Thermocapillary migration of a two-dimensional liquid droplet on a solid surface

A two-dimensional liquid droplet placed on a non-uniformly heated solid surface will move towards the region of colder temperatures if the temperature gradient in the solid surface is large enough. Such behaviour is analysed for a thin viscous droplet using lubrication theory to develop an evolution equation for the shape of the droplet. For the small mobility capillary numbers examined in this work, the contact-line motion is controlled by a dynamic relationship posed between the contact-line speed and the apparent contact angle. Results are obtained numerically and also approximately using a perturbation technique for small heating. The initial spreading or shrinking of the droplet when placed on the heated solid is biased toward the direction of decreasing temperature on the solid. Possible steady-state responses are either a motionless droplet or one moving at a constant velocity down the temperature gradient without change in shape. These behaviours are the result of a thermocapillary recirculation cell inside the droplet that distorts the free surface and alters the apparent contact angles. This change in the apparent contact angles then modifies the contact-line speed.

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Is contact angle a cause or an effect? – A cautionary tale

E3S Web of Conferences ◽

10.1051/e3sconf/202014603004 ◽

2020 ◽

Vol 146 ◽

pp. 03004

Author(s):

Douglas Ruth

Keyword(s):

Contact Angle ◽

Solid Surface ◽

Contact Angles ◽

Two Dimensions ◽

Experimental Results ◽

Flow In Porous Media ◽

Two Dimensional ◽

Wide Range ◽

Fluid Drop ◽

Surrounding Fluid

The most influential parameter on the behavior of two-component flow in porous media is “wettability”. When wettability is being characterized, the most frequently used parameter is the “contact angle”. When a fluid-drop is placed on a solid surface, in the presence of a second, surrounding fluid, the fluid-fluid surface contacts the solid-surface at an angle that is typically measured through the fluid-drop. If this angle is less than 90°, the fluid in the drop is said to “wet” the surface. If this angle is greater than 90°, the surrounding fluid is said to “wet” the surface. This definition is universally accepted and appears to be scientifically justifiable, at least for a static situation where the solid surface is horizontal. Recently, this concept has been extended to characterize wettability in non-static situations using high-resolution, two-dimensional digital images of multi-component systems. Using simple thought experiments and published experimental results, many of them decades old, it will be demonstrated that contact angles are not primary parameters – their values depend on many other parameters. Using these arguments, it will be demonstrated that contact angles are not the cause of wettability behavior but the effect of wettability behavior and other parameters. The result of this is that the contact angle cannot be used as a primary indicator of wettability except in very restricted situations. Furthermore, it will be demonstrated that even for the simple case of a capillary interface in a vertical tube, attempting to use simply a two-dimensional image to determine the contact angle can result in a wide range of measured values. This observation is consistent with some published experimental results. It follows that contact angles measured in two-dimensions cannot be trusted to provide accurate values and these values should not be used to characterize the wettability of the system.

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Macroscopic Wetting Behavior of a Two-Dimensional Meniscus Under a Horizontal Plate

Journal of Fluids Engineering ◽

10.1115/1.2817145 ◽

1995 ◽

Vol 117 (2) ◽

pp. 303-308 ◽

Cited By ~ 2

Author(s):

Kenji Katoh ◽

Hideomi Fujita ◽

Hideharu Sasaki

Keyword(s):

Solid Surface ◽

Contact Angles ◽

Two Dimensional ◽

Horizontal Plate ◽

Wetting Behavior ◽

Made In

The purpose of this study is to investigate macroscopic wetting behavior and to verify the validity of the assumption made in the analysis of the preceding report that the complicated effects of the microscopic structures of the solid surface such as roughness or heterogeneity on the macroscopic wetting behavior are simply represented by the values of the apparent contact angles. The unstable phenomenon of a two-dimensional meniscus under a horizontal plate, in which the meniscus falls spontaneously at a certain height of the plate, is considered theoretically from a thermodynamic viewpoint. The results of the analysis based on the above assumption agree with those by an analysis in which the effect of microscopic structures of the solid surface, such as roughness and heterogeneity, are taken into consideration. Therefore, the validity of the assumption made in the preceding report is verified.

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Sessile Droplets on Deformable Substrates

Colloids and Interfaces ◽

10.3390/colloids2040056 ◽

2018 ◽

Vol 2 (4) ◽

pp. 56

Author(s):

Gulraiz Ahmed ◽

Nektaria Koursari ◽

Anna Trybala ◽

Victor M. Starov

Keyword(s):

Free Energy ◽

Contact Line ◽

Liquid Droplet ◽

Excess Free Energy ◽

Surface Elasticity ◽

Contact Angles ◽

Interfacial Behavior ◽

Phase Contact ◽

Technological Advances ◽

Three Phase

Wetting of deformable substrates has gained significant interest over the past decade due to a multiplicity of industrial and biological applications. Technological advances in the area of interfacial science have given rise to the ability to capture interfacial behavior between a liquid droplet and an elastic substrate. Researchers have developed several theories to explain the interaction between the two phases and describe the process of wetting of deformable/soft substrates. A summary of the most recent advances on static wetting of deformable substrates is given in this review. It is demonstrated that action of surface forces (disjoining/conjoining pressure) near the apparent three-phase contact line should be considered. Any consideration of equilibrium droplets on deformable (as well as on non-deformable) substrates should be based on consideration of the excess free energy of the system. The equilibrium shapes of both droplet and deformable substrate should correspond to the minimum of the excess free energy of the system. It has never been considered in the literature that the obtained equilibrium profiles must satisfy sufficient Jacobi’s condition. If Jacobi’s condition is not satisfied, it is impossible to claim that the obtained solution really corresponds to equilibrium. In recently published studies, equilibrium of droplets on deformable substrates: (1) provided a solution that corresponds to the minimum of the excess free energy; and (2) the obtained solution satisfies the Jacobi’s condition. Based on consideration of disjoining/conjoining pressure acting in the vicinity of the apparent three-phase contact line, the hysteresis of contact angle of sessile droplets on deformable substrates is considered. It is shown that both advancing and receding contact angles decrease as the elasticity of the substrate is increased and the effect of disjoining/conjoining pressure is discussed. Fluid inside the droplet partially wets the deformable substrate. It is shown that just these forces coupled with the surface elasticity determine the deformation of the deformable substrates.

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Inertial and viscous effects on dynamic contact angles

Journal of Fluid Mechanics ◽

10.1017/s0022112097008112 ◽

1998 ◽

Vol 357 ◽

pp. 249-278 ◽

Cited By ~ 86

Author(s):

R. G. COX

Keyword(s):

Reynolds Number ◽

Solid Surface ◽

Contact Line ◽

Capillary Number ◽

Slip Length ◽

Stress Singularity ◽

Dynamic Contact Angle ◽

Dynamic Contact ◽

Contact Angles ◽

Viscous Effects

An investigation is made into the dynamics involved in the movement of the contact line when a single liquid with an interface moves into a vacuum over a smooth solid surface. In order to remove the stress singularity at the contact line, it is postulated that slip between the liquid and the solid or some other mechanism occurs very close to the contact line. It is assumed that the flow produced is inertia dominated with the Reynolds number based on the slip length being very large. Following a procedure similar to that used by Cox (1986) for the viscous-dominated situation (in which the Reynolds number based on the macroscopic length scale was assumed very small) using matched asymptotic expansions, we obtain the dependence of the macroscopic dynamic contact angle on the contact line velocity over the solid surface for small capillary number and small slip length to macroscopic lengthscale ratio. These results for the inertia-dominated situation are then extended (at the lowest order in capillary number) to an intermediate Reynolds number situation with the Reynolds number based on the slip length being very small and that based on the macroscopic lengthscale being very large.

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