On the sea spray aerosol originated from bubble bursting jets. (10th March 2020) - Blanco–Rodríguez, Francisco J.; Gordillo, J. M.
Abstract : Abstract : Here we provide a theoretical framework revealing that the radius R_d of the top droplet ejected from a bursting bubble of radius R_b and Bo0.05 can be expressed as R_d/R_b=K_b(1-(Oh/Oh_c^′ )^1/2) for OhOh_c^′ or as R_d≈ 18 [STIX]x1D707_l^2/([STIX]x1D70C_l[STIX]x1D70E) for OhOh_c^′ , with the numerically fitted constants K_b≈ 0.2, Oh_c^′ ≈ 0.03, Oh=[STIX]x1D707_l/[STIX]x1D70C_l R_b [STIX]x1D70E1 the Ohnesorge number, Bo=[STIX]x1D70C_l g R_b^2/[STIX]x1D70E the Bond number, and [STIX]x1D70C_l, [STIX]x1D707_l and [STIX]x1D70E indicating the liquid density, dynamic viscosity and interfacial tension coefficient, respectively. These predictions, which do not only have solid theoretical roots but are also much more accurate than the usual 10 % rule used in the context of marine spray generation via whitecaps for R_b1 mm, agree very well with both experimental data and numerical simulations for the values of Oh and Bo investigated. Moreover, making use of a criterion which reveals the mechanism that controls the growth rate of capillary instabilities, we also explain here why no droplets are ejected from the tip of the fast Worthington jet for Oh0.04 . In addition, our results predict the generation of submicron-sized aerosol particles with diameters below 100 nm and velocities [STIX]x1D70E/[STIX]x1D707_l for bubble radii 10 [STIX]x03BCmR_b20 [STIX]x03BCm, within the range found in natural conditions and in good agreement with experiments – a fact suggesting that our study could be applied in the modelling of sea spray aerosol production.