Young Angle Research Articles

Contact angles for perfectly wetting pure liquids evaporating into air: Between de Gennes-type and other classical models

Even when a liquid is perfectly wetting on a smooth substrate (zero Young's angle), it can manifest finite contact angles if evaporating. These angles are of a dynamic, evaporation-induced nature, a compromise between the tendencies to spread and to evaporate. They form as a result of the resolution of a macroscopic evaporation-flux singularity at a microscopic scale in a tiny vicinity of the contact line referred to as the microregion. A critical evaluation generalizes and unifies the various models thereof, for nonpolar liquids undergoing diffusion-limited evaporation into air, and compares them with experiment.

An improved threshold dynamics method for wetting dynamics

We propose a modified threshold dynamics method for wetting dynamics, which significantly improves the behavior near the contact line compared to the previous method (J. Comput. Phys. 330 (2017) 510–528). The new method is also based on minimizing the functional consisting of weighted interface areas over an extended domain including the solid phase. However, each interface area is approximated by the Lyapunov functional with a different Gaussian kernel. We show that a correct contact angle (Young's angle) is obtained in the leading order by choosing correct Gaussian kernel variances. We also show the Gamma convergence of the functional to the total surface energy. The method is simple, unconditionally stable with O(NlogN) computational complexity per time step and is not sensitive to the inhomogeneity or roughness of the solid surface. It is also shown that the dynamics of the contact point is consistent with the dynamics of the interface away from the contact point. Numerical examples have shown significant improvements in the accuracy of the contact angle and the hysteresis behavior of the contact angle.

Thermal fluctuations of an interface near a contact line.

The effect of thermal fluctuations near a contact line of a liquid interface partially wetting an impenetrable substrate is studied analytically and numerically. Promoting both the interface profile and the contact line position to random variables, we explore the equilibrium properties of the corresponding fluctuating contact line problem based on an interfacial Hamiltonian involving a "contact" binding potential. To facilitate an analytical treatment, we consider the case of a one-dimensional interface. The effective boundary condition at the contact line is determined by a dimensionless parameter that encodes the relative importance of thermal energy and substrate energy at the microscopic scale. We find that this parameter controls the transition from a partial wetting to a pseudopartial wetting state, the latter being characterized by a thin prewetting film of fixed thickness. In the partial wetting regime, instead, the profile typically approaches the substrate via an exponentially thinning prewetting film. We show that, independently of the physics at the microscopic scale, Young's angle is recovered sufficiently far from the substrate. The fluctuations of the interface and of the contact line give rise to an effective disjoining pressure, exponentially decreasing with height. Fluctuations therefore provide a regularization of the singular contact forces occurring in the corresponding deterministic problem.

Sharp interface model for solid-state dewetting problems with weakly anisotropic surface energies

We propose a sharp interface model for simulating solid-state dewetting where the surface energy is (weakly) anisotropic. The morphology evolution of thin films is governed by surface diffusion and contact line migration. The mathematical model is based on an energy variational approach. Anisotropic surface energies lead to multiple solutions of the contact angle equation at contact points. Introduction of a finite contact point mobility is both physically based and leads to robust, unambiguous determination of the contact angles. We implement the mathematical model in an explicit finite difference scheme with cubic spline interpolation for evolving marker points. Following validation of the mathematical and numerical approaches, we simulate the evolution of thin film islands, semi-infinite films, and films with holes as a function of film dimensions, Young's angle $\theta_i$, anisotropy strength and crystal symmetry, and film crystal orientation relative to the substrate normal. We find that the contact point retraction rate can be well described by a power-law, $l \sim t^n$. Our results demonstrate that the exponent $n$ is not universal -- it is sensitive to the Young's angle $\theta_i$ (and insensitive to anisotropy). In addition to classical wetting (where holes in a film heal) and dewetting (where holes in a film grow), we observe cases where a hole through the film heals but leave a finite size hole/bubble between the continuous film and substrate or where the hole heals leaving a continuous film that is not bonded to the substrate. Surface energy anisotropy (i) increases the instability that leads to island break-up into multiple islands, (ii) enhances hole healing, and (iii) leads to finite island size even under some conditions where the Young's angle $\theta_i$ suggests that the film wets the substrate.

Use of electrowetting to measure dynamic interfacial tensions of a microdrop

The adsorption of surface active species to liquid-liquid and to solid-liquid interfaces can have dramatic effects in microfluidics. In this paper we show how electrowetting on dielectric can be used to monitor a dynamic liquid-liquid interfacial tension (IFT) with a time resolution of O(1 s) using amplitude modulation of the AC voltage. This straightforward method, which requires less than a microlitre of sample, is demonstrated for aqueous drops containing Triton X-100 surfactant on a Teflon AF-coated substrate and with heptane as the immiscible oil ambient. Under these conditions, next to extracting the oil-water IFT (γ(ow)), also the effective water-substrate IFT difference (Δγ(ws)) can be obtained from the oil-water IFT and the Young's angle. Both γ(ow) and γ(ws) decrease over time due to adsorption. The measured dynamic oil-water IFT compares well to results of pendant drop experiments.

Numerical simulation of the shape of charged drops over a solid surface

In this work we study the static shape of charged drops of a conducting fluid placed over a solid substrate, surrounded by a gas, and in absence of gravitational forces. The problem can be posed, since Gauss, in a variational setting consisting of obtaining the configurations of a given mass of fluid that minimize (or in general make extremal) a certain energy involving the areas of the solid-liquid interface and of the liquid-gas interface, as well as the electric capacity of the drop. In [6] we have found, as a function of two parameters, Young's angle θY and the potential at the drop's surface V0, the axisymmetric minimizers of the energy. In the same article we have also described their shape and showed the existence of symmetry-breaking bifurcations such that, for given values of θY and V0, configurations for which the axial symmetry is lost are energetically more favorable than axially symmetric configurations. We have proved the existence of such bifurcations in the limits of very flat and almost spherical equilibrium shapes. In this work we study all other cases numerically. When dealing with radially perturbed equilibrium shapes we lose the axially symmetric properties and need to do a full three-dimensional approximation in order to compute area and capacity and hence the energy. We use a boundary element method that we have already implemented in [3] to compute the surface charge density. From the surface charge density we can obtain the capacity of the body. One conclusion of this study is that axisymmetric drops cannot spread indefinitely by introducing sufficient amount of electric charges, but can reach only a limiting (saturation) size, after which the axial symmetry would be lost and finger-like shapes energetically preferred.

The Shape of Charged Drops over a Solid Surface and Symmetry-Breaking Instabilities

We study the static shape of charged drops of a conducting fluid placed over a solid substrate, surrounded by a gas, and in absence of gravitational forces. The question can be formulated as a variational problem where a certain energy involving the areas of the solid-liquid interface and of the liquid-gas interface, as well as the electric capacity of the drop, has to be minimized. As a function of two parameters, Young's angle and the potential at the drop's surface , we find the axisymmetric minimizers of the energy and describe their shape. We also discuss the existence of symmetry-breaking bifurcations such that, for given values of and , configurations for which the axial symmetry is lost are energetically more favorable than axially symmetric configurations. We prove the existence of such bifurcations in the limits of very flat and almost spherical equilibrium shapes. All other cases are studied numerically with a boundary integral method. One conclusion of this study is that axisymmetric drops cannot spread indefinitely by introducing sufficient amount of electric charges, but can reach only a limiting (saturation) size, after which the axial symmetry would be lost and finger-like shapes energetically preferred.