The moving contact line with a 180° advancing contact angle

1984 ◽  
Vol 27 (12) ◽  
pp. 2785 ◽  
Author(s):  
C. G. Ngan ◽  
E. B. Dussan V
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Advancing Contact Angle

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.

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.

Numerical analysis of moving contact line with contact angle hysteresis using feedback deceleration technique

2012 ◽  
Vol 24 (4) ◽  
pp. 042105 ◽  
Author(s):  
Jun Kwon Park ◽  
Kwan Hyoung Kang
Keyword(s):  
Contact Angle ◽  
Numerical Analysis ◽  
Contact Line ◽  
Contact Angle Hysteresis ◽  
Moving Contact Line ◽  
Moving Contact

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.

Contact-line dynamics of a diffuse fluid interface

2000 ◽  
Vol 402 ◽  
pp. 57-88 ◽  
Author(s):  
DAVID JACQMIN
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Chemical Potential ◽  
Equilibrium Contact Angle ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Potential Gradients ◽  
Inner Region ◽  
Chemical Potential Gradients ◽  
Contact Line Dynamics

An investigation is made into the moving contact line dynamics of a Cahn–Hilliard–van der Waals (CHW) diffuse mean-field interface. The interface separates two incompressible viscous fluids and can evolve either through convection or through diffusion driven by chemical potential gradients. The purpose of this paper is to show how the CHW moving contact line compares to the classical sharp interface contact line. It therefore discusses the asymptotics of the CHW contact line velocity and chemical potential fields as the interface thickness ε and the mobility κ both go to zero. The CHW and classical velocity fields have the same outer behaviour but can have very different inner behaviours and physics. In the CHW model, wall–liquid bonds are broken by chemical potential gradients instead of by shear and change of material at the wall is accomplished by diffusion rather than convection. The result is, mathematically at least, that the CHW moving contact line can exist even with no-slip conditions for the velocity. The relevance and realism or lack thereof of this is considered through the course of the paper.The two contacting fluids are assumed to be Newtonian and, to a first approximation, to obey the no-slip condition. The analysis is linear. For simplicity most of the analysis and results are for a 90° contact angle and for the fluids having equal dynamic viscosity μ and mobility κ. There are two regions of flow. To leading order the outer-region velocity field is the same as for sharp interfaces (flow field independent of r) while the chemical potential behaves like r−ξ, ξ = π/2/max{θeq, π − θeq}, θeq being the equilibrium contact angle. An exception to this occurs for θeq = 90°, when the chemical potential behaves like ln r/r. The diffusive and viscous contact line singularities implied by these outer solutions are resolved in the inner region through chemical diffusion. The length scale of the inner region is about 10√μκ – typically about 0.5–5 nm. Diffusive fluxes in this region are O(1). These counterbalance the effects of the velocity, which, because of the assumed no-slip boundary condition, fluxes material through the interface in a narrow boundary layer next to the wall.The asymptotic analysis is supplemented by both linearized and nonlinear finite difference calculations. These are made at two scales, experimental and nanoscale. The first set is done to show CHW interface behaviour and to test the qualitative applicability of the CHW model and its asymptotic theory to practical computations of experimental scale, nonlinear, low capillary number flows. The nanoscale calculations are carried out with realistic interface thicknesses and diffusivities and with various assumed levels of shear-induced slip. These are discussed in an attempt to evaluate the physical relevance of the CHW diffusive model. The various asymptotic and numerical results together indicate a potential usefullness for the CHW model for calculating and modelling wetting and dewetting flows.

scholarly journals Numerical Investigation of Different Dynamic Contact Angle Models for a Droplet Impacting a Surface in OpenFOAM

2019 ◽  
Vol 3 (1) ◽  
pp. 9-17
Author(s):  
Ndivhuwo Musehane ◽  
Rhameez Herbst
Keyword(s):  
Surface Tension ◽  
Contact Angle ◽  
Contact Line ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Navier Stokes ◽  
Spreading Process ◽  
Moving Contact Line ◽  
Continuity Equations ◽  
Moving Contact

Computational Fluid Dynamics (CFD) is used to study the spreading process of a water droplet with a radius of 0.00275mm impacting a wax surface at a velocity of 1.18ms−1 . This type of flow is considered to be Multiphase, incompressible, laminar, surface tension dominated and is governed by the Navier stokes and continuity equations. To accurately model the spreading process 3 different contact angle models are investigated, two of which take into account the moving contact line. The governing equations are solved using the open source C++ library OpenFOAM, which uses a Finite Volume Method (FVM) of discretization and a Volume Of Fluid (VOF) interface capturing method. The VOF method is known to produce unphysical velocities when high pressure gradients exist between the two phases, thus a numerical improvement is implemented to reduce the magnitudes of the unphysical velocities. The improvement reduces the magnitudes of the unphysical velocities and as shown in literature their magnitudes increase with an increase in surface tension dominance. The improvement is implemented together with different contact angle models and results obtained show that contact angle models that take into account the moving contact line gives a good correlation of the spreading diameter obtained numerically with the one obtained experimentally.

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