key: cord-0182404-a47onmje
authors: Singh, Navinder; Kaur, Manpreet
title: On the airborne aspect of COVID-19 coronovirus
date: 2020-04-20
journal: nan
DOI: nan
sha: a48eeb25c5903aa336e949ffd2aa4da5577cabb9
doc_id: 182404
cord_uid: a47onmje

It is a widely accepted view that COVID 19 is either transmitted via surface contamination or via close contact of an un-infected person with an infected person. Surface contamination usually happens when infected water droplets from exhalation/sneeze/cough of COVID sick person settle on nearby surfaces. To curb this, social distancing and good hand hygiene advise is advocated by World health Organization (WHO). We argue that COVID 19 coronovirus can also be airborne in a puff cloud loaded with infected droplets generated by COVID sick person. An elementary calculation shows that a $5~mu m$ respiratory infected droplet can remain suspended for about 9.0 minutes and a $2~mu m$ droplet can remain suspended for about an hour! And social distancing advise of 3 feet by WHO and 6 feet by CDC (Centers for Disease Control and Prevention) may not be sufficient in some circumstances as discussed in the text.

Let h be the typical height of a human being (∼ 1.6 meter). Human exhalation generates mucosalivary droplets of varied size from 0.5 µm to 12 µm [3] . Consider the trajectory of a droplet. Time taken to fall from height h using Newtonian mechanics neglecting air drag is given by (2h/g), where g is acceleration due to gravity. For h = 1.6 meters this time is roughly 0.6 sec (less than a second). In this case we say that droplets are not airborne and 1 Airborne aspect of COVID-19 settle to nearby surfaces in a time less than a second.

But this picture is radically modified when air drag is taken into account. The equation of motion including drag force ( f d ) for the vertical downward direction is given by

Here f d Stokes' drag force given by 6πηrv(t).

η is the viscosity of air, r is the radius of water 

where τ = m 6πηr . And the instantaneous height (measured from the top end) v(t) = dh(t) dt is given by

Let time taken to fall down be t 0 and h(t 0 ) = h the typical height of a person. The total time taken t 0 to fall down from height h is t 0 ≃ h gτ ≃ 544.0 seconds, which is about 9 minutes! This is very surprising. In nil wind conditions, typical droplets of size 5 µm can take 9 minutes to settle down! Smaller droplets can take even more time! This time scale is inversely proportional to the square of the radius of droplet:

where ρ is the density of water droplet. the total force has two components:

is the random force whose average is zero ξ(t) = 0 but correlated in time.

Simplest form of correlation is delta correla- 

World Health Organization (WHO)

Electronic transport theories: from weakly correlated to strongly correlated systems