On the physics of transient ejection from bubble bursting

Abstract

Using a dynamical scaling analysis of the flow variables and their evolution due to bubble bursting, here we predict the size and speed of ejected droplets for the whole range of experimental Ohnesorge and Bond numbers where ejection occurs. The transient ejection, which requires the backfire of a vortex ring inside the liquid to preserve physical symmetry, shows a delicate balance between inertia, surface tension and viscous forces around a critical Ohnesorge number, akin to an apparent singularity. Like in other natural phenomena, this balance makes the process extremely sensitive to initial conditions. Our model generalizes or displaces other recently proposed ones, impacting on, for instance, the statistical description of sea spray.

The ocean fine spray

“…As Neel and Deike (33) have recently pointed out, there is a very significant difference between the bulk and the surface bubble size distribution that eventually bursts for (i) clean seawater and bubbles around 1 mm and larger, and (ii) probably when the residence time at the surface before bursting is long enough to allow accumulation and coalescence (37). This seems to be the case of the average bubble size Ro = 20 reported by Jiang et al in their supplementary information (16) which, incidentally, approximately coincides with the critical Laplace number Lac described in (30). This could explain the wide distribution of droplet sizes measured in that case, in line with the results of (33).…”

“…In contrast, the direct optical measurements of (33) reliably cover droplet sizes up to 0.4mm. These latter authors find two types of droplets (see figure 3) that can be attributed to film breakup (the collapsing data independent of the surfactant concentration C) or jetting (the peaks around 0.2 mm), which would agree with jet droplet size predictions (30,31,38). With these considerations in mind, an ensemble pdf can be constructed and fitted to the experimental data after the appropriate scaling of the probabilities reported by (33).…”

“…In a recent work, Berny et al (27) have also pointed to jet droplets as the potential cause of aerosols in the range down to 0.1 µm with maximum number probability density, according to these authors, around 0.5 µm. Indeed, dimensional analysis and up-to-date models reveal that jet drops from bursting seawater bubbles with sizes from about 15 to 40 microns can yield at least tens of submicron jet droplets with sizes down to about 200 nm (28)(29)(30). Moreover, Berny et al (31) observe the ejection of secondary jet droplets, sensitive to initial conditions of the bursting process, much smaller than the primary ones.…”

“…These scales allow the rationalization and comparison of the different extremely rapid mechanisms of droplet generation. Using all data provided by (16,27,31,33) among other valuable information and data resources, jet and film droplet generation from seawater are here exhaustively revised under current available theoretical proposals (16,30) and experimental evidences. Disaggregated data and detailed experimental description in (16) allow reliable statistical resolution of ambiguities in the origin of droplets in the micron and submicron range.…”

Role of Contamination in Optimal Droplet Production by Collective Bubble Bursting

“…When it pops, it may eject drops, according to two mechanisms: the cap film puncturing, retraction and destabilization into a mist of film drops (Blanchard, 1963; Lhuissier & Villermaux, 2012), or the later collapse of the cavity into a vertical upwards jet that destabilizes into jet drops (Brasz et al., 2018; Duchemin et al., 2002; Ghabache et al., 2014; Ghabache & Séon, 2016; Spiel, 1994, 1997; Woodcock et al., 1953). These two production mechanisms have been extensively studied and documented for single bubbles, leading to various scalings laws to describe the mean size, distribution and number of ejected film (Lhuissier & Villermaux, 2012) and jet drops (Berny et al., 2021; Deike et al., 2018; Gañán‐Calvo, 2017; Gañán‐Calvo & López‐Herrera, 2021; Gordillo & Rodríguez‐Rodríguez, 2019; Lai et al., 2018) as a function of the controlling non‐dimensional length scales $${R}_{b}/{l}_{\mu }=La$$ (Laplace number) and $${R}_{b}/{l}_{c}=\sqrt{Bo}$$ ($$Bo$$ is the Bond number), with $${R}_{b}$$ the bubble size, $${l}_{\mu }={\mu }^{2}/\gamma \rho $$ the visco‐capillary length, $${l}_{c}=\sqrt{\gamma /\rho g}$$ the gravity‐capillary length, $$\mu $$ and $$\rho $$ the liquid viscosity and density, $$\gamma $$ the surface tension and …”