Hospital-acquired infection (HAI) is an important public health issue with unacceptable levels of morbidity and mortality, over the last 5 years. Disease can be transmitted by air (over large distances), by direct/indirect contact or a combination of both routes. While contact transmission of disease forms the majority of HAI cases, transmission through the air is harder to control, but one where the engineering sciences can play an important role in limiting the spread. This forms the focus of this themed volume. In this paper, we describe the current hospital environment and review the contributions from microbiologists, mechanical and civil engineers, and mathematicians to this themed volume on the airborne transmission of infection in hospitals. The review also points out some of the outstanding scientific questions and possible approaches to mitigating transmission.

We describe an experimental study of the forces acting on a square cylinder (of width $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}b$ ) which occupies 10–40 % of a channel (of width $w$ ), fixed in a free-surface channel flow. The force experienced by the obstacle depends critically on the Froude number upstream of the obstacle, ${\mathit{Fr}}_1$ (depth $h_1$ ), which sets the downstream Froude number, ${\mathit{Fr}}_2$ (depth $h_2$ ). When ${\mathit{Fr}}_1<{\mathit{Fr}}_{1c}$ , where ${\mathit{Fr}}_{1c}$ is a critical Froude number, the flow is subcritical upstream and downstream of the obstacle. The drag effect tends to decrease or increase the water depth downstream or upstream of the obstacle, respectively. The force is form drag caused by an attached wake and scales as $\overline{F_{D}}\simeq C_D \rho b u_1^2 h_1/2$ , where $C_D$ is a drag coefficient and $u_1$ is the upstream flow speed. The empirically determined drag coefficient is strongly influenced by blocking, and its variation follows the trend $C_D=C_{D0}(1+C_{D0}b/2w)^2$ , where $C_{D0}=1.9$ corresponds to the drag coefficient of a square cylinder in an unblocked turbulent flow. The r.m.s. lift force is approximately 10–40 % of the mean drag force and is generated by vortex shedding from the obstacle. When ${\mathit{Fr}}_1={\mathit{Fr}}_{1c}\, (<1)$ , the flow is choked and adjusts by generating a hydraulic jump downstream of the obstacle. The drag force scales as $\overline{F}_D\simeq C_K \rho b g (h_1^2-h_2^2)/2$ , where experimentally we find $C_K\simeq 1$ . The r.m.s. lift force is significantly smaller than the mean drag force. A consistent model is developed to explain the transitional behaviour by using a semi-empirical form of the drag force that combines form and hydrostatic components. The mean drag force scales as $\overline{F_{D}}\simeq \lambda \rho b g^{1/3} u_1^{4/3} h_1^{4/3}$ , where $\lambda $ is a function of $b/w$ and ${\mathit{Fr}}_1$ . For a choked flow, $\lambda =\lambda _c$ is a function of blocking ( $b/w$ ). For small blocking fractions, $\lambda _c= C_{D0}/2$ . In the choked flow regime, the largest contribution to the total drag force comes from the form-drag component.

We analyse the characteristics of a force-ventilated isolation room, and the contributions to transport caused by the movement of people and doors opening/closing. The spread of fine droplets and particles can be understood, to leading order, by considering the movement of passive contaminants. A scaled (1:10) model of an isolation room (with water instead of air) was used to analyse the dilution of a passive contaminant (food dye), released either instantaneously or at a constant rate. The high level of turbulence, typical of isolation rooms, ensures that the dye concentration is uniform within the model room and mixing is perfect, and the measured mean concentration can be predicted theoretically. In a second series of experiments, the exchange generated by a door opening/closing is measured for different opening angles. A dipolar vortex is generated at the tip of the door which moves into the centre of the room, with a large coherent structure moving along the wall. The exchange volume is comparable to the swept volume of the door. Larger droplets and particles do not move passively. Their movement within a turbulent flow is studied by combining a Lagrangian model of particle movement with a kinematic simulation of a pseudo turbulent flow. The results show that while the mean fall velocity of particles is largely unchanged, turbulence significantly enhances horizontal and vertical dispersion. The horizontal spread as a function of the level of turbulence and droplet properties is estimated. The conclusions from both studies are brought together and discussed in the context of the airborne spread of contaminants within a general hospital room.

The concept of ‘drift’, which has been exploited in many high Reynolds number and inviscid flow problems, is here applied to examine transport by a spherical viscous droplet (of radius $a$) moving in a Stokes flow. In an unbounded flow, the velocity in the direction of translation of a spherical droplet is positive everywhere because streamlines, in the fluid frame of reference, ‘close’ at infinity. Fluid particles are displaced a positive distance, $X$, forward, which is expressed in terms of the initial distance from the stagnation streamline $\rho_0$. Asymptotic expressions are developed for $X$ in the limits of $\rho_0/a\,{\ll}\,1$ and $\gg 1$. The nature of the singularity of the centreline displacement changes from $O(-a\log(\rho_0/a))$ to $O(a^2/\rho_0)$ as the viscosity of the droplet, compared to the ambient fluid, increases. By employing a mass-conservation argument, asymptotic expressions are calculated for the partial drift volume, $D_p$, associated with a circular material surface of radius $\rho_m$ which starts far in front of a droplet that translates a finite distance. Since the velocity perturbation decays slowly with distance from the droplet, $D_p$ tends to become unbounded as $\rho_m$ increases, in contrast to inviscid flows. The presence of a rigid wall ensures that the velocity perturbation decays sufficiently rapidly that fluid particles, which do not lie on the stagnation streamline, are displaced a finite distance away from the wall. The distortion of a material surface lying a distance $h_L$ above a wall, by the droplet, starting a distance $h_S$ from the wall and moving away, is studied. The volume transported away from the wall, calculated using a multipolar flow approximation, is $D_p = \pi h_L^2 a(3\lambda+2)/(\lambda+1)$, and is weakly dependent on the starting position of the droplet, in accordance with numerical results. When the material surface is close to the wall ($h_L/a \ll 1$), the volume transported away from a wall is significantly smaller than for inviscid flows because the no-slip condition on the rigid wall tends to inhibit ‘scouring’. When the material surface is far from the wall ($h_L/a\gg 1$), the viscously dominated flow transports a larger volume of fluid away from the wall because the flow decays slowly with distance from the droplet. These results can be generalized to arbitrarily shaped bodies, since the transport processes are dominated by the strength of the Stokeslet. The effect of boundaries and inertia on fluid transport processes is briefly discussed.

The inviscid compressible flow generated by a rigid body of volume ${\cal V}$ moving unsteadily with a velocity ${\bm U}$ in a rapidly compressed homentropic flow is considered. The fluid is compressed isentropically at a rate ${\bm \nabla}\,{\bm \cdot}\,{\bm v}_0$ uniformly over a scale much larger than the size of the body and the body moves slowly enough that the Mach number $M$ is low. The flow is initially irrotational and remains so during compression. The perturbation to the flow generated by the body moving unsteadily is non-divergent within an evolving region ${\cal D}$ of distance $\int_0^t c_1\,{\rm d}t$ from the body, where $c_1$ is the speed of sound. Within ${\cal D}$, the flow is dominated by a source of strength $({\bm \nabla} \,{\bm \cdot}\, {\bm v}_0){\cal V}$ and a dipolar contribution which is independent of the rate of compression, while outside ${\cal D}$, compressional waves propagate away from the body. When the body is much smaller than the characteristic distance $\|({\bm \nabla}{\bm v}_0)|_{{\bm x}_0}\|/\|({\bm \nabla} {\bm \nabla} {\bm v}_0 )|_{{\bm x}_0}\|$ and the size of the region ${\cal D}$, the separation of length scales enables the force on the body to be calculated analytically from the momentum flux far from the body (but within the region ${\cal D}$). The contribution to the total force arising from fluid compression is $\rho(t) ({\bm \nabla} \,{\bm \cdot}\, {\bm v}_0) {\cal V} ({\bm U}-{\bm v}_0)\,{\bm \cdot}\, \boldsymbol{\alpha} $, where ${\bm v}_0$ is the velocity field in the absence of the particles and $\boldsymbol{\alpha}$ is the virtual inertia tensor. Thus a body experiences a drag (thrust) force during fluid compression (expansion) because the density of the fluid displaced forward by the body increases (decreases) with time. The analysis indicates that the sum of the compressional and added-mass force is equal to the rate of decrease of fluid impulse ${\bm P} = \rho(t){\cal V}({\bm U}-{\bm v}_0)\,{\bm \cdot}\, \boldsymbol{\alpha}$. Thus the concept of fluid impulse naturally extends to the class of flows where the fluid density changes with time, but is spatially uniform. These new results are applied to consider the inviscid dynamics of a rigid sphere and cylinder projected into a uniformly compressed or expanded fluid. When the fluid rapidly expands, a rigid body ultimately moves with a constant velocity because the total force, which is proportional to the density of the fluid, tends rapidly to zero. When the body moves perpendicular to the axis of compression, it slows down and stops when the density of the fluid is comparable to the density of the body. However, a body moving parallel to the axis of compression is accelerated by pressure gradients which are proportional to fluid density and increases in time.

The choriocapillaris is a capillary bed located in a thin layer adjacent to the outer retina and is part of the oxygen delivery system to the photoreceptors of the eye. The blood flow is approximately planar and is serviced by microvessels, which join the choriocapillaris through inlets perpendicular to its plane. Capillaries are densely organised and separated by avascular septal posts, which direct the blood flow. The capillary bed is composed of a juxtaposition of tessellating vascular units called lobules, which are filled and drained independently from each other. A theoretical analysis of the blood flow in an idealised model of a lobule of the choriocapillaris is developed and studied. Lobules are modelled as tessellating polygonal prisms, where the upper and lower surfaces correspond to planar parallel membranes. The septae are modelled as cylinders randomly distributed between the two membranes. Feeding arterioles and draining venules are modelled as inlets and outlets connecting at the lower surface of the prism perpendicularly to the plane of the lobule. An inlet is placed inside the lobule, while an outlet is placed at each of the vertices. The polygonal prism can be formally subdivided into a set of triangular prisms with one inlet and two outlets, each of them located at one of the vertices. The triangular prisms are taken to be isosceles, and are therefore characterised by a vertex angle ${\it\omega}$ at the inlet and a span $L$ . The flow is viscously dominated, and is investigated in the lubrication limit, in which the characteristic thickness of the prism is much smaller than the diameter of the cylinders. As a result of the geometry, a stagnation point is located midway between the outlets. A separation streamline joins the inlet and the stagnation point. The pressure drop ${\rm\Delta}\tilde{p}$ and the average fluid particle residence time $\langle \tilde{T}\rangle$ are analysed as a function of the angle at the inlet ${\it\omega}$ and the septae volume fraction ${\it\Phi}$ . When no cylinders are present ( ${\it\Phi}=0$ ), an analytical expression for the pressure field is calculated by conformal mapping. Close to the triangle walls, the flow is quasi-parallel and characterised by a shorter fluid particle residence time. In the vicinity of the stagnation point, the velocity decreases and the residence time diverges logarithmically with the distance to the stagnation streamline. The minimum in pressure drop corresponds to a maximum in residence time, and is obtained for ${\it\omega}={\rm\pi}/2$ . Asymptotic expressions for the pressure drop and average residence time are formulated in both the limits $\Vert {\it\omega}\Vert \ll 1$ and $\Vert {\rm\pi}-{\it\omega}\Vert \ll 1$ . The impact of ${\it\Phi}$ on the flow is characterised by solving the equations for the flow numerically and using the Darwin drift framework. We show that the pressure drop is approximately proportional to $1+2{\it\Phi}$ for relatively small ${\it\Phi}$ , and that $\langle \tilde{T}\rangle$ is proportional to $1-{\it\Phi}$ regardless of the void fraction or shape of the septae. In the case ${\it\Phi}=0$ , the average residence time equals the volume of the domain divided by the volumetric flux. This analysis provides a new perspective on the blood flow dynamics within the choriocapillaris. Lobules form systems, where perfusion and corpuscle transport are a function of the angle that any two venular openings make with an arteriolar opening, the surface area perfused and the void volume fraction. The blood flow velocity and residence time are significantly heterogeneous, which may be responsible for the high degree of selective localisation observed in the pathogenesis of some inflammatory and degenerative diseases of the eye.