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.

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.

The initial value problem for the non-homogeneous Navier—Stokes equations with general slip boundary condition

2000 ◽  
Vol 130 (4) ◽  
pp. 827-835 ◽  
Author(s):  
S. Itoh ◽  
A. Tani
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Solid Boundary ◽  
Dimensional Problem ◽  
Navier Stokes Equations ◽  
Slip Boundary

The initial-boundary value problem for the non-homogeneous Navier-Stokes equations including the slipping on the solid boundary is considered. The unique solvability is established locally in time for the three-dimensional problem and globally in time for the two-dimensional problem without so-called smallness restrictions.

scholarly journals Involving the Navier–Stokes equations in the derivation of boundary conditions for the lattice Boltzmann method

2011 ◽  
Vol 369 (1944) ◽  
pp. 2184-2192 ◽  
Author(s):  
Joris C. G. Verschaeve
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Grid Spacing ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Boltzmann Method

By means of the continuity equation of the incompressible Navier–Stokes equations, additional physical arguments for the derivation of a formulation of the no-slip boundary condition for the lattice Boltzmann method for straight walls at rest are obtained. This leads to a boundary condition that is second-order accurate with respect to the grid spacing and conserves mass. In addition, the boundary condition is stable for relaxation frequencies close to two.

scholarly journals Regularity Criteria for Navier-Stokes Equations with Slip Boundary Conditions on Non-flat Boundaries via Two Velocity Components

2019 ◽  
Vol 9 (1) ◽  
pp. 633-643
Author(s):  
Hugo Beirão da Veiga ◽  
Jiaqi Yang
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
Regularity Criteria ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Whole Space ◽  
Space Case

Abstract H.-O. Bae and H.J. Choe, in a 1997 paper, established a regularity criteria for the incompressible Navier-Stokes equations in the whole space ℝ3 based on two velocity components. Recently, one of the present authors extended this result to the half-space case $\begin{array}{} \displaystyle \mathbb{R}^3_+ \end{array}$. Further, this author in collaboration with J. Bemelmans and J. Brand extended the result to cylindrical domains under physical slip boundary conditions. In this note we obtain a similar result in the case of smooth arbitrary boundaries, but under a distinct, apparently very similar, slip boundary condition. They coincide just on flat portions of the boundary. Otherwise, a reciprocal reduction between the two results looks not obvious, as shown in the last section below.

scholarly journals Flow of a viscous compressible fluid produced in a circular tube by an impulsive point source

2011 ◽  
Vol 668 ◽  
pp. 100-112 ◽  
Author(s):  
B. U. FELDERHOF ◽  
G. OOMS
Keyword(s):  
Compressible Fluid ◽  
Numerical Scheme ◽  
Stokes Equations ◽  
Circular Tube ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Viscous Compressible Fluid ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Sudden Impulse

The flow of a viscous compressible fluid in a circular tube generated by a sudden impulse at a point on the axis is studied on the basis of the linearized Navier–Stokes equations. A no-slip boundary condition is assumed to hold on the wall of the tube. An efficient numerical scheme has been developed for the calculation of flow velocity and pressure disturbance as a function of position and time.

Liquid Leak Predictions in Micro and Nano-Porous Gaskets

2010 ◽  
Author(s):  
Lotfi Grine ◽  
Abdel-Hakim Bouzid
Keyword(s):  
Stokes Equations ◽  
Slip Flow ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Gas Leak ◽  
Flow Through ◽  
Parameter Approach ◽  
Experimental And Theoretical Studies

In recent years, few experimental and theoretical studies have been conducted to predict gas leak rate through gaskets. However a very limited work is done on liquid leak rates through gaskets. A new method based on a slip flow model to predict liquid flow through nano-porous gaskets is presented. A recent study [1] had shown that the leakage prediction based on the porosity parameter approach was successful in predicting gaseous leaks and an extrapolation of the latter to liquid leaks is the purpose of this study. In the present article, an analytical-computational methodology based on the number and pore size to predict liquid nanoflow in the slip flow regime through gaskets is presented. The formulation is based on the Navier-Stokes equations associated to slip boundary condition at the wall. The mass leak rates through a gasket considered as a porous media under variable experimentally conditions of (fluid media, pressure, and gasket stress) were conducted on a test bench. Gaseous and liquid leaks are measured and comparisons are made with the analytical predictions.

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.

Transient flow of a viscous compressible fluid in a circular tube after a sudden point impulse

2010 ◽  
Vol 644 ◽  
pp. 97-106 ◽  
Author(s):  
B. U. FELDERHOF
Keyword(s):  
Compressible Fluid ◽  
Transient Flow ◽  
Stokes Equations ◽  
Circular Tube ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Viscous Compressible Fluid ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Short Time

The flow of a viscous compressible fluid in a circular tube generated by a sudden impulse at a point on the axis is studied on the basis of the linearized Navier–Stokes equations. A no-slip boundary condition is assumed to hold on the wall of the tube. Owing to the finite velocity of sound the flow behaviour differs qualitatively from that of an incompressible fluid. The flow velocity and the pressure disturbance at any fixed point different from the source point vanish at short time and decay at long times with a t−3/2 power law.

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