Marangoni-driven spreading of miscible liquids in the binary pendant drop geometry

Abstract

When two liquids with different surface tensions come into contact, the liquid with lower surface tension spreads over the other. This Marangoni-driven spreading has been studied for various geometries and surfactants, but the dynamics of the binary geometry (drop-drop) has hardly been quantitatively investigated, despite its relevance for drop encapsulation applications. Here we use laser-induced fluorescence (LIF) to temporally resolve the distance L(t) over which a low-surface-tension drop spreads over a miscible high-surface-tension drop. L(t) is measured for various surface tension differences between the liquids and for various viscosities, revealing a power-law L(t) ∼ t α with a spreading exponent α ≈ 0.75. This value is consistent with previous results for viscosity-limited spreading over a deep bath. A single power law of rescaled distance as a function of rescaled time reasonably captures our experiments, as well as different geometries, miscibilities, and surface tension modifiers (solvents and surfactants). This result enables engineering the spreading dynamics of a wide range of liquid-liquid systems.

Physicochemical hydrodynamics of droplets out of equilibrium

“…is the droplet radius) over many orders of magnitude [75,80,81]. For case (a) of figure 2 -sessile droplets -the dynamics can be much richer, as, depending on the surface tension difference ∆σ, it can either show enhanced coalescence similar to the case in figure 2b , or, more remarkably, delayed coalescence, due to a competition between capillary pressure and dynamic pressure, induced by the Marangoni flow, see figure 2a.…”

“…In the case of coalescence of fully miscible droplets, the surface tension difference at the interface will lead to Marangoni flow, with the droplet of smaller surface tension being pulled over that with the larger one, while the counteracting force in general is of viscous nature. The droplets can either be sessile [73,74,78] or pendant [75] from a nozzle with a large contact angle, or even hitting each other in flight [76,79], or -both as sessile droplets -sitting on top of each other [77], see figure 2.…”

“…[73,74]. In (b1) we sketch a side view of two pendent droplets [75], with the one with lower surface tension creeping over the one with higher surface tension. A detailed sketch of the process is shown in (b2), with the viscous velocity profile caused by the viscous force, counteracting the Marangoni force, which here however wins, leading to encapsulation.…”

“…A detailed sketch of the process is shown in (b2), with the viscous velocity profile caused by the viscous force, counteracting the Marangoni force, which here however wins, leading to encapsulation. Sketches adapted from [75]. (c) Similarly, an encapsulation is also possible for jetted droplets of different liquids [76].…”

Surface jets and internal mixing during the coalescence of impacting and sessile droplets

“…2c the jet is confined to the free surface so a sharp fluid interface is maintained in the bulk. Such surface flows could be utilized to encapsulate a sessile droplet by a second droplet, possibly with different fluid properties [55], or to modify its interfacial properties. Alternatively, for droplets deposited to form a continuous line, a sharp transition in line properties may be desired where the presence of such a surface flow could be detrimental.…”