Simulations of contact-line motion: Slip and the dynamic contact angle

1989 ◽  
Vol 63 (7) ◽  
pp. 766-769 ◽  
Author(s):  
Peter A. Thompson ◽  
Mark O. Robbins
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Contact Line Motion

scholarly journals Moving contact lines and dynamic contact angles: a ‘litmus test’ for mathematical models, accomplishments and new challenges

2020 ◽  
Vol 229 (10) ◽  
pp. 1945-1977 ◽  
Author(s):  
Yulii D. Shikhmurzaev
Keyword(s):  
Contact Angle ◽  
Mathematical Models ◽  
Contact Line ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Dynamic Wetting ◽  
Line Speed ◽  
Moving Contact ◽  
New Challenges ◽  
Litmus Test

Abstract After a brief overview of the ‘moving contact-line problem’ as it emerged and evolved as a research topic, a ‘litmus test’ allowing one to assess adequacy of the mathematical models proposed as solutions to the problem is described. Its essence is in comparing the contact angle, an element inherent in every model, with what follows from a qualitative analysis of some simple flows. It is shown that, contrary to a widely held view, the dynamic contact angle is not a function of the contact-line speed as for different spontaneous spreading flows one has different paths in the contact angle-versus-speed plane. In particular, the dynamic contact angle can decrease as the contact-line speed increases. This completely undermines the search for the ‘right’ velocity-dependence of the dynamic contact angle, actual or apparent, as a direction of research. With a reference to an earlier publication, it is shown that, to date, the only mathematical model passing the ‘litmus test’ is the model of dynamic wetting as an interface formation process. The model, which was originated back in 1993, inscribes dynamic wetting into the general physical context as a particular case in a wide class of flows, which also includes coalescence, capillary breakup, free-surface cusping and some other flows, all sharing the same underlying physics. New challenges in the field of dynamic wetting are discussed.

Simulation of Spreading Dynamics of a EWOD Droplet With Dynamic Contact Angle and Contact Angle Hysteresis

2009 ◽  
Author(s):  
Fangjun Hong ◽  
Ping Cheng ◽  
Zhen Sun ◽  
Huiying Wu
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Low Voltage ◽  
Contact Angle Hysteresis ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Dielectric Surface ◽  
Contact Radius ◽  
Droplet Spreading ◽  
Spreading Dynamics

In this paper, the electrowetting dynamics of a droplet on a dielectric surface was investigated numerically by a mathematical model including dynamic contact angle and contact angle hysteresis. The fluid flow is described by laminar N-S equation, the free surface of the droplet is modeled by the Volume of Fluid (VOF) method, and the electrowetting force is incorporated by exerting an electrical force on the cells at the contact line. The Kilster’s model that can deal with both receding and advancing contact angle is adopted. Numerical results indicate that there is overshooting and oscillation of contact radius in droplet spreading process before it ceases the movement when the excitation voltage is high; while the overshooting is not observed for low voltage. The explanation for the contact line overshooting and some special characteristics of variation of contact radius with time were also conducted.

Implications of Contact Line Dynamics on Taylor Bubble Flow Morphology

2010 ◽  
Author(s):  
Alexandru Herescu ◽  
Jeffrey S. Allen
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Hydraulic Jump ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Film Deposition ◽  
Hydrophobic Coating ◽  
Glass Capillaries ◽  
Flow Morphology ◽  
Deposited Film

Film deposition experiments are performed in circular glass capillaries of 500 μm diameter. Two surface wettabilities are considered, contact angle of 30° for water on glass and of 105° when a hydrophobic coating is applied. It was observed that the liquid film deposited as the meniscus translates with a velocity U presents a ridge that also moves in the direction of the flow. The ridge is bounded by a contact line moving at a velocity UCL as well as a front of velocity UF, and it translates over the deposited stagnant film. The behavior of the ridge presents striking dissimilarities when the wettability is changed. Both UCL and UF are approximately twice as large for the non-wetting case at the same capillary number Ca. The Taylor bubbles forming due to the growth of the ridge are also differentiated by wettability, being much shorter in the non-wetting case. The dynamics of the contact line is studied experimentally and a criterion is proposed to explain the occurrence of a shock at the advancing front of the ridge. The hydraulic jump cannot be explained by the Froude condition of shock formation in shallow waters, or by an inertial dewetting of the deposited film. For a dynamic contact angle of θd = 6° and according to the proposed criterion, a hydraulic jump forms at the front of the ridge when a critical velocity is reached.

Bridge Dynamics for Capillary-Based Liquid Deposition

2012 ◽  
Author(s):  
Artur Lutfurakhmanov ◽  
Yechun Wang ◽  
Douglas L. Schulz
Keyword(s):  
Experimental Data ◽  
Contact Line ◽  
Liquid Droplet ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Non Invasive ◽  
Contact Line Motion ◽  
Liquid Deposition ◽  
Good Agreement ◽  
Bridge Dynamics

A new capillary-based lithography technique of liquid droplet deposition is further developed. Main advantage of this method in comparison with others techniques is that it is non-invasive both to the substrate and to the writing tip. The method is studied both theoretically and experimentally. To adequately describe bridge dynamics between the capillary and the substrate, proper boundary conditions must be set in the model for the liquid-surface interface. Based on literature review, two laws of contact line motion are identified: Tanner’s law and Blake’s equation. These two approaches are tested in multiple experiments with different retraction speeds from 3 microns/s to 300 microns/s. Analysis of the experimental data show that both Tanner’s and Blake’s equation can describe the correlation between the contact line velocity and the dynamic contact angle. In addition, both laws are employed in the direct numerical simulation of the bridge dynamics using 3D spectral boundary element method. Modeling results are compared with experimental data and show good agreement.

scholarly journals Experimental investigation on the effect of accelerating motion of contact line on the dynamic contact angle

2014 ◽  
Vol 80 (809) ◽  
pp. FE0004-FE0004 ◽  
Author(s):  
Takahiro ITO ◽  
Shoji HIRUTA ◽  
Ryota SHIMURA ◽  
Kenji KATOH ◽  
Tatsuro WAKIMOTO ◽  
...  
Keyword(s):  
Contact Angle ◽  
Experimental Investigation ◽  
Contact Line ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Accelerating Motion

scholarly journals On the microhydrodynamics of superspreading

2011 ◽  
Vol 670 ◽  
pp. 1-4 ◽  
Author(s):  
C. MALDARELLI
Keyword(s):  
Contact Angle ◽  
Aqueous Phase ◽  
Contact Line ◽  
Sessile Drop ◽  
Numerical Study ◽  
Dynamic Contact Angle ◽  
Hydrophobic Surface ◽  
Dynamic Contact ◽  
Spreading Rate ◽  
Spreading Rates

Droplets of an aqueous phase placed on a very hydrophobic, waxy surface bead-up rather than spread, forming a sessile drop with a relatively large contact angle at the edge of the drop. Surfactant molecules, when dissolved in the aqueous phase, can facilitate the wetting of an aqueous drop on a hydrophobic surface. One class of surfactants, superwetters, can cause aqueous droplets to move very rapidly over a hydrophobic surface, thereby completely wetting the surface (superspreading). A recent numerical study of the hydrodynamics of superspreading by Karapetsas, Craster & Matar (J. Fluid Mech., this issue, vol. 670, 2011, pp. 5–37) provides a clear explanation of how these surfactants cause such a dramatic change in wetting behaviour. The study shows that large spreading rates occur when the surfactant can transfer directly from the air/aqueous to the aqueous/hydrophobic solid interface at the contact line. This transfer reduces the concentration of surfactant on the fluid interface, which would otherwise be elevated due to the advection accompanying the drop spreading. The reduced concentration creates a Marangoni force along the fluid surface in the direction of spreading, and a concave rim in the vicinity of the contact line with a large dynamic contact angle. Both of these effects act to increase the spreading rate. The molecular structure of the superwetters allows them to assemble on a hydrophobic surface, enabling the direct transfer from the fluid to the solid surface at the contact line.

Slipping moving contact lines: critical roles of de Gennes’s ‘foot’ in dynamic wetting

2019 ◽  
Vol 873 ◽  
pp. 110-150
Author(s):  
Hsien-Hung Wei ◽  
Heng-Kwong Tsao ◽  
Kang-Ching Chu
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Capillary Number ◽  
Dynamic Contact Angle ◽  
Wall Slip ◽  
Dynamic Contact ◽  
Colloid Interface ◽  
Dynamic Wetting ◽  
Moving Contact Line ◽  
Moving Contact

In the context of dynamic wetting, wall slip is often treated as a microscopic effect for removing viscous stress singularity at a moving contact line. In most drop spreading experiments, however, a considerable amount of slip may occur due to the use of polymer liquids such as silicone oils, which may cause significant deviations from the classical Tanner–de Gennes theory. Here we show that many classical results for complete wetting fluids may no longer hold due to wall slip, depending crucially on the extent of de Gennes’s slipping ‘foot’ to the relevant length scales at both the macroscopic and microscopic levels. At the macroscopic level, we find that for given liquid height $h$ and slip length $\unicode[STIX]{x1D706}$, the apparent dynamic contact angle $\unicode[STIX]{x1D703}_{d}$ can change from Tanner’s law $\unicode[STIX]{x1D703}_{d}\sim Ca^{1/3}$ for $h\gg \unicode[STIX]{x1D706}$ to the strong-slip law $\unicode[STIX]{x1D703}_{d}\sim Ca^{1/2}\,(L/\unicode[STIX]{x1D706})^{1/2}$ for $h\ll \unicode[STIX]{x1D706}$, where $Ca$ is the capillary number and $L$ is the macroscopic length scale. Such a no-slip-to-slip transition occurs at the critical capillary number $Ca^{\ast }\sim (\unicode[STIX]{x1D706}/L)^{3}$, accompanied by the switch of the ‘foot’ of size $\ell _{F}\sim \unicode[STIX]{x1D706}Ca^{-1/3}$ from the inner scale to the outer scale with respect to $L$. A more generalized dynamic contact angle relationship is also derived, capable of unifying Tanner’s law and the strong-slip law under $\unicode[STIX]{x1D706}\ll L/\unicode[STIX]{x1D703}_{d}$. We not only confirm the two distinct wetting laws using many-body dissipative particle dynamics simulations, but also provide a rational account for anomalous departures from Tanner’s law seen in experiments (Chen, J. Colloid Interface Sci., vol. 122, 1988, pp. 60–72; Albrecht et al., Phys. Rev. Lett., vol. 68, 1992, pp. 3192–3195). We also show that even for a common spreading drop with small macroscopic slip, slip effects can still be microscopically strong enough to change the microstructure of the contact line. The structure is identified to consist of a strongly slipping precursor film of length $\ell \sim (a\unicode[STIX]{x1D706})^{1/2}Ca^{-1/2}$ followed by a mesoscopic ‘foot’ of width $\ell _{F}\sim \unicode[STIX]{x1D706}Ca^{-1/3}$ ahead of the macroscopic wedge, where $a$ is the molecular length. It thus turns out that it is the ‘foot’, rather than the film, contributing to the microscopic length in Tanner’s law, in accordance with the experimental data reported by Kavehpour et al. (Phys. Rev. Lett., vol. 91, 2003, 196104) and Ueno et al. (Trans. ASME J. Heat Transfer, vol. 134, 2012, 051008). The advancement of the microscopic contact line is still led by the film whose length can grow as the $1/3$ power of time due to $\ell$, as supported by the experiments of Ueno et al. and Mate (Langmuir, vol. 28, 2012, pp. 16821–16827). The present work demonstrates that the behaviour of a moving contact line can be strongly influenced by wall slip. Such slip-mediated dynamic wetting might also provide an alternative means for probing slippery surfaces.

Reinitialization of the Level-Set Function in 3d Simulation of Moving Contact Lines

2016 ◽  
Vol 20 (5) ◽  
pp. 1163-1182 ◽  
Author(s):  
Shixin Xu ◽  
Weiqing Ren
Keyword(s):  
Boundary Condition ◽  
Contact Angle ◽  
Level Set ◽  
Contact Line ◽  
Dynamic Contact Angle ◽  
Coupled System ◽  
Dynamic Contact ◽  
Moving Contact ◽  
Level Set Function ◽  
Set Function

AbstractThe level set method is one of the most successful methods for the simulation of multi-phase flows. To keep the level set function close the signed distance function, the level set function is constantly reinitialized by solving a Hamilton-Jacobi type of equation during the simulation. When the fluid interface intersects with a solid wall, a moving contact line forms and the reinitialization of the level set function requires a boundary condition in certain regions on the wall. In this work, we propose to use the dynamic contact angle, which is extended from the contact line, as the boundary condition for the reinitialization of the level set function. The reinitialization equation and the equation for the normal extension of the dynamic contact angle form a coupled system and are solved simultaneously. The extension equation is solved on the wall and it provides the boundary condition for the reinitialization equation; the level set function provides the directions along which the contact angle is extended from the contact line. The coupled system is solved using the 3rd order TVD Runge-Kutta method and the Godunov scheme. The Godunov scheme automatically identifies the regions where the angle condition needs to be imposed. The numerical method is illustrated by examples in three dimensions.

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