The wetting and dewetting of solid surfaces is ubiquitous in physical systems across a range of length scales, and it is well known that there are maximum speeds at which these processes are stable. ...Past this maximum, flow transitions occur, with films deposited on solids (dewetting) and the outer fluid entrained into the advancing one (wetting). These new flow states may be desirable, or not, and significant research effort has focused on understanding when and how they occur. Up until recently, numerical simulations captured these transitions by focussing on steady calculations. This review concentrates on advances made in the computation of the time-dependent problem, utilising dynamical systems theory. Facilitated via a linear stability analysis, unstable solutions act as ‘edge states’, which form the ‘point of no return’ for which perturbations from stable flow cease decaying and, significantly, show the system can become unstable before the maximum speed is achieved.
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•We review recent developments on applying dynamical systems theory to the moving contact-line problem.•In 2D, eigenmodes of the steady states can be calculated, and the system become unstable before reaching the maximum speed.•Three experimental papers are reviewed, where these recent developments have the potential to be applied.
The phenomenon of capillary rise or imbibition is governed by the inertia, the capillary force, the gravitational force and viscous force of fluids. Besides, the geometry also plays an important role ...on the imbibition dynamics since the motion of contact line could be affected by the sharp transition of geometry, and the oscillation of meniscus could be observed due to the confinement of contact line. The imbibition is a multiphase flow problem, which involves the movement of contact line and differences of fluid density and viscosity. In this paper, an axisymmetric lattice Boltzmann (LB) model based on the phase-field theory is proposed for investigating the oscillation phenomenon in the imbibition process. We also introduce a dimensionless Weber number to further analyze the pinning and depinning of contact line at the edge of capillary tube, and consider the effects of tube length and contact angle. The process of liquid spreading onto the top surface of capillary tube is presented, and several distinct phenomena are observed: depinning up and depinning down, pinning up and depinning down, pinning up and pinning down, pinning below the top edge. These transitions among different phenomena are dependent on the Weber number, which indicates the relative importance of inertial force compared to the surface tension force.
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•Propose an axisymmetric lattice Boltzmann model for pinning and depinning phenomena.•Present several distinct phenomena of pinning and depinning for the contact line.•Obtain the critical Weber number for pinning/depinning transition.
A phase-field moving contact line model is presented for a two-phase system with soluble surfactants. With the introduction of some scalar auxiliary variables, the original free energy functional is ...transformed into an equivalent form, and then a new governing system is obtained. The resulting model consists of two Cahn–Hilliard-type equations and incompressible Navier–Stokes equation with variable densities, together with the generalized Navier boundary condition for the moving contact line. We prove that the proposed model satisfies the total energy dissipation with time. To numerically solve such a complex system, we develop a nonlinearly coupled scheme with unconditional energy stability. A splitting method based on pressure stabilization is used to solve the Navier–Stokes equation. Some subtle implicit–explicit treatments are adopted to discretize convection and stress terms. A stabilization term is artificially added to balance the explicit nonlinear term associated with the surface energy at the fluid–solid interface. We rigorously prove that the proposed scheme can preserve the discrete energy dissipation. An efficient finite difference method on staggered grids is used for the spatial discretization. Numerical results in both two and three dimensions demonstrate the accuracy and energy stability of the proposed scheme. Using our model and numerical scheme, we investigate the wetting behavior of droplets on a solid wall. Numerical results indicate that surfactants can affect the wetting properties of droplet by altering the value of contact angles.
We address the dynamics of a surfactant-laden droplet on a solid surface in simple shear flow numerically. Our analysis uses the front-tracking method to take surfactant transport into account. The ...interfacial tension and the slip coefficient, both of which depend heavily on the surfactant concentration, are fully integrated into the generalized Navier boundary condition to model the moving contact lines. Accurate prediction of droplet motion indicates that the surfactant can change droplet behavior drastically. Surfactant-induced effects, such as interfacial tension reduction, the Marangoni stress, and wettability alternation, are investigated for various capillary numbers, surface wettabilities, elasticity numbers, and surface Péclet numbers. Deformation and motion of a sliding droplet are enhanced by the Marangoni effect, which is associated with an interfacial tension gradient. When the capillary number reaches a critical value, the sliding-to-detachment and detachment-to-pinch-off transitions occur. Both transitions can be triggered and accelerated by a surfactant, especially when convection is dominant. As a result, the critical capillary number decreases, but exhibits a non-monotonic relationship with the elasticity number and Péclet number. The mechanisms that underlie the effect of Marangoni stress are discussed by analyzing the distributions of the surfactant concentration and the hydrodynamic forces exerted on the droplet. Accumulation of surfactants near the receding contact line reverses the local concentration gradient, attempts to change its direction along the interface, and delays droplet detachment. Furthermore, the strong surfactant dilution reduces both the surfactant concentration and the interfacial tension gradient, and thereby increasing the critical value for droplet pinch-off.
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The ‘Eye-on-a-Chip’ was presented by Chan et al. (2015a, 2015b) as a ‘microfluidic’ tool to assess emulsification of silicone oil (SO) tamponades used in vitreoretinal surgery. This device features a ...thin cylindrical cavity replicating a cross-section of the eye which rotates back and forward, driving the motion of an oil and an aqueous phase. Flow patterns were studied in Eye-on-a-Chip geometries fabricated from polymethylmethacrylate with 1 mm and 2 mm high cavities, for saline, 0.5 Pa s and 1.0 Pa s SOs, and saline/SO combinations using particle-image velocimetry. The flow behaviour and acceleration times for regular disc geometries indicated that fluid motion was driven by the base and roof of the cavity, while circulation flows characteristic of the eye were not observed. The presence of a lens insert created eddies near this feature. No emulsification was observed. The 2D ‘Eye-on-a-Chip’ does not replicate the flow characteristics of the human eye. Reports of emulsification being observed in the device are discussed in the light of these findings.
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•The Eye-on-a-chip geometry does not reproduce the flow patterns in the eye.•Emulsification was not observed in tests conducted with smooth walls.•The results indicate that reported emulsification arises from contact line motion phenomena.
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Hypothesis
Although extensive research has been conducted on the dynamic wetting of Newtonian fluids, limited insights have been gained for viscoelastic fluids, particularly on ...engineered surfaces. We hypothesize that differences in dynamic wetting on microstructured surfaces exist between such fluids, which may be attributed to variations in viscosity and elasticity as well as changes in the microscopic morphology of the moving contact line.
Experiments
To systematically investigate the wetting differences between Newtonian and viscoelastic fluids on microstructured surfaces, we conducted forced wetting experiments of glycerol-water and carboxymethyl cellulose aqueous solutions on microstructured polytetrafluoroethylene surfaces through a modified Wilhelmy plate method.
Findings
Results demonstrated an apparent difference in the relationship between the dynamic contact angle and moving velocity with different microstructured surfaces for Newtonian and viscoelastic fluids. The power-law exponent between the capillary number and cubic of the dynamic contact angle increases with the strengthening of shear thinning and elastic effects. In contrast, this exponent is rarely influenced by the scale of microstructured surfaces, particularly in highly viscous regions where viscous force dominates. In addition, viscosity affects the viscous bending and distance that liquid molecules jump at the contact line. These findings have potential applications in coating complex fluids on engineered surfaces.
In this study, we propose an immersed boundary-phase field fluid-surfactant model that incorporates moving contact lines on complex geometries. To accurately capture the interface, we introduce an ...additional phase field variable to represent the solid phase, which remains fixed throughout the process. The modified Cahn–Hilliard equations are utilized to describe the interface. In order to address stiffness issues, a stabilization technique is incorporated into the calculations. To prevent streamlines from penetrating into solid obstacles, a boundary condition-enforced immersed boundary method is applied at the solid boundaries. The desired contact angle is ensured using the characteristic moving contact line method. All variables are treated independently in the computations, and the numerical results demonstrate the accuracy and excellent performance of our model on curved substrates with surfactants.
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