Quasistatic Regime

We investigate the dewetting of a droplet on a smooth horizontal solid surface for different slip lengths and equilibrium contact angles. Specifically, we solve for the axisymmetric Stokes flow using the boundary element method with (i) the Navier-slip boundary condition at the solid/liquid boundary and (ii) a time-independent equilibrium contact angle at the contact line. When decreasing the rescaled slip length $\tilde{b}$ with respect to the initial central height of the droplet, the typical non-sphericity of a droplet first increases, reaches a maximum at a characteristic rescaled slip length $\tilde{b}_{m}\approx O(0.1{-}1)$ and then decreases. Regarding different equilibrium contact angles, two universal rescalings are proposed to describe the behaviour of the non-sphericity for rescaled slip lengths larger or smaller than $\tilde{b}_{m}$. Around $\tilde{b}_{m}$, the early time evolution of the profiles at the rim can be described by similarity solutions. The results are explained in terms of the structure of the flow field governed by different dissipation channels: elongational flows for $\tilde{b}\gg \tilde{b}_{m}$, friction at the substrate for $\tilde{b}\approx \tilde{b}_{m}$ and shear flows for $\tilde{b}\ll \tilde{b}_{m}$. Following the changes between these dominant dissipation mechanisms, our study indicates a crossover to the quasistatic regime when $\tilde{b}$ is many orders of magnitude smaller than $\tilde{b}_{m}$.

Liquid Slippage in Confined Flows: Effect of Periodic Micropatterns of Arbitrary Pitch and Amplitude

2016 ◽  
Author(s):  
Avinash Kumar ◽  
Subhra Datta ◽  
Dinesh Kalyanasundaram
Keyword(s):  
Slip Length ◽  
Fluid Dynamic ◽  
Low Cost ◽  
Slip Boundary Condition ◽  
Friction Reduction ◽  
Fourier Decomposition ◽  
Slip Boundary ◽  
Local Degree ◽  
Effective Slip Length ◽  
Effective Slip

The recently confirmed violation of the no-slip boundary condition in the flow of small-molecule liquids through microchannels and nanochannels has technological implications such as friction reduction. However, for significant friction reduction at low cost, the microchannel wall needs to be chemically inhomogeneous. The direct fluid dynamic consequence of this requirement is a spatial variation in the local degree of liquid slippage. In this work, the pressure-driven flow in a channel with periodically patterned slippage on the channel walls is studied using a spectrally accurate semi-analytical approach based on Fourier decomposition. The method puts no restrictions on the pitch (or wavelength) and amplitude of the pattern. The predicted effective slip length in the limits of small pattern amplitude and thick channels is found to be consistent with previously published results. The effective degree of slippage decreases with the patterning amplitude. Finer microchannels and longer pattern wavelengths promote slippage.

scholarly journals The mechanics of the Tollmien-Schlichting wave

1996 ◽  
Vol 312 ◽  
pp. 107-124 ◽  
Author(s):  
Peter G. Baines ◽  
Sharan J. Majumdar ◽  
Humio Mitsudera
Keyword(s):  
Boundary Layer ◽  
Outer Part ◽  
Slip Boundary Condition ◽  
Slip Condition ◽  
Linear Solution ◽  
Slip Boundary ◽  
Uniform Shear ◽  
Blasius Boundary Layer ◽  
Partial Mode ◽  
Tollmien Schlichting

We describe a mechanistic picture of the essential dynamical processes in the growing Tollmien-Schlichting wave in a Blasius boundary layer and similar flows. This picture depends on the interaction between two component parts of a disturbance (denoted ‘partial modes’), each of which is a complete linear solution in some idealization of the system. The first component is an inviscid mode propagating on the vorticity gradient of the velocity profile with the free-slip boundary condition, and the second, damped free viscous modes in infinite uniform shear with the no-slip condition. There are two families of these viscous modes, delineated by whether the phase lines of the vorticity at the wall are oriented with or against the shear, and they are manifested as resonances in a forced system. The interaction occurs because an initial ‘inviscid’ disturbance forces a viscous response via the no-slip condition at the wall. This viscous response is large near the resonance associated with the most weakly damped viscous mode, and in the unstable parameter range it has suitable phase at the outer part of the boundary layer to increase the amplitude of the inviscid partial mode by advection.

Numerical Simulation of Newtonian Fluid Flow in a T-Channel with no Slip/Slip Boundary Conditions on a Solid Wall

2017 ◽  
Vol 743 ◽  
pp. 480-485
Author(s):  
Evgeny Borzenko ◽  
Olga Dyakova
Keyword(s):  
Boundary Condition ◽  
Fluid Flow ◽  
Solid Wall ◽  
Simple Procedure ◽  
Slip Boundary Condition ◽  
Navier Slip ◽  
Slip Boundary ◽  
Pressure Profiles ◽  
Slip Yield Stress ◽  
Solid Walls

The planar flow of a Newtonian incompressible fluid in a T-shaped channel is investigated. Three fluid interaction models with solid walls are considered: no slip boundary condition, Navier slip boundary condition and slip boundary condition with slip yield stress. The fluid flow is provided by uniform pressure profiles at the boundary sections of the channel. The problem is numerically solved using a finite difference method based on the SIMPLE procedure. Characteristic flow regimes have been found for the described models of liquid interaction with solid walls. The estimation of the influence of the Reynolds number, pressure applied to the boundary sections and the parameters of these models on the flow pattern was performed. The criterial dependences describing main characteristics of the flow under conditions of the present work have been demonstrated.

A New Partial Slip Boundary Condition for the Lattice-Boltzmann Method

2013 ◽  
Author(s):  
Marc-Florian Uth ◽  
Alf Crüger ◽  
Heinz Herwig
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Slip Model ◽  
Navier Stokes Equations ◽  
Navier Slip ◽  
Slip Boundary ◽  
Boltzmann Method

In micro or nano flows a slip boundary condition is often needed to account for the special flow situation that occurs at this level of refinement. A common model used in the Finite Volume Method (FVM) is the Navier-Slip model which is based on the velocity gradient at the wall. It can be implemented very easily for a Navier-Stokes (NS) Solver. Instead of directly solving the Navier-Stokes equations, the Lattice-Boltzmann method (LBM) models the fluid on a particle basis. It models the streaming and interaction of particles statistically. The pressure and the velocity can be calculated at every time step from the current particle distribution functions. The resulting fields are solutions of the Navier-Stokes equations. Boundary conditions in LBM always not only have to define values for the macroscopic variables but also for the particle distribution function. Therefore a slip model cannot be implemented in the same way as in a FVM-NS solver. An additional problem is the structure of the grid. Curved boundaries or boundaries that are non-parallel to the grid have to be approximated by a stair-like step profile. While this is no problem for no-slip boundaries, any other velocity boundary condition such as a slip condition is difficult to implement. In this paper we will present two different implementations of slip boundary conditions for the Lattice-Boltzmann approach. One will be an implementation that takes advantage of the microscopic nature of the method as it works on a particle basis. The other one is based on the Navier-Slip model. We will compare their applicability for different amounts of slip and different shapes of walls relative to the numerical grid. We will also show what limits the slip rate and give an outlook of how this can be avoided.

Influence of the Key Factors on the Wall Slip Phenomenon in Micro Flow

2012 ◽  
Vol 472-475 ◽  
pp. 2415-2421
Author(s):  
Pei Qian He ◽  
Yan Lou ◽  
Xiao Yu Wu
Keyword(s):  
Shear Stress ◽  
Flow Analysis ◽  
Wall Slip ◽  
Slip Boundary Condition ◽  
Key Factors ◽  
Slip Coefficient ◽  
Slip Boundary ◽  
Navier’S Slip ◽  
Micro Flow ◽  
Slip Phenomenon

Aimed at the wall slip phenomenon of micro flow, the wall slip boundary condition was added to simulate the process of the micro flow by Polyflow based on the traditional flow analysis method. The effect of the wall slip on the micro flow was verified by comparing the pressure difference data obtained from the simulation with the quoted test data. In addition, based on the Generalized Navier’s slip law, the shear stress and slip coefficient were researched by the numerical simulation analyses to find out the influence of the key factors on the phenomenon of wall slip. The results show that the phenomenon of wall slip is an important factor that cannot be ignored in the micro flow. And only under the high shear stress, the wall slip phenomenon will have an obvious influence on the micro flow. Along with the decrease of the slip coefficient, the wall slip phenomenon becomes more apparent and the micro flow tends to be stable.

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