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

Abstract

We investigate the entrainment of liquid films on a partially wetting plate vertically withdrawn from a reservoir of viscous liquid using a combination of diffuseinterface numerical simulation and lubrication analysis.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.

Recent advances in and future challenges for mesoscopic hydrodynamic modelling of complex wetting

“…Ref. [104] for situations involving moving contact lines (also used in [43,106]). Also in the context of surface waves on a falling film, a regularised Kuramoto-Sivashinsky (KS) equation has been analysed where the long-wave curvature is replaced by the exact curvature [17].…”

Measurements and simulation of liquid films during drainage displacements and snap-off in constricted capillary tubes

“…Another reason for the discrepancy is that Bretherton's law assumes a contact angle of zero, whereas the contact angle in the experiment is around 30 . Therefore, the wetting transition from a finite contact angle to the thin-film regime at low capillary numbers has some effect on the deposited thin-film thickness [41]. Fig.…”

Film deposition and dynamics of a self-propelled wetting droplet on a conical fibre

“…2011; Gao et al. 2016). A mathematical model describing this film coating was developed in the seminal works by Landau & Levich (1942) and Derjaguin (1943).…”

“…Coating a film onto a substrate as a liquid is forced to move along it is a technique used in painting and industrial applications such as lithography, which has been studied since the early twentieth century (Quéré 1999). Dip coating is one way to coat a plate as it is withdrawn from a liquid reservoir above a critical plate velocity (Snoeijer et al 2006;Maleki et al 2011;Gao et al 2016). A mathematical model describing this film coating was developed in the seminal works by Landau & Levich (1942) and Derjaguin (1943).…”