The elastocapillary Landau–Levich problem

Abstract

We study the classical Landau-Levich dip-coating problem for the case in which the interface possesses both elasticity and surface tension. The aim of the study is to develop a complete asymptotic theory of the elastocapillary Landau-Levich problem in the limit of small flow speeds. As such, the paper also extends our previous study on purely elastic Landau-Levich flow (Dixit & Homsy J. Fluid Mech., vol. 732, 2013, pp. 5-28) to include the effect of surface tension. The elasticity of the interface is described by the Helfrich model and surface tension is modelled in the usual way. We define an elastocapillary number, , which represents the relative strength of elasticity to surface tension. Based on the size of , we can define three different regimes of interest. In each of these regimes, we carry out asymptotic expansions in the small capillary (or elasticity) numbers, which represents the balance of viscous forces to surface tension (or elasticity).In the weak elasticity regime, the film thickness is a small correction to the classical Landau-Levich law and can be written aswhere l c is the capillary length, Ca is the capillary number and E = /Ca 2/3 . In the elastocapillary regime, the film thickness is a function of through the power-law relationshiph ∞,ec =h ∞,e L f ( )Ca 4/7 , ∼ O(1), whereh ∞,e is a numerical coefficient obtained in our previous study, L is the elastocapillary length, and f ( ) represents the functional dependence of film thickness on the elastocapillary parameter.

A viscosity-mediated model for relating gloss and film thickness of coatings

“…Nonetheless, intense debate is still found nowadays regarding 𝑛's value. In general, 𝑛 can be found to fall between 1.43-1.50 (closer to theoretical predictions mostly based on Landau-Levich theory [39], [40]) and 2.00 (verifying most empirical observations and simpler modeling strategies [41]). A remarkable exception is that of asphalts [42] ,…”

Stability of gravity-driven particle-laden flows – roles of shear-induced migration and normal stresses

“…We have specifically refrained from accessing higher particle volume fractions and Péclet numbers in our calculations, both of which could lead to a jammed state at the interface. Accumulation of particles at the free interface can lead to the interface behaving like an elastic solid (Dixit & Homsy 2013a) and also alter the surface tension (Dixit & Homsy 2013b). Another aspect that becomes important is the glass transition that typically occurs at volume fraction ≈ 0.59 (Ikeda, Berthier & Sollich 2012).…”

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

“…Some studies have focused on how other physical effects influence the film deposition such as gravity (Derjaguin 1943; Snoeijer et al. 2008), inertia (De Ryck & Quéré 1996; Orsini & Tricoli 2017), surfactants (Carroll & Lucassen 1973), particles on the interface (Colosqui, Morris & Stone 2013; Dixit & Homsy 2013 a , b ), van der Waals forces for deposited films of nanometric scales (Quéré, di Meglio & Brochard-Wyart 1989) as well as effects of substrate roughness (Krechetnikov & Homsy 2005) and confinement due to the reservoir (Kim & Nam 2017). Much of the extensive literature on the film deposition dynamics has been summarized in several review articles (Ruschak 1985; Quéré 1999; Weinstein & Ruschak 2004; Rio & Boulogne 2017).…”