Analogies between elastic and capillary interfaces

Abstract

In this paper we exploit some analogies between flows near capillary interfaces and near elastic interfaces. We first consider the elastohydrodynamics of a ball bearing and the motion of a gas bubble inside a thin channel. It is shown that there is a strong analogy between these two lubrication problems, and the respective scaling laws are derived side by side. Subsequently, the paper focuses on the limit where the involved elastic interfaces become extremely soft. It is shown that soft gels and elastomers, like liquids, can be shaped by their surface tension. We highlight some recent advances on this class of elastocapillary phenomena.

The elastic Landau–Levich problem on a slope

“…If the surface tension is modified, for example by surfactants, the structure and thickness of the film may differ from the classical picture. Fluid interfaces with high surfactant concentrations have been shown to behave elastically (Vella, Aussillous & Mahadevan 2004), and it was following this motivation that Dixit & Homsy (2013) first analysed the elastic equivalent of the Landau-Levich problem. Their approach, with a vertical plate, includes an elastic sheet at the surface of the fluid in which the in-plane tension and bending stresses are calculated.…”

“…The analysis presented in this paper is more generally applicable to other problems involving elasticity and viscous flows. Snoeijer (2016) discussed analogies between elastic and capillary interfaces, including the link between the Landau-Levich problem and a horizontal elastic scraper as analysed by Seiwert, Quere & Clanet (2013). The elastic scraper produces a similar scaling for the film thickness, although governed by the length of the scraper, where here the scaling is intrinsically set by gravity.…”

Impact of the Wetting Length on Flexible Blade Spreading

“…With a finite reservoir, the viscous forces of the lubricated film are exerted over an externally imposed distance l w that varies during the spreading. This is fundamentally different from the capillary-elasticity analogy approach, where the pressure applies over an internal dynamical length l x ∼ (eL 2 ) 1/3 [9,12] vary-ing with the blade and liquid parameters. This in turn impacts the scaling of the film thickness, which writes e ∼ L ηV bL 2 E * I 3/4 in the blade-meniscus analogy [12][13][14].…”

“…Flexible blade spreading is central in numerous industrial processes such as paper coating, which inspired early studies [4][5][6][7][8]. More recently, this problem has been studied in the light of an elasticity-capillarity analogy [9] and compared with another well-known system, dip coating [10,11]. Following this approach, the elastic forces induced by the local curvature of the sheet replace surface tension forces [12][13][14].…”

How capillarity affects the propagation of elastic waves in soft gels

“…Wave propagation at interfaces raises the question of additional forces competing with elasticity. Indeed, solid interfaces, like liquid ones, possess a surface tension γ that dominates bulk elasticity at small scale, below the elastocapillary length ec = γ/µ where µ is the solid shear modulus [8][9][10]. Depositing liquid drops on soft substrates allows to probe the competition between elasticity and capillarity, as the wetting ridge induced by the contact line sets the drop's statics and dynamics [11].…”