Experimental study of substrate roughness and surfactant effects on the Landau-Levich law

Abstract

In this work we present an experimental study of deviations from the classical Landau-Levich law in the problem of dip coating. Among the examined causes leading to deviations are the nature of the liquid-gas and liquid-solid interfaces. The thickness of the coating film created by withdrawal of a plate from a bath was measured gravimetrically over a wide range of capillary numbers for both smooth and well-characterized rough substrates, and for clean and surfactant interface cases. In view of the dependence of the lifetime of a film on the type of liquid and substrate, and liquid-gas and liquid-solid interfaces, we characterized the range of measurability of the film thickness in the parameter space defined by the withdrawal capillary number, the surfactant concentration, and substrate roughness size. We then study experimentally the effect of a film thickening due to the presence of surfactants. Our recent theory based on a purely hydrodynamic role of the surface active substance suggests that there is a sorption-controlled coating regime in which Marangoni effects should lead to film thinning. However, our experiments conducted in this regime demonstrate film thickening, calling into question the conventional wisdom, which is that Marangoni stresses ͑as accounted by the conventional interfacial boundary conditions͒ lead to film thickening. Next we examine the effect of well-characterized substrate roughness on the coated film thickness, which also reveals its influence on wetting-related processes and an effective boundary condition at the wall. In particular, it is found that roughness results in a significant thickening of the film relative to that on a smooth substrate and a different power of capillary number than the classical Landau-Levich law.

Surfactant effects in the Landau–Levich problem

“…Thus, we could not expect the same factor α for low and high speeds. However, our measurements of film thickness on a planar substrate (Krechetnikov & Homsy 2005) also demonstrate no significant variation of α with the speed, thus posing further questions as to the origins of the film thickening. In order to understand the physical mechanisms leading to thinning, we examine the distribution of surfactant along the interface in figure 9 for different bulk concentrations.…”

“…The experimental studies of surfactant effects, which are of interest here, are due to Groenveld (1970) and Krechetnikov & Homsy (2005) for flat substrates; Bretherton (1961) for coating the inner walls of circular tubes; and Carroll & Lucassen (1973), Ramdane & Quéré (1997), Quéré & de Ryck (1998) and Shen et al (2002) on fibre coating. Historically, in the classical Bretherton problem (cf.…”

“…the notion is applicable to the surfactant case as well. For further discussion, see Krechetnikov & Homsy 2005). The extent of this region (along the plate dimension) l is determined by the balance of viscous and capillary stresses and by matching the curvature in the static and dynamic meniscus regions,…”

Breakdown of the Bretherton law due to wall slippage

“…It is also the condition that ensures steady flow, since viscous drag can be generated by sharp velocity gradients on solid boundaries to counterbalance the applied forcing. While the no-slip condition has been widely used in many practical flows, considerable wall slip, intrinsic or apparent, might exist in a number †Email address for correspondence: hhwei@mail.ncku.edu.tw (de Gennes 1979), pumping in hydrophobic microchannels with/without surface structures (Tretheway & Meinhart 2002;Tsai et al 2009), draining on chemically decorated substrates (Craig, Neto & Williams 2001;Zhu & Granick 2001), and coating on uneven/structured plates (Krechetnikov & Homsy 2005;Seiwert, Clanet & Quéré 2011).…”

Thin liquid film entrainment by moving solids

“…This influence has been studied by Krechetnikov and Homsy (Krechetnikov and Homsy, 2005) who have carried out experimental work concerning the substrate roughness effects on the Landau-Levich' law, but a lower velocities that the critical one.…”