Water–propylene glycol sessile droplet shapes and migration: Marangoni mixing and separation of scales

Abstract

New light is shed on morphological features of water–propylene glycol sessile droplets evaporating into ambient air at not too high relative humidity. Such droplets adopt a Marangoni-contracted shape even on perfectly wetting substrates, an effect well known since Cira et al. (Nature, 519, 2015). We here highlight a strong separation of scales normally occurring for such droplets. Namely, there is a narrow high-curvature zone localized at the foot of the droplet, where the apparent contact angle is formed, while the core of the droplet merely adheres to the classical (capillary–gravity) static shape. Experimentally, we rely upon interferometry to discern such fine key details. We detect a maximum of the droplet slope profile in the foot region, which amounts to the apparent contact angle. Theoretically, a local description of the foot region is devised. We indicate a crucial role of convective mixing by the solutal Marangoni flow, here accounted for by the Taylor dispersion, which proves to underlie the separation of scales and ensure self-consistency of the local model. Migration of such droplets in a humidity gradient is also approached within the same experimental and theoretical framework. It is considered that the resulting back–front asymmetry of the apparent contact angles drives the motion similarly to a wettability gradient, although the drag (‘Cox–Voinov’) factor is here found to be different. The predictions, comparing well with the measurements (our own and from the literature), are based on rigorous models, isothermal and as reduced as possible, without any fitting parameters or microphysics effects.

How liquid–liquid phase separation induces active spreading

“…1 ) . For the binary mixtures, we observe a deviation from the Cox–Voinov law: PG–water droplets spread slower, due to a gradually decaying Marangoni contraction ( 25 , 36 ), whereas, surprisingly, the phase-separating binary droplets spread much faster, evidencing a direct coupling of phase separation to the spreading process, in the opposite direction compared to the Marangoni flows in the miscible region. Besides larger capillary numbers, phase separation generates exponents greater than 1, increasing with the glycol–ether mass fraction ( Fig.…”

“…As a control experiment without phase separation, for instance to clarify the impact of thermal ( 32 , 33 ) or solutal ( 34 ) Marangoni convection, we replace DPnP with a glycol of similar surface activity, propylene glycol (PG) ( ; Sigma-Aldrich, 99.5%) ( 35 , 36 ). Note that PG and water are well miscible, meaning that their mixture does not exhibit liquid–liquid phase separation throughout our experimental conditions.…”

“…Only much later, due to the gradual depletion of water from the droplet, the Marangoni flows decay and hence the droplet spreads slowly ( Movie S3 and SI Appendix , Fig. S2 ) ( 25 , 36 ).…”

A thermodynamically consistent diffuse interface model for the wetting phenomenon of miscible and immiscible ternary fluids

“…For the wetting phenomenon of one-and two-component fluids, distinct types of models have been developed in the literature, such as sharp interface model (Chamakos et al 2016;Du et al 2021), phase-field model (Yue & Feng 2012;Ben Said et al 2014;Cai et al 2015;Wu et al 2019bWu et al , 2020Wu et al , 2022Zhu et al 2020), lattice Boltzmann (Attar & Körner 2009;Bala et al 2019), volume of fluid (Hirt & Nichols 1981;Malgarinos et al 2014), level-set methods (Zheng & Zhang 2000;Buscaglia & Ausas 2011) and thin-film models (Thiele 2018). The sharp interface method has mathematically a zero interfacial thickness.…”

How liquid-liquid phase separation induces active spreading

“…S1 and Table S1). In the one-phase region, due to solutal Marangoni flows, the droplet maintains a quasi-stationary, contracted state with a nonzero apparent contact angle θ app and a high mobility, i.e., an unpinned contact line [27][28][29][30][31][32][33][34] (Fig. 1a).…”