STOKES FLOW NEAR A MOVING CONTACT LINE WITH YIELD-STRESS BOUNDARY CONDITION

1989 ◽  
Vol 42 (1) ◽  
pp. 99-113 ◽  
Author(s):  
P. A. DURBIN
Keyword(s):  
Boundary Condition ◽  
Yield Stress ◽  
Contact Line ◽  
Stokes Flow ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Stress Boundary Condition ◽  
Stress Boundary

Considerations on the moving contact-line singularity, with application to frictional drag on a slender drop

1988 ◽  
Vol 197 ◽  
pp. 157-169 ◽  
Author(s):  
P. A. Durbin
Keyword(s):  
Boundary Condition ◽  
Yield Stress ◽  
Contact Line ◽  
Slip Boundary Condition ◽  
Frictional Drag ◽  
Slip Boundary ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Slip Region ◽  
Stress Boundary

It has previously been shown that the no-slip boundary condition leads to a singularity at a moving contact line and that this forces one to admit some form of slip. Present considerations on the energetics of slip due to shear stress lead to a yield stress boundary condition. A model for the distortion of the liquid state near solid boundaries gives a physical basis for this boundary condition. The yield stress condition is illustrated by an analysis of a slender drop rolling down an incline. That analysis provides a formula for the frictional drag resisting the drop movement. With the present boundary condition the length of the slip region becomes a property of the fluid flow.

Contact Line Dynamics in Liquid-Vapor Flows Using Lattice Boltzmann Method

2006 ◽  
Author(s):  
Shi-Ming Li ◽  
Danesh K. Tafti
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Contact Line ◽  
Lattice Boltzmann ◽  
Solid Wall ◽  
Hydrodynamic Theory ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Boltzmann Method ◽  
Contact Line Dynamics

A mean-field free-energy lattice Boltzmann method (LBM) is applied to simulate moving contact line dynamics. It is found that the common bounceback boundary condition leads to an unphysical velocity at the solid wall in the presence of surface forces. The magnitude of the unphysical velocity is shown proportional to the local force term. The velocity-pressure boundary condition is generalized to solve the problem of the unphysical velocity. The simulation results are compared with three different theories for moving contact lines, including a hydrodynamic theory, a molecular kinetic theory, and a linear cosine law of moving contact angle versus capillary number. It is shown that the current LBM can be used to replace the three theories in handling moving contact line problems.

scholarly journals Capillary retraction of the edge of a stretched viscous sheet

2018 ◽  
Vol 844 ◽  
Author(s):  
James P. Munro ◽  
John R. Lister
Keyword(s):  
Boundary Condition ◽  
Surface Tension ◽  
Stokes Flow ◽  
Similarity Solution ◽  
Far Field ◽  
Long Wavelength ◽  
Stress Boundary Condition ◽  
Stress Boundary

Surface tension causes the edge of a fluid sheet to retract. If the sheet is also stretched along its edge then the flow and the rate of retraction are modified. A universal similarity solution for the Stokes flow in a stretched edge shows that the scaled shape of the edge is independent of the stretching rate, and that it decays exponentially to its far-field thickness. This solution justifies the use of a stress boundary condition in long-wavelength models of stretched viscous sheets, and gives the detailed shape of the edge of such a sheet, resolving the position of the sheet edge to the order of the thickness.

The moving contact line: the slip boundary condition

1976 ◽  
Vol 77 (4) ◽  
pp. 665-684 ◽  
Author(s):  
E. B. Dussan V.
Keyword(s):  
Boundary Condition ◽  
Flow Field ◽  
Contact Line ◽  
Slip Length ◽  
Slip Boundary Condition ◽  
Flow Fields ◽  
Length Scale ◽  
Slip Boundary ◽  
Moving Contact Line ◽  
Moving Contact

The singularity at the contact line which is present when the usual fluidmechanical modelling assumptions are made is removed by permitting the fluid to slip along the wall. The aim of this study is to assess the sensitivity of the overall flow field to the form of the slip boundary condition. Explicit solutions are obtained for three different slip boundary conditions. Two length scales emerge: the slip length scale and the meniscus length scale. It is found that on the slip length scale the flow fields are quite different; however, when viewed on the meniscus length scale, i.e. the length scale on which almost all fluidmechanical measurements are made, all of the flow fields appear the same. It is found that the characteristic of the slip boundary condition which affects the overall flow field is the magnitude of the slip length.

Curvature boundary condition for a moving contact line

2016 ◽  
Vol 310 ◽  
pp. 329-341 ◽  
Author(s):  
J. Luo ◽  
X.Y. Hu ◽  
N.A. Adams
Keyword(s):  
Boundary Condition ◽  
Contact Line ◽  
Moving Contact Line ◽  
Moving Contact
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