# A Multi-Scale Approach for Modelling Airborne Transport of Mucosalivary Fluid
## 1 Introduction  
COVID-19, which is a disease caused by the SARS-CoV-2 virus, was recognized as a global pandemic in March 2020 by the World Health Organization (WHO). More than 600 million cases and more than 6 millions deaths were reported worldwide as of September 2022 [1]. SARS-CoV-2 virus airborne transmission was confirmed as the dominant route to spread the virus itself [2]. Moreover, typical infection mechanisms are the discussed in [PERSON] et al. [3] and they can be classified as follows: (i) direct transfer of large saliva droplets to the receiver's conjunctiva, mouth, or nose; (ii) physical contact with droplets deposited on the surface and subsequent absorption to the nasal mucosa of the receiver; and (iii) inhalation of respiratory ejected aerosolized particles. The physical phenomena governing the aforementioned mechanisms are mainly inertia, gravity, buoyancy, aerodynamic drag, and evaporation [4]. In such context, a critical role is related to evaporation which continuously decreases the droplets' mass until they are reduced to a non-volatile dry nuclei also known as droplet nuclei [5]. Specifically, dry nuclei formation process is strictly related to droplets' chemical composition as well as the environmental relative humidity and temperature. Hence, it is important to remark that human saliva is more complex than pure water. Indeed, in addition to water, which represents \(\sim\)99% of its mass, also mucus, amylase, electrolytes, sodium chloride, white blood cells, epithelial cells, proteins and enzymes are typically contained within saliva droplets [6], creating a complex water solution. In most cases, water's evaporation can produce a supersaturated solution condition which triggers nuclei crystallization and their growth that is finalized in solid dry particles [7]. Droplet nuclei are also often characterized by small diameters and, for this reason, they are not highly influenced by gravity as largerdroplets [8]. Moreover, saliva dry nuclei can reach significant distances remaining airborne for longer periods (up to hours) [9]. Therefore, it is very simple to recognize the complexities of the physical phenomena involved in the propagation of a saliva cloud produced by extra-ordinary respiratory activities. In addition, their deep understanding is essential in order to define appropriate guidelines for face masks wearing as well as social distancing. Unfortunately, distancing rules are insufficient to contain the spread of aerosols carrying SARS-CoV-2. Thus, the physics behind the saliva droplets spread must be also correctly understood also for designing effective engineering solutions to be implemented in closed environments [10]. A lot of review and research papers, relying on numerical and experimental techniques, have been published in the recent months in order to gain new insights into routes of SARS-CoV-2 transmission process and on the efficacy of prevention methods [11; 12]. Considering the complex nature of mucosalivary fluid is probably the biggest modeling challenge and only very few papers addressed this topic at the time of this writing [7; 13; 14; 15]. In all the literature cases non-volatile components are replaced by NaCl. However, this approach has been applied to a very limited number of cases to date and, for example, is not still clear the most appropriate concentration of NaCl. This paper, which is an extended version of our former conference paper [16], presents our latest results in foregoing research area. In particular, a new computational approach, relying on the OpenFOAM library [17], is presented. Special care was devoted to modeling crystallization kinetics triggered from NaCl/water solution supersaturation. Indeed, our approach that will be accurately discussed in the paper, is intended to allow the modelling of droplets' behaviour at micro-scale level which is activated by meso-scale evaporative phenomena. This research is oriented to advance the state-of-art concerning the saliva chemical composition accounting.