A diffuse interface fractional time-stepping technique for incompressible two-phase flows with moving contact lines

Diffuse-interface models may be used to compute moving contact lines because the Cahn–Hilliard diffusion regularizes the singularity at the contact line. This paper investigates the basic questions underlying this approach. Through scaling arguments and numerical computations, we demonstrate that the Cahn–Hilliard model approaches a sharp-interface limit when the interfacial thickness is reduced below a threshold while other parameters are fixed. In this limit, the contact line has a diffusion length that is related to the slip length in sharp-interface models. Based on the numerical results, we propose a criterion for attaining the sharp-interface limit in computing moving contact lines.

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On the wetting dynamics in a Couette flow

Journal of Fluid Mechanics ◽

10.1017/jfm.2013.202 ◽

2013 ◽

Vol 724 ◽

Cited By ~ 5

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.

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Can diffuse-interface models quantitatively describe moving contact lines?

The European Physical Journal Special Topics ◽

10.1140/epjst/e2011-01434-y ◽

2011 ◽

Vol 197 (1) ◽

pp. 37-46 ◽

Cited By ~ 31

Author(s):

P. Yue ◽

J. J. Feng

Keyword(s):

Diffuse Interface ◽

Contact Lines ◽

Interface Models ◽

Moving Contact ◽

Moving Contact Lines

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A numerical investigation of the propulsion of water walkers

Journal of Fluid Mechanics ◽

10.1017/s0022112010004763 ◽

2010 ◽

Vol 668 ◽

pp. 363-383 ◽

Cited By ~ 33

Author(s):

PENG GAO ◽

JAMES J. FENG

Keyword(s):

Two Dimensions ◽

Diffuse Interface ◽

Viscous Force ◽

Contact Lines ◽

Moving Contact ◽

Element Simulation ◽

Thrust Generation ◽

Moving Contact Lines ◽

Recovery Stroke ◽

Fishing Spiders

This paper presents a finite-element simulation of the interfacial flow during propulsion of water walkers such as fishing spiders and water striders. The unsteady stroke of the driving leg is represented by a two-dimensional cylinder moving on a specified trajectory. The interface and the moving contact lines are handled by a diffuse-interface model. We explore the mechanism of thrust generation in terms of the interfacial morphology and flow structures. Results show that the most important component of the thrust is the curvature force related to the deformation of the menisci and the asymmetry of the dimple. For water walkers with thick legs, the pressure force due to the inertia of the water being displaced by the leg is also important. The viscous force is negligible. An extensive parametric study is performed on the effect of leg velocity, stroke depth, leg diameter and surface wettability. The propulsive force is insensitive to the contact angle on the leg. However, the hydrophobicity of the leg helps it detach from the surface during the recovery stroke and thus decreases the resistance. It is also important for averting or delaying penetration of the interface at large rowing velocity and depth. In two dimensions, surface waves are more efficient than vortices in transferring the momentum imparted by the leg to the water.

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