In this paper, we develop a first principles model that connects respiratory droplet physics with the evolution of a pandemic such as the ongoing Covid-19. The model has two parts. First, we model the growth rate of the infected population based on a reaction mechanism. The advantage of modeling the pandemic using the reaction mechanism is that the rate constants have sound physical interpretation. The infection rate constant is derived using collision rate theory and shown to be a function of the respiratory droplet lifetime. In the second part, we have emulated the respiratory droplets responsible for disease transmission as salt solution droplets and computed their evaporation time, accounting for droplet cooling, heat and mass transfer, and finally, crystallization of the dissolved salt. The model output favourably compares with the experimentally obtained evaporation characteristics of levitated droplets of pure water and salt solution, respectively, ensuring fidelity of the model. The droplet evaporation/desiccation time is, indeed, dependent on ambient temperature and is also a strong function of relative humidity. The multi-scale model thus developed and the firm theoretical underpinning that connects the two scales-macro-scale pandemic dynamics and micro-scale droplet physics-thus could emerge as a powerful tool in elucidating the role of environmental factors on infection spread through respiratory droplets.

The multiscale dynamics of a shock–droplet interaction is crucial in understanding the atomisation of droplets due to external airflow. The interaction phenomena are classified into wave dynamics (stage I) and droplet breakup dynamics (stage II). Stage I involves the formation of different wave structures after an incident shock impacts the droplet surface. These waves momentarily change the droplet's ambient conditions, while in later times they are mainly influenced by shock-induced airflow. Stage II involves induced airflow interaction with the droplet that leads to its deformation and breakup. Primarily, two modes of droplet breakup, i.e. shear-induced entrainment and Rayleigh–Taylor piercing (RTP) (based on the modes of surface instabilities) were observed for the studied range of Weber numbers $(We\sim 30\text{--}15\,000)$ . A criterion for the transition between two breakup modes is obtained, which successfully explains the observation of RTP mode of droplet breakup at high Weber numbers $(We\sim 800)$ . For $We > 1000$ , the breakup dynamics is governed by the shear-induced surface waves. After formation, the Kelvin–Helmholtz waves travel on the droplet surface and merge to form a liquid sheet near the droplet equator. Henceforth, the liquid sheet undergoes breakup processes via nucleation of several holes. The breakup process is recurrent until the complete droplet disintegrates or external drag acting on the droplet is insufficient for further disintegration. At lower Weber numbers, the droplet undergoes complete deformation like a flattened disk, and a multibag mode of breakup based on RTP is observed.

Face masks prevent transmission of infectious respiratory diseases by blocking large droplets and aerosols during exhalation or inhalation. While three-layer masks are generally advised, many commonly available or makeshift masks contain single or double layers. Using carefully designed experiments involving high-speed imaging along with physics-based analysis, we show that high-momentum, large-sized (>250 micrometer) surrogate cough droplets can penetrate single- or double-layer mask material to a significant extent. The penetrated droplets can atomize into numerous much smaller (<100 micrometer) droplets, which could remain airborne for a significant time. The possibility of secondary atomization of high-momentum cough droplets by hydrodynamic focusing and extrusion through the microscale pores in the fibrous network of the single/double-layer mask material needs to be considered in determining mask efficacy. Three-layer masks can effectively block these droplets and thus could be ubiquitously used as a key tool against COVID-19 or similar respiratory diseases.

We isolate a nano-colloidal droplet of surrogate mucosalivary fluid to gain fundamental insights into airborne nuclei’s infectivity and viral load distribution during the COVID-19 pandemic. The salt-water solution containing particles at reported viral loads is acoustically trapped in a contactless environment to emulate the drying, flow, and precipitation dynamics of real airborne droplets. Similar experiments validate observations with the surrogate fluid with samples of human saliva samples from a healthy subject. A unique feature emerges regarding the final crystallite dimension; it is always 20%–30% of the initial droplet diameter for different sizes and ambient conditions. Airborne-precipitates nearly enclose the viral load within its bulk while the substrate precipitates exhibit a high percentage (∼80–90%) of exposed virions (depending on the surface). This work demonstrates the leveraging of an inert nano-colloidal system to gain insights into an equivalent biological system.

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