scholarly journals Evaporation of sessile drops: a three-dimensional approach

2015 ◽  
Vol 772 ◽  
pp. 705-739 ◽  
Author(s):  
P. J. Sáenz ◽  
K. Sefiane ◽  
J. Kim ◽  
O. K. Matar ◽  
P. Valluri
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Evaporation Rate ◽  
Three Dimensional ◽  
Complex Case ◽  
Interface Temperature ◽  
Angle Distribution ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Sessile Drops

The evaporation of non-axisymmetric sessile drops is studied by means of experiments and three-dimensional direct numerical simulations (DNS). The emergence of azimuthal currents and pairs of counter-rotating vortices in the liquid bulk flow is reported in drops with non-circular contact area. These phenomena, especially the latter, which is also observed experimentally, are found to play a critical role in the transient flow dynamics and associated heat transfer. Non-circular drops exhibit variable wettability along the pinned contact line sensitive to the choice of system parameters, and inversely dependent on the local contact-line curvature, providing a simple criterion for estimating the approximate contact-angle distribution. The evaporation rate is found to vary in the same order of magnitude as the liquid–gas interfacial area. Furthermore, the more complex case of drops evaporating with a moving contact line (MCL) in the constant contact-angle mode is addressed. Interestingly, the numerical results demonstrate that the average interface temperature remains essentially constant as the drop evaporates in the constant-angle (CA) mode, while this increases in the constant-radius (CR) mode as the drops become thinner. It is therefore concluded that, for increasing substrate heating, the evaporation rate increases more rapidly in the CR mode than in the CA mode. In other words, the higher the temperature the larger the difference between the lifetimes of an evaporating drop in the CA mode with respect to that evaporating in the CR mode.

Numerical and theoretical analyses of the dynamics of droplets driven by electrowetting on dielectric in a Hele-Shaw cell

2018 ◽  
Vol 839 ◽  
pp. 468-488 ◽  
Author(s):  
Yasufumi Yamamoto ◽  
Takahiro Ito ◽  
Tatsuro Wakimoto ◽  
Kenji Katoh
Keyword(s):  
Theoretical Model ◽  
Contact Line ◽  
Three Dimensional ◽  
Simulation Method ◽  
Movement Speed ◽  
Electrowetting On Dielectric ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Droplet Movement ◽  
Hele Shaw Cell

Droplet movement by electrowetting on dielectric (EWOD) in a Hele-Shaw cell is analysed theoretically and numerically. We propose a simple theoretical model for the motion, which describes well the voltage dependency of droplet speed below the saturation voltage as measured experimentally. The simulation method for numerical analyses is constructed by using the Young–Lippmann equation to represent EWOD and the generalised Navier boundary condition to represent the moving contact line in the context of the front-tracking method. With an adjusted slip parameter, the present full three-dimensional numerical simulation reproduces well the shape evolution and movement speed of droplets as observed experimentally. We verify the proposed theoretical model in numerical experiments with various shapes and voltages. Furthermore, we analyse theoretically the behaviour of the contact line at the onset of droplet motion as observed in the simulation and experiment, and we are able to estimate very well the time scale on which the contact angle changes.

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.

Moving contact lines in liquid/liquid/solid systems

1997 ◽  
Vol 334 ◽  
pp. 211-249 ◽  
Author(s):  
YULII D. SHIKHMURZAEV
Keyword(s):  
Mathematical Model ◽  
Surface Tension ◽  
Contact Angle ◽  
Flow Field ◽  
Contact Line ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Three Phase

A general mathematical model which describes the motion of an interface between immiscible viscous fluids along a smooth homogeneous solid surface is examined in the case of small capillary and Reynolds numbers. The model stems from a conclusion that the Young equation, σ1 cos θ = σ2 − σ3, which expresses the balance of tangential projection of the forces acting on the three-phase contact line in terms of the surface tensions σi and the contact angle θ, together with the well-established experimental fact that the dynamic contact angle deviates from the static one, imply that the surface tensions of contacting interfaces in the immediate vicinity of the contact line deviate from their equilibrium values when the contact line is moving. The same conclusion also follows from the experimentally observed kinematics of the flow, which indicates that liquid particles belonging to interfaces traverse the three-phase interaction zone (i.e. the ‘contact line’) in a finite time and become elements of another interface – hence their surface properties have to relax to new equilibrium values giving rise to the surface tension gradients in the neighbourhood of the moving contact line. The kinematic picture of the flow also suggests that the contact-line motion is only a particular case of a more general phenomenon – the process of interface formation or disappearance – and the corresponding mathematical model should be derived from first principles for this general process and then applied to wetting as well as to other relevant flows. In the present paper, the simplest theory which uses this approach is formulated and applied to the moving contact-line problem. The model describes the true kinematics of the flow so that it allows for the ‘splitting’ of the free surface at the contact line, the appearance of the surface tension gradients near the contact line and their influence upon the contact angle and the flow field. An analytical expression for the dependence of the dynamic contact angle on the contact-line speed and parameters characterizing properties of contacting media is derived and examined. The role of a ‘thin’ microscopic residual film formed by adsorbed molecules of the receding fluid is considered. The flow field in the vicinity of the contact line is analysed. The results are compared with experimental data obtained for different fluid/liquid/solid systems.

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.

scholarly journals Forced dewetting on porous media

2007 ◽  
Vol 574 ◽  
pp. 343-364 ◽  
Author(s):  
OLIVIER DEVAUCHELLE ◽  
CHRISTOPHE JOSSERAND ◽  
STEPHANE ZALESKI
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Capillary Number ◽  
Porous Plate ◽  
Capillary Length ◽  
Moving Contact Line ◽  
Lubrication Equation ◽  
Moving Contact ◽  
Medium Permeability ◽  
Critical Capillary Number

We study the dewetting of a porous plate withdrawn from a liquid bath. The contact angle is fixed to zero and the flow is assumed to be almost parallel to the plate (lubrication approximation). The ordinary differential equation involving the position of the water surface is analysed in phase space by means of numerical integration. We show the existence of a stationary moving contact line with zero contact angle below a critical value of the capillary number η U/γ. Above this value, no stationary contact line can exist. An analytical model, based on asymptotic matching is developed, which reproduces the dependence of the critical capillary number on the angle of the plate with respect to the horizontal (3/2 power law), provided the capillary length is much larger than the square root of the porous-medium permeability. In addition, it is shown that the classical lubrication equation leads not only to the well-known Landau–Levich–Derjaguin films, but also to a family of films for which thickness is not imposed by the problem parameters.

Moffatt vortices induced by the motion of a contact line

2014 ◽  
Vol 746 ◽  
Author(s):  
E. Kirkinis ◽  
S. H. Davis
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Solid Substrate ◽  
Hydrodynamic Theory ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Secular Equations ◽  
Limiting Case

AbstractA recent hydrodynamic theory of liquid slippage on a solid substrate (Kirkinis & Davis, Phys. Rev. Lett., vol. 110, 2013, 234503) gives rise to a sequence of eddies (Moffatt vortices) that co-move with a moving contact line (CL) in a liquid wedge. The presence of these vortices is established through secular equations that depend on the dynamic contact angle $\alpha $ and capillary number Ca. The limiting case $\alpha \rightarrow 0$ is associated with the appearance of such vortices in a channel. The vortices are generated by the relative motion of the interfaces, which in turn is due to the motion of the CL. This effect has yet to be observed in experiment.

Moving contact-line mobility measured

2018 ◽  
Vol 841 ◽  
pp. 767-783 ◽  
Author(s):  
Yi Xia ◽  
Paul H. Steen
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Experimental Approach ◽  
Sessile Drop ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Contact Angles ◽  
Stick Slip ◽  
Moving Contact Line ◽  
Moving Contact

Contact-line mobility characterizes how fast a liquid can wet or unwet a solid support by relating the contact angle $\unicode[STIX]{x0394}\unicode[STIX]{x1D6FC}$ to the contact-line speed $U_{CL}$. The contact angle changes dynamically with contact-line speeds during rapid movement of liquid across a solid. Speeds beyond the region of stick–slip are the focus of this experimental paper. For these speeds, liquid inertia and surface tension compete while damping is weak. The mobility parameter $M$ is defined empirically as the proportionality, when it exists, between $\unicode[STIX]{x0394}\unicode[STIX]{x1D6FC}$ and $U_{CL}$, $M\unicode[STIX]{x0394}\unicode[STIX]{x1D6FC}=U_{CL}$. We discover that $M$ exists and measure it. The experimental approach is to drive the contact line of a sessile drop by a plane-normal oscillation of the drop’s support. Contact angles, displacements and speeds of the contact line are measured. To unmask the mobility away from stick–slip, the diagram of $\unicode[STIX]{x0394}\unicode[STIX]{x1D6FC}$ against $U_{CL}$, the traditional diagram, is remapped to a new diagram by rescaling with displacement. This new diagram reveals a regime where $\unicode[STIX]{x0394}\unicode[STIX]{x1D6FC}$ is proportional to $U_{CL}$ and the slope yields the mobility $M$. The experimental approach reported introduces the cyclically dynamic contact angle goniometer. The concept and method of the goniometer are illustrated with data mappings for water on a low-hysteresis non-wetting substrate.

Experimental and theoretical study of dewetting corner flow

2014 ◽  
Vol 762 ◽  
pp. 393-416 ◽  
Author(s):  
Hyoungsoo Kim ◽  
Christian Poelma ◽  
Gijs Ooms ◽  
Jerry Westerweel
Keyword(s):  
Flow Pattern ◽  
Contact Line ◽  
Dynamic Pressure ◽  
Three Dimensional ◽  
Internal Flow ◽  
Pressure Effects ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Corner Flow ◽  
Analytical Results

AbstractWe study a partial dewetting corner flow with a moving contact line at a finite Reynolds number, $0<\mathit{Re}<O(100)$. When the speed of the moving contact line increases, the receding contact line appears with a corner shape that is also observed in a gravity-driven liquid droplet on an incline and on a plate withdrawn from a bath. In the current problem, $\mathit{Re}\,{\it\epsilon}$ is larger than unity, where ${\it\epsilon}$ is the aspect ratio of the flow structure. Therefore, classical lubrication theory is no longer appropriate. We develop a modified three-dimensional lubrication model for the dewetting corner structure at $\mathit{Re}\,{\it\epsilon}>1$ by taking into account the internal flow pattern and by scaling arguments. The key requirement is that the streamlines in the corner are straight and (nearly) parallel. In this case, we can obtain a modified pressure consisting of the capillary pressure and the dynamic pressure. This model describes the three-dimensional dewetting corner structure at the rear of the moving droplets at $\mathit{Re}\,{\it\epsilon}>1$ and furthermore shows that the dynamic pressure effects become dominant at a small half-opening angle. Additionally, this model provides analytical results for the internal flow, which is a self-similar flow pattern. To validate the analytical results, we perform high-speed shadowgraphy and tomographic particle image velocimetry (PIV). We find a good agreement between the theoretical and the experimental results.

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