On the wetting dynamics in a Couette flow

2013 ◽  
Vol 724 ◽  
Author(s):  
Peng Gao ◽  
Xi-Yun Lu
Keyword(s):  
Contact Angle ◽  
Couette Flow ◽  
Apparent Contact Angle ◽  
Wetting Transition ◽  
Contact Lines ◽  
Two Phase ◽  
Moving Contact ◽  
Moving Contact Lines ◽  
Liquid Systems ◽  
Critical Capillary Number

AbstractThe dynamics of moving contact lines in a two-phase Couette flow is investigated by using a matched asymptotic procedure. The walls are assumed to be partially wetting, and the microscopic contact angle is finite but sufficiently small so that the lubrication approach can be used. Explicit formulas are derived to characterize the shear-induced interface deformation and the critical capillary number for the onset of wetting transition. It is found that the apparent contact angle vanishes for liquid–air systems and remains finite for liquid–liquid systems when the wetting transition occurs.

scholarly journals Applying Contact Angle to a Two-Dimensional Multiphase Smoothed Particle Hydrodynamics Model

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Amirsaman Farrokhpanah ◽  
Babak Samareh ◽  
Javad Mostaghimi
Keyword(s):  
Contact Angle ◽  
Triple Point ◽  
Smoothed Particle Hydrodynamics ◽  
Equilibrium Contact Angle ◽  
Shear Stresses ◽  
Contact Lines ◽  
Moving Contact ◽  
Moving Contact Lines ◽  
Particle Hydrodynamics ◽  
Smoothed Particle

Equilibrium contact angle of liquid drops over horizontal surfaces has been modeled using smoothed particle hydrodynamics (SPH). The model is capable of accurate implementation of contact angles to stationary and moving contact lines. In this scheme, the desired value for stationary or dynamic contact angle is used to correct the profile near the triple point. This is achieved by correcting the surface normals near the contact line and also interpolating the drop profile into the boundaries. Simulations show that a close match to the chosen contact angle values can be achieved for both stationary and moving contact lines. This technique has proven to reduce the amount of nonphysical shear stresses near the triple point and to enhance the convergence characteristics of the solver.

scholarly journals Relaxation of a dewetting contact line. Part 1. A full-scale hydrodynamic calculation

2007 ◽  
Vol 579 ◽  
pp. 63-83 ◽  
Author(s):  
JACCO H. SNOEIJER ◽  
BRUNO ANDREOTTI ◽  
GILES DELON ◽  
MARC FERMIGIER
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Apparent Contact Angle ◽  
Universal Relation ◽  
Contact Lines ◽  
Viscous Effects ◽  
Solid Plate ◽  
Static Approach ◽  
Critical Capillary Number ◽  
Wetting Liquid

The relaxation of a dewetting contact line is investigated theoretically in the so-called ‘Landau–Levich’ geometry in which a vertical solid plate is withdrawn from a bath of partially wetting liquid. The study is performed in the framework of lubrication theory, in which the hydrodynamics is resolved at all length scales (from molecular to macroscopic). We investigate the bifurcation diagram for unperturbed contact lines, which turns out to be more complex than expected from simplified ‘quasi-static’ theories based upon an apparent contact angle. Linear stability analysis reveals that below the critical capillary number of entrainment, Cac, the contact line is linearly stable at all wavenumbers. Away from the critical point, the dispersion relation has an asymptotic behaviour σ∝|q| and compares well to a quasi-static approach. Approaching Cac, however, a different mechanism takes over and the dispersion evolves from ∼|q| to the more common ∼q2. These findings imply that contact lines cannot be described using a universal relation between speed and apparent contact angle, but viscous effects have to be treated explicitly.

Moving contact lines on a two-dimensional rough surface

1985 ◽  
Vol 154 ◽  
pp. 1-28 ◽  
Author(s):  
Kalvis M. Jansons
Keyword(s):  
Contact Angle ◽  
Rough Surface ◽  
Rough Surfaces ◽  
Contact Angle Hysteresis ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Contact Lines ◽  
Stick Slip ◽  
Moving Contact ◽  
Moving Contact Lines

The dynamic contact angle for a contact line moving over a solid surface with random sparse spots of roughness is determined theoretically in the limit of zero capillary number. The model exhibits many of the observed characteristics of moving contact lines on real rough surfaces, including contact-angle hysteresis and stick-slip. Several types of rough surface are considered, and a comparison is made between periodic and random rough surfaces.

A theoretical study of two-phase flow through a narrow gap with a moving contact line: viscous fingering in a Hele-Shaw cell

1990 ◽  
Vol 221 ◽  
pp. 53-76 ◽  
Author(s):  
Steven J. Weinstein ◽  
E. B. Dussan ◽  
Lyle H. Ungar
Keyword(s):  
Thin Films ◽  
Contact Angle ◽  
Contact Line ◽  
Viscous Fingering ◽  
Contact Lines ◽  
Fluid Interface ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Moving Contact Lines ◽  
Hele Shaw Cell

The problem of viscous fingering in a Hele-Shaw cell with moving contact lines is considered. In contrast to the usual situation where the displaced fluid coats the solid surface in the form of thin films, here, both the displacing and the displaced fluids make direct contact with the solid. The principal differences between these two situations are in the ranges of attainable values of the gapwise component of the interfacial curvature (the component due to the bending of the fluid interface across the small gap of the Hele-Shaw cell), and in the introduction of two additional parameters for the case with moving contact lines. These parameters are the receding contact angle, and the sensivity of the dynamic angle to the speed of the contact line. Our objective is the prediction of the shape and widths of the fingers in the limit of small capillary number, Uμ/σ. Here, U denotes the finger speed, μ denotes the dynamic viscosity of the more viscous displaced fluid, and σ denotes the surface tension of the fluid interface. As might be expected, there are similarities and differences between the two problems. Despite the fact that different equations arise, we find that they can be analysed using the techniques introduced by McLean & Saffman and Vanden-Broeck for the thin-film case. The nature of the multiplicity of solutions also appears to be similar for the two problems. Our results indicate that when contact lines are present, the finger shapes are sensitive to the value of the contact angle only in the vicinity of its nose, reminiscent of experiments where bubbles or wires are placed at the nose of viscous fingers when thin films are present. On the other hand, in the present problem at least two distinct velocity scales emerge with well-defined asymptotic limits, each of these two cases being distinguished by the relative importance played by the two components of the curvature of the fluid interface. It is found that the widths of fingers can be significantly smaller than half the width of the cell.

Asymptotic theory of fluid entrainment in dip coating

2018 ◽  
Vol 844 ◽  
pp. 1026-1037 ◽  
Author(s):  
Jian Qin ◽  
Peng Gao
Keyword(s):  
Contact Line ◽  
Analytical Formula ◽  
Dip Coating ◽  
Wetting Transition ◽  
Contact Lines ◽  
Moving Contact ◽  
Moving Contact Lines ◽  
Two Fluid ◽  
Large Speed ◽  
Line Movement

When a contact line moves with a sufficiently large speed, liquid or gas films can be entrained on a solid depending on the direction of contact-line movement. In this work, the contact-line dynamics in the situation of a generic two-fluid system is investigated. We demonstrate that the hydrodynamics of a contact line, no matter whether advancing or receding, can formally reduce to that of a receding one with small interfacial slopes. Since the latter can be well treated under the classical lubrication approximation, this analogy allows us to derive an asymptotic solution of the interfacial profiles for arbitrary values of contact angle and viscosity ratio. For the dip-coating geometry, we obtain, with no adjustable parameters, an analytical formula for the critical speed of wetting transition, which in particular predicts the onset of both liquid and gas entrainment. Moreover, the present analysis also builds a novel connection between the Cox–Voinov law and classical lubrication theory for moving contact lines.

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