Vicinity Of Contact Line Research Articles

Hysteresis of Contact Angle of Sessile Droplets on Deformable Substrates: Influence of Disjoining Pressure

Liquid droplet placed on a deformable / soft substrate causes the substrate to deform. Combined action of capillary pressure and surface forces, which act in the vicinity of the apparent three-phase contact line and substrate's elasticity determine both the liquid shape and the substrate deformation. A theory of contact angle hysteresis of sessile liquid droplets on deformable/soft substrate is developed in terms of disjoining pressure isotherm, Πh, which accounts for the action of surface forces in the vicinity of the contact line. Minimum of excess free energy of the droplet on deformable substrate results in two interconnected equations for droplet and deformed substrate shapes in terms of disjoining pressure isotherm. A simplified s-shaped disjoining pressure isotherm, which allows direct calculations of static advancing/receding contact angles on deformable substrates, is adopted. Elasticity of the substrate is assumed to obey a simple Winkler's model for elastic surfaces. The obtained results are in agreement with the contact angle hysteresis theory developed earlier for non-deformable substrates. Calculated values of both advancing and receding contact angles for droplets on deformable substrate depend on droplet volume (which has a direct experimental confirmation). Advancing and receding contact angles of droplets on deformable substrates are lower as compared with those on a non-deformable substrate. The results of the derived model on hysteresis of contact angle on deformable substrates qualitatively agree with known experimental observations.

Numerical study on the stick-slip motion of contact line moving on heterogeneous surfaces

We present a numerical study of a moving contact line (CL) crossing the intersecting region of hydrophilic and hydrophobic patterns on a solid wall using lattice Boltzmann methods (LBMs). To capture the interface between the two phases properly, we applied a phase field model coupled with the LBM. The evolutions of the CL velocity, dynamic contact angle, and apparent contact angle are analyzed for the so-called “stick” and “slip” processes. In the two processes, the evolution of the quantities follows different rules shortly after the initial quick transition, which is probably caused by finite interfacial thickness or non-equilibrium effects. For the stick process, the CL is almost fixed and energy is extracted from the main flow to rebuild the meniscus’ profile. The evolution of the meniscus is mainly governed by mass conservation. The CL is depinned after the apparent contact angle surpasses the dynamic one, which implies that the interfacial segment in the vicinity of contact line is bended. For the slip process, the quantities evolve with features of relaxation. In the microscopic scale, the velocity of the CL depends on the balance between unbalanced Young’s capillary force and viscous drag. To predict the apparent contact angle evolution, a model following the dynamics of an overdamped spring-mass system is proposed. Our results also show that the capillary flows in a channel with heterogeneous wall can be described generally with the Poiseuille flow superimposed by the above transient one.

Unified slip boundary condition for fluid flows.

Determining the correct matching boundary condition is fundamental to our understanding of several everyday problems. Despite over a century of scientific work, existing velocity boundary conditions are unable to consistently explain and capture the complete physics associated with certain common but complex problems, such as moving contact lines and corner flows. The widely used Maxwell and Navier slip boundary conditions make an implicit assumption that velocity varies only in the wall normal direction. This makes their boundary condition inapplicable in the vicinity of contact lines and corner points, where velocity gradient exists both in the wall normal and wall tangential directions. In this paper, by identifying this implicit assumption we are able to extend Maxwell's slip model. Here, we present a generalized velocity boundary condition that shows that slip velocity is a function of not only the shear rate but also the linear strain rate. In addition, we present a universal relation for slip length, which shows that, for a general flow, slip length is a function of the principal strain rate. The universal relation for slip length along with the generalized velocity boundary condition provides a unified slip boundary condition to model a wide range of steady Newtonian fluid flows. We validate the unified slip boundary for simple Newtonian liquids by using molecular dynamics simulations and studying both the moving contact line and corner flow problems.

Fluid structure in the immediate vicinity of an equilibrium three-phase contact line and assessment of disjoining pressure models using density functional theory

We examine the nanoscale behavior of an equilibrium three-phase contact line in the presence of long-ranged intermolecular forces by employing a statistical mechanics of fluids approach, namely, density functional theory (DFT) together with fundamental measure theory (FMT). This enables us to evaluate the predictive quality of effective Hamiltonian models in the vicinity of the contact line. In particular, we compare the results for mean field effective Hamiltonians with disjoining pressures defined through (i) the adsorption isotherm for a planar liquid film, and (ii) the normal force balance at the contact line. We find that the height profile obtained using (i) shows good agreement with the adsorption film thickness of the DFT-FMT equilibrium density profile in terms of maximal curvature and the behavior at large film heights. In contrast, we observe that while the height profile obtained by using (ii) satisfies basic sum rules, it shows little agreement with the adsorption film thickness of the DFT results. The results are verified for contact angles of 20°, 40°, and 60°.

Validity of the equations for the contact angle on real surfaces

The wetting property between liquid and solid is very important in many industries besides natural systems. The simplest method to determine the wetting property is just dropping a liquid drop on a solid surface and measuring a contact angle from the shape of the drop. Since the Young’s equation has been used as a basic equation to relate a contact angle and interfacial tensions over 200 years, it is important to understand a derivation and limits of the Young’s equation. We derived the Young’s equation following energy minimization with simple mathematics. By expanding the derivation, the modified forms of the Cassie-Baxter equation and the Wenzel equation were also derived. From analyses of the derivations, it was deduced that a contact angle on an ideal surface is only related to the infinitesimal region in the vicinity of contact line, not internal area surrounded by the contact line. Although the Cassie-Baxter model and the Wenzel model were not rigorously built, they have been widely used for a superhydrophobic surface, because the apparent forms are similar to those of rigorously derived models when the contact line can easily move on the surface.

Coarse-graining MARTINI model for molecular-dynamics simulations of the wetting properties of graphitic surfaces with non-ionic, long-chain, and T-shaped surfactants

We report on a molecular dynamics investigation of the wetting properties of graphitic surfaces by various solutions at concentrations 1-8 wt. % of commercially available non-ionic surfactants with long hydrophilic chains, linear or T-shaped. These are surfactants of length up to 160 Å. It turns out that molecular dynamics simulations of such systems ask for a number of solvent particles that can be reached without seriously compromising computational efficiency only by employing a coarse-grained model. The MARTINI force field with polarizable water offers a framework particularly suited for the parameterization of our systems. In general, its advantages over other coarse-grained models are the possibility to explore faster long time scales and the wider range of applicability. Although the accuracy is sometimes put under question, the results for the wetting properties by pure water are in good agreement with those for the corresponding atomistic systems and theoretical predictions. On the other hand, the bulk properties of various aqueous surfactant solutions indicate that the micellar formation process is too strong. For this reason, a typical experimental configuration is better approached by preparing the droplets with the surfactants arranged in the initial state in the vicinity of contact line. Cross-comparisons are possible and illuminating, but equilibrium contact angles as obtained from simulations overestimate the experimental results. Nevertheless, our findings can provide guidelines for the preliminary assessment and screening of surfactants. Most importantly, it is found that the wetting properties mainly depend on the length and apolarity of the hydrophobic tail, for linear surfactants, and the length of the hydrophilic headgroup for T-shaped surfactants. Moreover, the T-shaped topology appears to favor the adsorption of surfactants onto the graphitic surface and faster spreading.

Flow and Stability of Rivulets on Heated Surfaces With Topography

Surfaces with topography promote rivulet flow patterns, which are characterized by a high cumulative length of contact lines. This property is very advantageous for evaporators and cooling devices, since the local evaporation rate in the vicinity of contact lines (microregion evaporation) is extremely high. The liquid flow in rivulets is subject to different kinds of instabilities, including the long-wave falling film instability (or the kinematic-wave instability), the capillary instability, and the thermocapillary instability. These instabilities may lead to the development of wavy flow patterns and to the rivulet rupture. We develop a model describing the hydrodynamics and heat transfer in flowing rivulets on surfaces with topography under the action of gravity, surface tension, and thermocapillarity. The contact line behavior is modeled using the disjoining pressure concept. The perfectly wetting case is described using the usual h−3 disjoining pressure. The partially wetting case is modeled using the integrated 6–12 Lennard-Jones potential. The developed model is used for investigating the effects of the surface topography, gravity, thermocapillarity, and the contact line behavior on the rivulet stability. We show that the long-wave thermocapillary instability may lead to splitting of the rivulet into droplets or into several rivulets, depending on the Marangoni number and on the rivulet geometry. The kinematic-wave instability may be completely suppressed in the case of the rivulet flow in a groove.

Deposition of Molten Ink Droplets on a Solid Surface

An experimental study on the deposition of micro-size droplets (∼39 μm in diameter) of molten wax ink on an aluminum surface is presented. Effects of initial temperature of droplets, substrate temperature and distance from printhead to substrate on the deposited droplet shape and textures were investigated. Depending on impact conditions, droplets may have either smooth or irregular edges, and the final shape may be either regular or two tiered. Analysis was conducted to compare the time scales for solidification, viscous damping and oscillation. A simple heat transfer model was developed, and temperature dependences of viscosity and surface tension were taken into account. The Ohnesorge number of droplets was investigated as a function of time to compare the transient effects of viscous damping and oscillation of the droplets after impact. The number of oscillations completed before the Ohnesorge number reaches unity agrees with the number of tiers formed. The height of the first tier was related to the value of the Ohnesorge number during the first oscillation. The thermal capillary effect was evaluated by defining and examining two Marangoni numbers for the spreading and post-spreading phases of the droplet impact. Splashing of droplets occurred and produced fingers around the droplet peripheries, which was mainly determined by local solidification and spreading dynamics in the vicinity of contact line.

207 接触線近傍の流れ場の測定及び線形理論との比較(GS5-2 流体(液体流れ))

207 接触線近傍の流れ場の測定及び線形理論との比較(GS5-2 流体(液体流れ))