Motion and coalescence of sessile drops driven by substrate wetting gradient and external flow

We investigate the entrainment of liquid films on a partially wetting plate vertically withdrawn from a reservoir of viscous liquid using a combination of diffuseinterface numerical simulation and lubrication analysis. So far available theoretical investigations were commonly conducted by focusing on separate parameter regions, and a complete description of the flow regimes with increasing plate speed is still missing. By solving the full Stokes equations, we present a complete scenario of film transition in the presence of moving contact line. With increasing plate speed, we identify numerically four successive flow regimes in terms of the interfacial morphologies: (1) a stationary meniscus, (2) a speed-independent thick film connected to the liquid bath through a stationary dimple, (3) coexistence of a thick film and the classical Landau-Levich-Derjaguin (LLD) film connected by a propagating capillary shock and (4) a film with a monotonically varying thickness. The characteristics of the film profiles in different regions of the interfaces are analysed with lubrication theory as applicable, and satisfactory agreements with the numerical results are obtained. In particular, we confirm that the onset of film deposition occurs at a vanishing apparent contact angle, consistent with the predictions of lubrication theory. Numerical results suggest that the critical capillary number for the onset of film deposition is smaller than that for the onset of LLD film despite the fact that it is higher than the experimentally observed one, showing that the thick film can be realized in the two-dimensional model. We also demonstrated that the LLD film is triggered by the bifurcation of the stationary dimple, which is found to admit multiple branches of stable and unstable solutions.

mentioning

confidence: 99%

Film deposition and transition on a partially wetting plate in dip coating

Gao

Feng

et al. 2016

“…For instance, if a T /(2b) = −1/2, expression (2.9) coincides with the double-well potential that is traditionally used for diffuse-interface modelling of mixtures of immiscible liquids (see e.g. Jacqmin 1999;Ding et al 2007;Ahmadlouydarab & Feng 2014;Prokopev et al 2019) to describe very different physical effects: motion of bubbles/droplets, movements of polymerisation or solidification fronts, etc.…”

Section: Phase Diagrammentioning

confidence: 86%

“…The latest form for the Korteweg force, −C∇µ, is used in the majority of the works that utilise the phase-field approach for the numerical studies (e.g. Jacqmin 1999;Ding et al 2007;Ahmadlouydarab & Feng 2014). It is necessary to note that the buoyancy term in equation (4.8) is now hidden in the Korteweg term, and this term can be explicitly written if expression (4.4) is substituted into equation (4.8).…”

Section: Discussionmentioning

confidence: 99%

Vibrational convection in a heterogeneous binary mixture. Part 1. Time-averaged equations

Vorobev

Lyubimova

2019

High-frequency vibrations of a container filled with a fluid generate pulsation flows that however are barely visible with the naked eye, and induce the slow but large-amplitude averaged flows that are important for various practical applications. In this work we derive a theoretical model that gives the averaged description of the influence of uniform high-frequency vibrations on an isothermal mixture of two slowly miscible liquids. The miscible multiphase system is described within the framework of the phase-field approach. The full Cahn–Hillard–Navier–Stokes equations are split into the separate systems for the quasi-acoustic, pulsating and averaged flow fields, eliminating the need for the resolution of the short time scale pulsation motion and thus making the analysis of the long-term evolution much more efficient. The resultant averaged model includes the effects of concentration diffusion and barodiffusion, the dynamic interfacial stresses and the generation of the hydrodynamic flows by non-homogeneities of the concentration field (when they are combined with the effects of gravity and vibrations). The resultant model for the vibrational convection in a heterogeneous mixture of two fluids separated by diffusive boundaries could be used for the description of processes of mixing/de-mixing, solidification/melting, polymerisation, etc. in the presence of vibrations.

“…Indeed, if A = − 1 2 (A is a non-dimensional phenomenological parameter that may be either negative or positive) function (2.19) turns into another popular expression, called a 'double-well potential', that is frequently used for numerical modelling of systems with immiscible interfaces (see e.g. Jacqmin 1999Jacqmin , 2000Ding et al 2007;Ahmadlouydarab & Feng 2014;Prokopev et al 2019).…”

Section: Phase-field Approachmentioning

confidence: 99%

Vibrational convection in a heterogeneous binary mixture. Part 2. Frozen waves

Vorobev

Lyubimova

2019

The action of high-frequency vibrations on a heterogeneous binary mixture that fills in a closed container is numerically modelled to validate the theoretical model obtained in the first part of the work, and to investigate the role of interfacial stresses in the evolution of miscible boundaries. Only weightlessness conditions are considered. A recent experimental study reports the threshold ignition of the frozen waves at a miscible interface even under weightlessness conditions, which cannot be explained on the basis of the classical approach that represents a binary mixture as a single-phase fluid with an impurity. This effect, however, can be well explained on the basis of the phase-field equations that were derived in the first part of our work. In particular, we found that when the vibrational forcing is sufficiently strong (the vibrational forcing is primarily determined by the amplitude of the vibrational velocity), above a certain threshold value, then the interface becomes shaped into a ‘frozen’ (time independent to the naked eye) structure of several pillars (the frozen waves) with axes perpendicular to the directions of the vibrations. The threshold level of the vibrations is determined by the interfacial stresses that need to be associated with miscible interfaces. The time needed for setting up the frozen pattern is relatively small, determined by hydrodynamic processes, however this time grows exponentially near the threshold. The frozen pattern remains stable either indefinitely long (if liquids are partially miscible) or until the interface becomes invisible due to diffusive smearing (if liquids are miscible in all proportions). A further increase of the vibrational forcing alters the number of the pillars, which happens discretely when the intensity of the vibrations surpasses a sequence of further critical levels. Correlation of the results with the previous experimental and theoretical studies validates the new approach making it a useful tool for tracing thermo- and hydrodynamic changes in heterogeneous mixtures.