Time-dependent free surface Stokes flow with a moving contact line. II. Flow over wedges and trenches

2004 ◽  
Vol 16 (5) ◽  
pp. 1660-1667 ◽  
Author(s):  
C. M. Gramlich ◽  
Ali Mazouchi ◽  
G. M. Homsy
Keyword(s):  
Free Surface ◽  
Contact Line ◽  
Stokes Flow ◽  
Time Dependent ◽  
Moving Contact Line ◽  
Moving Contact

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

scholarly journals Capillary damping of inviscid surface waves in a circular cylinder

2009 ◽  
Vol 627 ◽  
pp. 323-340 ◽  
Author(s):  
R. KIDAMBI
Keyword(s):  
Free Surface ◽  
Circular Cylinder ◽  
Surface Waves ◽  
Contact Line ◽  
Simple Procedure ◽  
Edge Condition ◽  
Complex Frequency ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Static Contact

We consider the effect of a wetting condition at the moving contact line on the frequency and damping of surface waves on an inviscid liquid in a circular cylinder. The velocity potential φ and the free surface elevation η are sought as complex eigenfunction expansions. The φ eigenvalues are the classical ones whereas the η eigenvalues are unknown and have to be computed so as to satisfy the wetting condition on the contact line and the other free surface conditions – these turn out to be complex in general. A projection of the latter conditions on to an appropriate basis leads to an eigenvalue problem, for the complex frequency Ω, which has to be solved iteratively with the wetting condition. The variation of Ω with liquid depth h, Bond number Bo, capillary coefficient λ and static contact angle θc0 is explored for the (1, 0),(2, 0),(0, 1),(3, 0) and (4, 0) modes. The damping vanishes for λ = 0 (pinned-end edge condition) and λ = ∞ (free-end edge condition) with a maximum in the interior while the frequency decreases with increasing λ, approaching limiting values at the endpoints. A comparison with the analytic results of Miles (J. Fluid Mech., vol. 222, 1991, p. 197) for the no-meniscus case and the experimental results of Cocciaro, Faetti, & Festa (J. Fluid Mech., vol. 246, 1993, p. 43), where a meniscus is present, is good. The study provides a simple procedure for calculating the inviscid capillary damping associated with the moving contact line in a circular cylinder of finite depth with meniscus effects also being considered.

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.

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

scholarly journals Validation and modification of asymptotic analysis of slow and rapid droplet spreading by numerical simulation

2013 ◽  
Vol 715 ◽  
pp. 283-313 ◽  
Author(s):  
Yi Sui ◽  
Peter D. M. Spelt
Keyword(s):  
Numerical Simulation ◽  
Asymptotic Analysis ◽  
Contact Line ◽  
Slip Length ◽  
Interface Shape ◽  
Droplet Spreading ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Line Region ◽  
Modified Theory

AbstractUsing a slip-length-based level-set approach with adaptive mesh refinement, we have simulated axisymmetric droplet spreading for a dimensionless slip length down to $O(1{0}^{\ensuremath{-} 4} )$. The main purpose is to validate, and where necessary improve, the asymptotic analysis of Cox (J. Fluid Mech., vol. 357, 1998, pp. 249–278) for rapid droplet spreading/dewetting, in terms of the detailed interface shape in various regions close to the moving contact line and the relation between the apparent angle and the capillary number based on the instantaneous contact-line speed, $\mathit{Ca}$. Before presenting results for inertial spreading, simulation results are compared in detail with the theory of Hocking & Rivers (J. Fluid Mech., vol. 121, 1982, pp. 425–442) for slow spreading, showing that these agree very well (and in detail) for such small slip-length values, although limitations in the theoretically predicted interface shape are identified; a simple extension of the theory to viscous exterior fluids is also proposed and shown to yield similar excellent agreement. For rapid droplet spreading, it is found that, in principle, the theory of Cox can predict accurately the interface shapes in the intermediate viscous sublayer, although the inviscid sublayer can only be well presented when capillary-type waves are outside the contact-line region. However, $O(1)$ parameters taken to be unity by Cox must be specified and terms be corrected to ${\mathit{Ca}}^{+ 1} $ in order to achieve good agreement between the theory and the simulation, both of which are undertaken here. We also find that the apparent angle from numerical simulation, obtained by extrapolating the interface shape from the macro region to the contact line, agrees reasonably well with the modified theory of Cox. A simplified version of the inertial theory is proposed in the limit of negligible viscosity of the external fluid. Building on these results, weinvestigate the flow structure near the contact line, the shear stress and pressure along the wall, and the use of the analysis for droplet impact and rapid dewetting. Finally, we compare the modified theory of Cox with a recent experiment for rapid droplet spreading, the results of which suggest a spreading-velocity-dependent dynamic contact angle in the experiments. The paper is closed with a discussion of the outlook regarding the potential of using the present results in large-scale simulations wherein the contact-line region is not resolved down to the slip length, especially for inertial spreading.

Depletion of λ-DNA near moving contact line

2016 ◽  
Vol 236 ◽  
pp. 50-62
Author(s):  
Hongrok Shin ◽  
Ki Wan Bong ◽  
Chongyoup Kim
Keyword(s):  
Contact Line ◽  
Moving Contact Line ◽  
Moving Contact
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