Local Well Posedness of the Near-Equilibrium Contact Line Problem in 2-Dimensional Stokes Flow

2017 ◽  
Vol 49 (2) ◽  
pp. 899-953 ◽  
Author(s):  
Yunrui Zheng ◽  
Ian Tice
Keyword(s):  
Contact Line ◽  
Stokes Flow ◽  
Well Posedness

scholarly journals The asymptotics of the moving contact line: cracking an old nut

2015 ◽  
Vol 764 ◽  
pp. 445-462 ◽  
Author(s):  
David N. Sibley ◽  
Andreas Nold ◽  
Serafim Kalliadasis
Keyword(s):  
Contact Line ◽  
Stokes Flow ◽  
Slip Length ◽  
Intermediate Region ◽  
Droplet Spreading ◽  
Flow Equations ◽  
Moving Contact Line ◽  
Perturbation Problem ◽  
Moving Contact ◽  
New Perspective

AbstractFor contact line motion where the full Stokes flow equations hold, full matched asymptotic solutions using slip models have been obtained for droplet spreading and more general geometries. These solutions to the singular perturbation problem in the slip length, however, all involve matching through an intermediate region that is taken to be separate from the outer–inner regions. Here, we show that the intermediate region is in fact an overlap region representing extensions of both the outer and the inner region, allowing direct matching to proceed. In particular, we investigate in detail how a previously seen result of the matching of the cubes of the free surface slope is justified in the lubrication setting. We also extend this two-region direct matching to the more general Stokes flow case, offering a new perspective on the asymptotics of the moving contact line problem.

Marine ice sheet dynamics. Part 2. A Stokes flow contact problem

2011 ◽  
Vol 679 ◽  
pp. 122-155 ◽  
Author(s):  
CHRISTIAN SCHOOF
Keyword(s):  
Contact Problem ◽  
Boundary Conditions ◽  
Boundary Layers ◽  
Contact Line ◽  
Stokes Flow ◽  
Flow Model ◽  
Layer Structure ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Continuous Transition

We develop an asymptotic theory for marine ice sheets from a first-principles Stokes flow contact problem, in which different boundary conditions apply to areas where ice is in contact with bedrock and inviscid sea water, along with suitable inequalities on normal stress and boundary location constraining contact and non-contact zones. Under suitable assumptions about basal slip in the contact areas, the boundary-layer structure for this problem replicates the boundary layers previously identified for marine ice sheets from depth-integrated models and confirms the results of these previous models: the interior of the grounded ice sheet can be modelled as a standard free-surface lubrication flow, while coupling with the membrane-like floating ice shelf leads to two boundary conditions on this lubrication flow model at the contact line. These boundary conditions determine ice thickness and ice flux at the contact line and allow the lubrication flow model with a contact line to be solved as a moving boundary problem. In addition, we find that the continuous transition of vertical velocity from grounded to floating ice requires the presence of two previously unidentified boundary layers. One of these takes the form of a viscous beam, in which a wave-like surface feature leads to a continuous transition in surface slope from grounded to floating ice, while the other provides boundary conditions on this viscous beam at the contact line.

Steady viscous flow near a stationary contact line

1988 ◽  
Vol 187 ◽  
pp. 35-43 ◽  
Author(s):  
Ian Proudman ◽  
Mir Asadullah
Keyword(s):  
Contact Line ◽  
Stokes Flow ◽  
Power Supply ◽  
Plane Boundary ◽  
Immiscible Liquids ◽  
Phase Theory ◽  
Viscous Incompressible Flow ◽  
Global Power ◽  
Complex Eigenvalues ◽  
Stationary Contact

The paper presents the asymptotic solution, near a stationary contact line at a plane boundary, for steady viscous incompressible flow of two immiscible liquids. The eigenvalues which determine this Stokes flow are determined by the contact angle α of the more viscous liquid and the ratio μ of the two viscosities. The dominant eigenvalues are found for all values of α and μ. As μ → 0 the results agree with those of Moffatt's (1964) one-phase theory for the case μ = 0 only when α > 81°. For α < 81° the two sets of results are qualitatively different. In particular, the eddy structure corresponding to complex eigenvalues occurs only in the α-range (34°, 81°). As μ increases from 0 to 1, this range steadily decreases to zero, which is located at 60°. The transport of energy across the liquid interface is almost always from the obtuse-angled sector to the acute-angled sector, irrespective of α, μ, and the location of the global power supply.

Time-dependent free surface Stokes flow with a moving contact line. I. Flow over plane surfaces

2004 ◽  
Vol 16 (5) ◽  
pp. 1647-1659 ◽  
Author(s):  
Ali Mazouchi ◽  
C. M. Gramlich ◽  
G. M. Homsy
Keyword(s):  
Free Surface ◽  
Contact Line ◽  
Stokes Flow ◽  
Time Dependent ◽  
Moving Contact Line ◽  
Moving Contact

Test of the stability of a three-phase contact line with negative line tension

1999 ◽  
Vol 96 (9) ◽  
pp. 1335-1339 ◽  
Author(s):  
ALAN E. VAN GIESSEN, DIRK JAN BUKMAN, B.
Keyword(s):  
Contact Line ◽  
Line Tension ◽  
Phase Contact ◽  
Three Phase ◽  
The Stability

Moving contact line

2001 ◽  
Vol 11 (PR6) ◽  
pp. Pr6-199-Pr6-212 ◽  
Author(s):  
Y. Pomeau
Keyword(s):  
Contact Line ◽  
Moving Contact Line ◽  
Moving Contact

Cauchy Problem for Equations with Fractional Differentiation Bessel Operator in the Space of Temperate Distributions

2003 ◽  
Vol 8 (1) ◽  
pp. 61-75
Author(s):  
V. Litovchenko
Keyword(s):  
Functional Analysis ◽  
Cauchy Problem ◽  
Fundamental Solution ◽  
Initial Function ◽  
Well Posedness ◽  
Fractional Differentiation ◽  
Basic Tool ◽  
Conjugate Space ◽  
Analysis Technique ◽  
The Cauchy Problem

The well-posedness of the Cauchy problem, mentioned in title, is studied. The main result means that the solution of this problem is usual C∞ - function on the space argument, if the initial function is a real functional on the conjugate space to the space, containing the fundamental solution of the corresponding problem. The basic tool for the proof is the functional analysis technique.

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