Capillary ripples in thin viscous films

Abstract

Capillary ripples on thin viscous films are important features of coating and lubrication flows. Here we present experiments based on Digital Holographic Microscopy, measuring the morphology of capillary ripples ahead of a viscous drop spreading on a prewetted surface with a nanoscale resolution. Our experiments reveal that upon increasing the spreading velocity, the amplitude of the ripples first increases and subsequently decreases. Above a critical spreading velocity, the ripples even disappear completely and this transition is accompanied by a divergence of the ripple wavelength. These observations are explained quantitatively using linear wave analysis, beyond the usual lubrication approximation, illustrating that new phenomena arise when the capillary number becomes order unity.

Spreading of viscoplastic droplets

“…Although some success has been enjoyed with Newtonian fluid (Jalaal et al. 2019 b ), we were also unable to clearly visualize any finer structure at the droplet edge such as the undulations that emerge in the lubrication theory and numerical simulations.

Figure 8.( a ) An example of an extrusion test for and .

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“…The decaying undulations converge to a sawtooth wave in h rr , with the corners corresponding to the sign switches of h − h ∞ . Unlike the decaying capillary waves of moving Newtonian contact lines, which have fixed wavelength (Tanner 1979;Tuck & Schwartz 1990;Jalaal et al 2019b), the viscoplastic undulations shorten with distance along the wavetrain. In appendix A, we outline how the waveform converges to piecewise-cubic polynomials, with an accumulation point at a finite outer radius.…”

“…The spreading of Newtonian droplets over a thin layer has been addressed previously for a range of physical regimes (see Bergemann, Juel & Heil (2018), Jalaal, Seyfert & Snoeijer (2019b), and references therein). The present article aims to provide a discussion on the viscoplastic version of this problem.…”

Axisymmetric evolution of gravity-driven thin films on a small sphere

“…Other problems containing similar order of connection include a thin drop sliding down an inclined plate (Benilov & Benilov 2015), a gas film below a Leidenfrost drop (van Limbeek et al. 2019), a bubble rising in a narrow tube (Lamstaes & Eggers 2017), dewetting fronts (Snoeijer & Eggers 2010) and capillary ripples (Jalaal, Seyfert & Snoeijer 2019) in lubrication flows. This seems to be a general pattern of the distribution of film structures, though the scaling laws depend on the specific geometry of each problem.…”

“…In the dip-coating problem (Gao et al 2016) for example, just above the critical plate speed of wetting transition, there is a dimple located above the static meniscus with a zero apparent contact angle (Snoeijer et al 2008), and the gravity-driven film at the top meets the dimple with a local ridge (Benilov et al 2010). Other problems containing similar order of connection include a thin drop sliding down an inclined plate (Benilov & Benilov 2015), a gas film below a Leidenfrost drop (van Limbeek et al 2019), a bubble rising in a narrow tube (Lamstaes & Eggers 2017), dewetting fronts (Snoeijer & Eggers 2010) and capillary ripples (Jalaal, Seyfert & Snoeijer 2019) in lubrication flows. This seems to be a general pattern of the distribution of film structures, though the scaling laws depend on the specific geometry of each problem.…”