Narrow escape problem for Brownian particles in a microsphere with internal circulation.

This paper considers the narrow escape problem of a Brownian particle within a two-dimensional domain with two escape windows and an internal circulation modeled by the flow within a Hill's vortex. To account for the spatially inhomogeneous flow within the domain, a Lagrangian study is undertaken using the complete equations of motion for a dense particle which is necessary to distinguish between the various regimes as the strength of the internal circulation is varied. For very low internal circulation the particle undergoes the conventional narrow escape problem, and agreement is good with the asymptotic expression. As the internal circulation is increased, regimes are identified with different scaling for the mean escape time. The potential application of this for drug delivery (were nanoparticles are encased in a microsphere) is discussed.

Form, shape and function: segmented blood flow in the choriocapillaris.

The development of fluid transport systems was a key event in the evolution of animals and plants. While within vertebrates branched geometries predominate, the choriocapillaris, which is the microvascular bed that is responsible for the maintenance of the outer retina, has evolved a planar topology. Here we examine the flow and mass transfer properties associated with this unusual geometry. We show that as a result of the form of the choriocapillaris, the blood flow is decomposed into a tessellation of functional vascular segments of various shapes delineated by separation surfaces across which there is no flow, and in the vicinity of which the transport of passive substances is diffusion-limited. The shape of each functional segment is determined by the distribution of arterioles and venules and their respective relative flow rates. We also show that, remarkably, the mass exchange with the outer retina is a function of the shape of each functional segment. In addition to introducing a novel framework in which the structure and function of the metabolite delivery system to the outer retina may be investigated in health and disease, the present work provides a general characterisation of the flow and transfers in multipole Hele-Shaw configurations.

Movement of airborne contaminants in a hospital isolation room.

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.