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Register a new userRelaxation of a dewetting contact line Part 1: A full-scale hydrodynamic calculation
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The relaxation of a dewetting contact line is investigated theoretically in the so-called Landau-Levich geometry in which a vertical solid plate is withdrawn from a bath of partially wetting liquid. The study is performed in the framework of lubrication theory, in which the hydrodynamics is resolved at all length scales (from molecular to macroscopic). We investigate the bifurcation diagram for unperturbed contact lines, which turns out to be more complex than expected from simplified quasi-static theories based upon an apparent contact angle. Linear stability analysis reveals that below the critical capillary number of entrainment, Ca_c, the contact line is linearly stable at all wavenumbers. Away from the critical point the dispersion relation has an asymptotic behaviour sigma~|q| and compares well to a quasi-static approach. Approaching Ca_c, however, a different mechanism takes over and the dispersion evolves from |q| to the more common q^2. These findings imply that contact lines can not be treated as universal objects governed by some effective law for the macroscopic contact angle, but viscous effects have to be treated explicitly.
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The dynamics of receding contact lines is investigated experimentally through controlled perturbations of a meniscus in a dip coating experiment. We first characterize stationary menisci and their breakdown at the coating transition. It is then shown that the dynamics of both liquid deposition and long-wavelength perturbations adiabatically follow these stationary states. This provides a first experimental access to the entire bifurcation diagram of dynamical wetting, confirming the hydrodynamic theory developed in Part 1. In contrast to quasi-static theories based on a dynamic contact angle, we demonstrate that the transition strongly depends on the large scale flow geometry. We then establish the dispersion relation for large wavenumbers, for which we find that sigma is linear in q. The speed dependence of sigma is well described by hydrodynamic theory, in particular the absence of diverging time-scales at the critical point. Finally, we highlight some open problems related to contact angle hysteresis that lead beyond the current description.
A solid object can be coated by a nonwetting liquid since a receding contact line cannot exceed a critical speed. We theoretically investigate this forced wetting transition for axisymmetric menisci on fibers of varying radii. First, we use a matched asymptotic expansion and derive the maximum speed of dewetting. For all radii we find the maximum speed occurs at vanishing apparent contact angle. To further investigate the transition we numerically determine the bifurcation diagram for steady menisci. It is found that the meniscus profiles on thick fibers are smooth, even when there is a film deposited between the bath and the contact line, while profiles on thin fibers exhibit strong oscillations. We discuss how this could lead to different experimental scenarios of film deposition.
In many macroscopic dynamic wetting problems, it is assumed that the macroscopic interface is quasistatic, and the dissipation appears only in the region close to the contact line. When approaching the moving contact line, a microscopic mechanism is required to regularize the singularity of viscous dissipation. On the other hand, if the characteristic size of a fluidic system is reduced to a range comparable to the microscopic regularization length scale, the assumption that viscous effects are localized near the contact line is no longer justified. In the present work, such microscopic length is the slip length. We investigate the dewetting of a droplet using the boundary element method. Specifically, we solve for the axisymmetric Stokes flow with i) the Navier-slip boundary condition at the solid/liquid boundary, and ii) a time-independent microscopic contact angle at the contact line. The profile evolution is computed for different slip lengths and equilibrium contact angles. When decreasing the slip length, the typical nonsphericity first increases, reaches a maximum at a characteristic slip length $tilde{b}_m$, and then decreases. Regarding different equilibrium contact angles, two universal rescalings are proposed to describe the behavior for slip lengths larger or smaller than $tilde{b}_m$. Around $tilde{b}_m$, the early time evolution of the profiles at the rim can be described by similarity solutions. The results are explained in terms of the structure of the flow field governed by different dissipation channels: viscous elongational flows for large slip lengths, friction at the substrate for intermediate slip lengths, and viscous shear flows for small slip lengths. Following the transitions between these dominant dissipation mechanisms, our study indicates a crossover to the quasistatic regime when the slip length is small compared to the droplet size.
The hydrodynamics of a liquid-vapour interface in contact with an heterogeneous surface is largely impacted by the presence of defects at the smaller scales. Such defects introduce morphological disturbances on the contact line and ultimately determine the force exerted on the wedge of liquid in contact with the surface. From the mathematical point of view, defects introduce perturbation modes, whose space-time evolution is governed by the interfacial hydrodynamic equations of the contact line. In this paper we derive the response function of the contact line to such generic perturbations. The contact line response may be used to design simplified 1+1 dimensional models accounting for the complexity of interfacial flows coupled to nanoscale defects, yet offering a more tractable mathematical framework to include thermal fluctuations and explore thermally activated contact line motion through a disordered energy landscape.
We model the advective Marangoni spreading of insoluble surfactant at the free surface of a viscous fluid that is confined within a two-dimensional rectangular cavity. Interfacial deflections are assumed small, with contact lines pinned to the walls of the cavity, and inertia is neglected. Linearizing the surfactant transport equation about the equilibrium state allows a modal decomposition of the dynamics, with eigenvalues corresponding to decay rates of perturbations. Computation of the family of mutually orthogonal two-dimensional eigenfunctions reveals singular flow structures near each contact line, resulting in spatially oscillatory patterns of wall shear stress and a pressure field that diverges logarithmically. These singularities at a stationary contact line are associated with dynamic compression of the surfactant monolayer; we show how they can be regularized by weak surface diffusion. Their existence highlights the need for careful treatment in computations of unsteady advection-dominated surfactant transport in confined domains.
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