We develop a thermodynamically consistent phase-field model for soluble surfactants in two-phase flows, incorporating both interfacial and solid surface adsorption. The model is derived via variational principles consistent with the second law of thermodynamics, resulting in modified free energies and boundary conditions that capture surfactant transport, adsorption and wetting dynamics. A key contribution of this work is the inclusion of surfactant adsorption on solid walls, which leads to qualitative agreement with experimental observations: unlike prior numerical studies that predicted hydrophilic surfaces becoming more hydrophilic and hydrophobic surfaces more hydrophobic, our model shows a shift towards increased hydrophilicity across all contact angles-consistent with experimental trends. Our results establish that solid adsorption provides the missing mechanism required for predictive modelling of surfactant-laden contact line dynamics.

Dynamic wetting poses a well-known challenge in classical sharp-interface formulation as the no-slip wall condition leads to a contact line singularity that is typically regularized with a Navier boundary condition, often requiring empirical fitting for the slip length. On the other hand, this paradox does not appear in phase-field models as the contact line moves through diffusive mass transport. In this work, we present a toy model that accounts for mass diffusion at the contact line within a sharp-interface framework. This model is based on a theoretical relation derived from the Cahn-Hilliard equations, which links the total diffusive mass transport to the curvature at the wall. From an estimate of the chemical potential on a curved interface, we obtain an expression for the width of the highly curved region δ and the apparent angle. In the sharp-interface model, we then introduce a fictitious boundary, displaced by a distance δ into the domain, where a Navier boundary condition is applied along a dynamic apparent contact angle that accounts for the local interface bending. The robustness of the model is assessed by comparing the toy model results with standard phase-field ones on two cases: the steady state profiles of a liquid bridge between two plates moving in opposite directions and the transient behaviors of a drop spreading on a solid with a prescribed equilibrium angle. This offers a practical and efficient alternative to solve contact line problems at lower cost in a sharp-interface framework with input parameters from phase-field models.

A computational and experimental study of the heat and fluid flow occurring in weld pools during gas tungsten arc welding of Type 304 stainless steel is carried out. A two-dimensional, time-dependent, axisymmetric, numerical model, based on a finite element approach, was developed. Great emphasis was put on the capability of the model to deal with simulations using highly resolved grids. The rather complete model considers buoyancy, electromagnetic and surface tension forces and additionally weld metal vaporisation and the temperature dependence of the coefficient of surface tension. To confirm the predicted characteristic weld pool shapes a comparison with experiments on GTA-welded Type 304 stainless steel plates is presented. Welds on steel containing extra low sulphur and high sulphur were carried out for different times and for varying heat input conditions. The electrode was held stationary and the work-piece was cooled by a copper plate. The experimentally obtained weld pool shapes coincide with the ones predicted in the computations. For welds on steels with low sulphur content it is found that the weld pool shape is deeper at the periphery than at the center at early times, while the depth at the center increases as times proceeds. Increasing the heat input the weld pool shape can be mainly characterised by the formation of two grooves: one at the periphery and one at the weld pool center which is deeper than the one at the periphery. A higher sulphur content in the base material deepens, as expected, the weld pool, while the width of the weld pool is decreased. Based on this comparison the mechanisms behind the development of the different weld pool shapes are explained.

Using experiments and numerical simulations, we investigate the spontaneous spread-ing of droplets of aqueous glycerol (Newtonian) and aqueous polymer (shear-thinning) solutions on smooth surfaces. We find that in the first millisecond the spreading of the shear-thinning solutions is identical to the spreading of water, regardless of the polymer concentration. In contrast, aqueous glycerol solutions show a different behavior, namely, a significantly slower spreading rate than water. In the initial rapid spreading phase, the dominating forces that can resist the wetting are inertial forces and contact-line friction. For the glycerol solutions, an increase in glycerol concentration effectively increases the contact-line friction, resulting in increased resistance to wetting. For the polymeric solutions, however, an increase in polymer concentration does not modify contact-line friction. As a consequence, the energy dissipation at the contact line cannot be controlled by varying the amount of additives for shear-thinning fluids. The reduction of the spreading rate of shear-thinning fluids on smooth surfaces in the rapid-wetting regime can only be achieved by increasing solvent viscosity. Our results have implications for phase-change applications where the control of the rapid spreading rate is central, such as anti-icing and soldering.

The experimental results of Xia and Steen for the contact line dynamics of a drop placed on a vertically oscillating surface are analyzed by numerical phase field simulations. The concept of contact line mobility or friction is discussed, and an angle-dependent model is formulated. The results of numerical simulations based on this model are compared to the detailed experimental results of Xia and Steen with good general agreement. The total energy input in terms of work done by the oscillating support, and the dissipation at the contact line, are calculated from the simulated results. It is found that the contact line dissipation is almost entirely responsible for the dissipation that sets the amplitude of the response. It is argued that angle-dependent line friction may be a fruitful interpretation of the relations between contact line speed and dynamic contact angle that are often used in practical computational fluid dynamics.

Textured hydrophobic surfaces that repel liquid droplets unidirectionally are found in nature such as butterfly wings and ryegrass leaves and are also essential in technological processes such as self-cleaning and anti-icing. In many occasions, surface textures are oriented to direct rebounding droplets. Surface macrostructures (>100 μm) have often been explored to induce directional rebound. However, the influence of impact speed and detailed surface geometry on rebound is vaguely understood, particularly for small microstructures. Here, we study, using a high-speed camera, droplet impact on surfaces with inclined micropillars. We observed directional rebound at high impact speeds on surfaces with dense arrays of pillars. We attribute this asymmetry to the difference in wetting behavior of the structure sidewalls, causing slower retraction of the contact line in the direction against the inclination compared to with the inclination. The experimental observations are complemented with numerical simulations to elucidate the detailed movement of the drops over the pillars. These insights improve our understanding of droplet impact on hydrophobic microstructures and may be useful for designing structured surfaces for controlling droplet mobility. 

The motion of the three-phase contact line between two immiscible fluids and a solid surface arises in a variety of wetting phenomena and technological applications. One challenge in continuum theory is the effective representation of molecular motion close to the contact line. Here, we characterize the molecular processes of the moving contact line to assess the accuracy of two different continuum two-phase models. Specifically, molecular dynamics simulations of a two-dimensional droplet between two moving plates are used to create reference data for different capillary numbers and contact angles. We use a simple-point-charge/extended water model. This model provides a very small slip and a more realistic representation of the molecular physics than Lennard-Jones models. The Cahn–Hilliard phase-field model and the volume-of-fluid model are calibrated against the drop displacement from molecular dynamics reference data. It is shown that the calibrated continuum models can accurately capture droplet displacement and droplet break-up for different capillary numbers and contact angles. However, we also observe differences between continuum and atomistic simulations in describing the transient and unsteady droplet behaviour, in particular, close to dynamical wetting transitions. The molecular dynamics of the sheared droplet provide insight into the line friction experienced by the advancing and receding contact lines. The presented results will serve as a stepping stone towards developing accurate continuum models for nanoscale hydrodynamics.

Droplet spreading and transport phenomenon is ubiquitous and has been studied by engineered surfaces with a variety of topographic features. To obtain a directional bias in dynamic wetting, hydrophobic surfaces with a geometrical asymmetry are generally used, attributing the directionality to one-sided pinning. Although the pinning may be useful for directional wetting, it usually limits the droplet mobility, especially for small volumes and over wettable surfaces. Here, we demonstrate a pinning-less approach to rapidly transport millimeter sized droplets on a partially wetting surface. Placing droplets on an asymmetrically structured surfaces with micron-scale roughness and applying symmetric horizontal vibration, they travel rapidly in one direction without pinning. The key, here, is to generate capillary-driven rapid contact-line motion within the time-scale of period of vibration. At the right regime where a friction factor local at the contact line dominates the rapid capillary motion, the asymmetric surface geometry can induce smooth and continuous contact-line movement back and forth at different speed, realizing directional motion of droplets even with small volumes over the wettable surface. We found that the translational speed is selective and strongly dependent on the droplet volume, oscillation frequency, and surface pattern properties, and thus droplets with a specific volume can be efficiently sorted out.

The impact of liquid drops on a rigid surface is central in cleaning, cooling, and coating processes in both nature and industrial applications. However, it is not clear how details of pores, roughness, and texture on the solid surface influence the initial stages of the impact dynamics. Here, we experimentally study drops impacting at low velocities onto surfaces textured with asymmetric (tilted) ridges. We found that the difference between impact velocity and the capillary speed on a solid surface is a key factor of spreading asymmetry, where the capillary speed is determined by the friction at a moving three-phase contact line. The line-friction capillary number Ca-f = mu V-f(0)/sigma (where mu V-theta(0), and sigma are the line friction, impact velocity, and surface tension, respectively) is defined as a measure of the importance of the topology of surface textures for the dynamics of droplet impact. We show that when Ca-f << 1, the droplet impact is asymmetric; the contact line speed in the direction against the inclination of the ridges is set by line friction, whereas in the direction with inclination, the contact line is pinned at acute corners of the ridges. When Ca-f >> 1, the geometric details of nonsmooth surfaces play little role.

Enhancement of boiling heat transfer on biphilic (mixed-wettability) surfaces faces a sudden reversal at low pressures, which is brought about by excessive contact-line spreading across the wetting heterogeneities. We employ the diffuse-interface approach to numerically study bubble expansion on a heating surface that consists of opposing wettabilities. The results show a dramatic shift in the dynamics of a traversing contact line across the wettability divide under different gravities, which correspond to variable bubble growth rates. Specifically, it is found that the contact-line propagation tends to follow closely the rapidly expanding bubble at low gravity, with only a brief interruption at the border between the hydrophobic and hydrophilic sections of the surface. Only when the bubble growth becomes sufficiently weakened at high gravity does the contact line get slowed down drastically to the point of being nearly immobilized at the edge of the hydrophilic surface. The following bubble expansion, which faces strong limitations in the direction parallel to the surface, features a consistent apparent contact angle at around 66.4 degrees, regardless of the wettability combination. A simple theoretical model based on the force-balance analysis is proposed to describe the physical mechanism behind such a dramatic transition in the contact-line behavior.