Analysis of a sea spray: Effect of simultaneous growth and fragmentation on droplet/particle size distribution of a multicomponent aerosol

Sea spray droplets are produced at the sea surface by bursting bubbles or wind-induced wave breaking. They are comprised of several chemical components and their interaction with the marine humid environment leads to their growth by condensation and absorption of other gases such as SO₂. Their atomization process is initiated by wind and there is a possibility that they undergo a secondary breakup at high winds when they are in the boundary-layer flow field near the sea surface. As sea spray droplets are comprised of several chemical components (in a solid as well as in a liquid phase), they are regarded as a class of aerosol droplets/particles in the marine boundary layer (MBL). The larger ones can reach the order of tens of micrometers in diameter and even up to the order of hundreds of micrometers. In the case of relatively large aerosol particles in a low number concentration (from several droplets to a few dozens per cubic centimeter) breakup/fragmentation rather than coalescence/coagulation is dominant. If that is combined with a high-relative-humidity environment, such as exists near the sea surface, then the combination of fragmentation and growth by condensation should be accounted for in environmental studies. Thus, in the present article, the effect of simultaneous growth and particle fragmentation on aerosol number and mass distributions is analyzed. Multicomponent particles are considered in the mathematical model, where each component differs in its growth rate. For a qualitative demonstration of the present growth-fragmentation mathematical model, the commonly used growth power law is employed, whereas for the mathematical representation of fragmentation, functional forms are chosen here in such a way that they obey the constant total mass constraint when only fragmentation is taking place. The mathematical results of the present study show that, due to fragmentation, an additional mode occurs in the size distribution. The gap between the modes is affected by growth, as smaller particles grow faster relative to larger ones. These modes and gaps resemble corresponding features observed in reported measurements of sea salt aerosol size distributions, and hence it is suggested here that fragmentation could be partially responsible for these features.