Our study reveals that for respiratory exhalation flows, the sizes of the largest droplets that would totally evaporate before falling 2 m away are between 60 and 100 microm, and these expelled large droplets are carried more than 6 m away by exhaled air at a velocity of 50 m/s (sneezing), more than 2 m away at a velocity of 10 m/s (coughing) and less than 1 m away at a velocity of 1 m/s (breathing). These findings are useful for developing effective engineering control methods for infectious diseases, and also for exploring the basic transmission mechanisms of the infectious diseases. There is a need to examine the air distribution systems in hospital wards for controlling both airborne and droplet-borne transmitted diseases.

The present study furthcr explores the fundamental singular solutions for Stokes flow that can be useful £or constructing solutions over a wide range of free-stream profiles and body shapes. The primary singularity is the Stokeslet, which is associatedwith a singular point force embedded in a Stokes flow. From its derivatives other fundamental singularities can be obtained, including rotlets, strcsslets, potential doublets and higher-order poles derived from them. For treating interior Stokes-flow problems new fundamental solutions are introduced; they include the Stokeson and its derivatives, called the roton and stresson.These fundamental singularities are employed here to construct exact solutions to a number of cxterior and interior Stokes-flow problems for several specific body shapes translating and rotating in a viscous fluid which may itself be providing a primary ilow. The different primary flows considered here include the uniform strcam, shear flows, parabolic profiles and extensional flows (hyperbolic profiles), while the body shapcs cover prolate spheroids, spheres and circular cylinders. The salient features of these exact solutions (all obtained in closed form) regarding the types of singularities required for tlhe construction of a solution in each specific case, their distribution densities and the rangc of validity of the solution, which may depend on the characteristic Reynolds numbers and governing geometrical parameters, arc discussed.

SUMMARYThe image system for the fundamental singularities of viscous (including potential) flow are obtained in the vicinity of an infinite stationary no-slip plane boundary. The image system for a: stokeslet, the fundamental singularity of Stokes flow; rotlet (also called a stresslet), the fundamental singularity of rotational motion; a source, the fundamental singularity of potential flow and also the image system for a source-doublet are discussed in terms of illustrative diagrams. Their far-fields are. obtained and interpreted in terms of singularities. Both the stokeslet and rotlet have similar far field characteristics: for force or rotational components parallel to the wall a far-field of a stresslet type 0 (r -2) is obtained, whereas normal components are of higher order O (r-3).

As one of the major potential sources for infectious droplet nuclei in a hospital environment, exhalation flows of an infected patient can interact with the respiratory activities of other close individuals and with the room ventilation systems. Our latest results provide information on the penetration of exhalation jets into the ambient environment in different ventilation systems. This work is useful in identifying an appropriate and effective ventilation method for removing droplet nuclei more effectively, and thus minimizing the risk of cross-infections in hospital wards with multiple beds.