Microscopic model on indoor propagation of respiratory droplets

Indoor propagation of airborne diseases is yet poorly understood. Here, we theoretically study a microscopic model based on the motions of virus particles in a respiratory microdroplet, responsible for airborne transmission of diseases, to understand their indoor propagation. The virus particles are driven by a driving force that mimics force due to gushing of air by devices like indoor air conditioning along with the gravity. A viral particle within the droplet experiences viscous drag due to the droplet medium, force due to interfacial tension at the droplet boundary, the thermal forces and mutual interaction forces with the other viral particles. We use Brownian Dynamics (BD) simulations and scaling arguments to study the motion of the droplet, given by that of the center of mass of the viral assembly. The BD simulations show that in presence of the gravity force alone, the time the droplet takes to reach the ground level, defined by the gravitational potential energy being zero, from a vertical height H,t_f∼γ^-0.1 dependence, where γ is the interfacial tension. In presence of the driving force of magnitude F₀ and duration τ₀, the horizontal propagation length, Y_max from the source increase linearly with τ₀, where the slope is steeper for larger F₀. Our scaling analysis explains qualitatively well the simulation observations and show long-distance transmission of airborne respiratory droplets in the indoor conditions due to F₀ ∼ nano-dyne.