Bursting of Dilute Emulsion-Based Liquid Sheets Driven by a Marangoni Effect

Abstract

We study the destabilization mechanism of thin liquid sheets expanding in air and show that dilute oil-in-water emulsion-based sheets disintegrate through the nucleation and growth of holes that perforate the sheet. The velocity and thickness fields of the sheet outside the holes are not perturbed by holes and hole opening follows a Taylor-Culick law. We find that a pre-hole, which widens and thins out the sheet with time, systematically precedes the hole nucleation. The growth dynamics of the pre-hole follows the law theoretically predicted for a liquid spreading on another liquid of higher surface tension due to Marangoni stresses. Classical Marangoni spreading experiments quantitatively corroborate our findings.The destabilization of free liquid films is of great importance for aerosol dispersions, and is involved in many practical situations [1,2] [6], and dilute oil-in-water emulsions [7]. However, despite its relative ubiquity, the bursting of liquid sheets through perforation events have not yet been carefully investigated nor modeled. The occurrence of perforation events in a spray directly decreases the fraction of small drops issued from the spray [8] as illustrated in the case of dilute emulsions, which are prone to induce the bursting of liquid sheets [7]. Dilute emulsions are also recognized as anti-drift adjuvants [8][9][10][11] and therefore commonly used as carrier fluids for pesticides delivery. Controlling the perforation processes would therefore allow one to finely tune the size distribution of drops issued from sprays, a goal of uttermost importance in many industrial processes. In this optics, a physical description of the mechanisms at play in perforation processes is desired. The commonly invoked conditions for perforation include a dewetting of inclusions by the fluid and an inclusion diameter equal to, or larger than, the thickness of the liquid sheet, so that inclusions cause perforation by puncturing both interfaces of the sheet [3]. But, to the best of our knowledge, those conditions have never been confronted to robust experimental facts. To unambiguously clarify the physical mechanisms at play, rationale experiments on individual perforation events are therefore required.In this Letter, we investigate the perforation mechanisms of an emulsion-based free liquid sheet issued from a single-drop experiment; resulting from the impact of one drop of fluid onto a small target [12][13][14]. During the sheet expansion, holes nucleate and grow. We show that each perforation event is preceded by the formation of a pre-hole that thins out the sheet and widens with time. We demonstrate that the pre-hole growth is governed by a Marangoni effect. The entry of emulsion oil droplets at the air/water interface leads to a spreading of the oil due to a surface tension gradient stress. This stress is counterbalanced by a viscous stress that drags the subsurface fluid, whose flow causes a local film thinning which ultimately lead to the rupture of the film. We show that the growth kinetics of pre-holes ...

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

“…For a droplet pair, the transition between deep and shallow carrier layers may depend on the thickness of the flow-induced viscous boundary layer as sketched in figure 1b. Deep-layer behavior is expected if the boundary layer thickness δ BL < D 1 /4, with D 1 ≈ 2 mm the inner drop's diameter (Vernay et al 2015). Using typical values for the density ρ = 1000 kg/m 3 , viscosity η = 1 mPa s, and time t = 10 ms, we obtain δ BL = (η 1 t/ρ 1 ) 1/2 ≈ 0.1 mm.…”

“…These values follow from balancing the surface tension gradient with dissipation in the viscous boundary layer that develops while spreading on a deep layer (Fay 1969;Hoult 1972;Joos & Pintens 1977;Foda & Cox 1980;Berg 2009), and were validated for immiscible, non-evaporative liquids (Dussaud & Troian 1998;Camp & Berg 1987), immiscible surfactant solutions (Joos & Van Hunsel 1985), and spreading over insoluble surfactants (Bergeron & Langevin 1996). This scaling is maintained for immiscible microdroplets spreading over free-flowing thin films (Vernay et al 2015). For miscible surfactant solutions, the spreading exponent is maintained around α = 0.75 for low solubility (Roché et al 2014;Wang et al 2015) but it can drop to α = 0.4 for highly soluble surfactants (Tarasov et al 2006).…”

Interplay between viscosity and elasticity in freely expanding liquid sheets

“…Upon impact the drop freely expands in air, reaches a maximal extension and then retracts due to surface tension [18][19][20][21][22]. Hence, the dissipation processes occurring at the fluid/surface interface are reduced, if not suppressed, possibly facilitating their modeling and/or experimental investigations.…”

Bursting dynamics of viscous film without circular symmetry: The effect of confinement

“…[7,8] Dewetting, i.e., bursting of a film deposited on a substrate, is another topic that has attracted much attention [9][10][11]. More practically, bursting is an important tool for generation of droplets [3,[12][13][14][15][16][17] or emulsions [18] with controlled sizes because at a later stage a liquid rim formed at the bursting tip destabilizes to break into droplets.The size of droplets is a crucial factor in various fields such as environmental science [19] or disease transfer [20] because contamination results often via droplets. Bubble bursting is also important to bioreactor efficiency, because bursting is one of the causes of cell damage [21][22][23].Taking a closer look at the bursting of liquid film suspended in air, which is the base of all the above mentioned issues, only two scaling regimes have been established, one is called inertial regime and the other viscous (or viscoelastic) regime.…”