On the sea spray aerosol originated from bubble bursting jets

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 Bo <= 0.05 can be expressed as R-d/R-b = K-b(1-(Oh/Oh(c)')(1/2)) for Oh less than or similar to Oh(c)' or as R-d approximate to 18 mu(2)(l)/(rho(l)sigma) for Oh greater than or similar to Oh(c)', with the numerically fitted constants K-b approximate to 0.2, Oh(c)' approximate to 0.03, Oh = mu(l)/root rho(l) R-b sigma << 1 the Ohnesorge number, Bo = rho(l) g R-b(2)/sigma the Bond number, and rho(l), mu(l) and sigma 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-b less than or similar to 1 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 Oh greater than or similar to 0.04. In addition, our results predict the generation of submicron-sized aerosol particles with diameters below 100 nm and velocities similar to sigma/mu(l) for bubble radii 10 mu m less than or similar to R-b less than or similar to 20 mu m, 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.