Transport phenomena in microfluidics and microbicide drug delivery systems

This dissertation offers a view of the fluid mechanics of low Reynolds numbers in the framework of biomedical engineering and healthcare. There are two main examples: namely the 'analysis of the mechanisms of enhanced mixing within droplets in a microserpentine channel' and 'the rational design of an anti-HIV microbicide gel vehicle'. These are explored through use of the lubrication approximation, which allows engagement of three important fields of investigation: mixing at the microscale, transport through convection and diffusion, mechanics of fluid-fluid interfaces.;The first part concerns the analysis of the mechanisms of enhanced mixing within droplets in a serpentine microchannel due to bumps on the walls. Experimental work on mixing in microfluidic devices has been prolific in recent years. Interest in probing reaction kinetics faster than the minute or hour timescale has intensified research in designing microchannel devices that would allow the reactants to be mixed on a timescale faster than that of the reaction. In that regard, particular attention has been paid to the design of microchannels in order to enhance the advection phenomena in these devices. Ultimately, in vitro studies of biological reactions could be performed in conditions that reflect their native intracellular environments. More recently, serpentine microchannels enabled mixing of aqueous solutions within droplets suspended in an oil carrier fluid. Most particularly, introduction of bumps along the outer side of the curved channel walls of these serpentine microchannels allowed for substantial enhanced mixing of highly concentrated proteins (crowded solutions) within long droplets. This first part concerns an analysis of the means by which the bumps in these serpentine microchannels accounted for enhanced mixing. Physically, as long droplets of crowded solutions progress into the microchannel and go past a bump, we demonstrate that thinning of the oil lubrication layer under the bump enhances the shear stress at the oil-droplet interface and that increased shear stress at the latter interface leads to greater advection velocities in the interior fluid within the long droplets. This is the basis for the enhancement of mixing. In addition, when the interior fluid is Newtonian, we show that mixing will be enhanced by bumps on the walls of the serpentine channel if the bumps are sufficiently close to each other. When these things are not true, the 'slip difference' (or net shear) between a smooth and bumpy serpentine microchannel relaxes to zero. Here lies the key insight. Also, the latter slip difference between bumpy and smooth mixers can be made non-zero by changing either the rheology of the interior fluid (from Newtonian to non-Newtonian for instance) or by modifying the structure of the oil-droplet interface (by filling it with insoluble surfactants for example). In that way, the interfacial velocity accelerates less than the centerline velocity under the bump - compared to the Newtonian case - which can result in a positive non-zero slip difference, that persists indefinitely, instead of relaxing to zero. Taken together, the insight provided by the analysis gives valuable guidance in the design of such mixers.;The second part addresses the development of models to enable the rational design of an anti-HIV microbicide vehicle. Indeed, microbicides are intended to prevent the transmission of HIV to women; as such they represent a new approach in the fight against HIV. Importantly, microbicides empower women by giving them control over prevention technology rather than relying on a male partner to use a condom. These topical vaginal gels, in clinical development, have received much attention, especially through the research of chemical components. However, very little attention has been given to the crucial drug delivery problem, which is the problem of how to deliver the 'microbicides' so that protection can be as effective as possible. In that regard, this dissertation addresses the modeling of the coating of the vaginal epithelium by a microbicide gel vehicle. We start initially by reviewing the published work of an initial model of a microbicide gel coating the vaginal epithelium in the simple case of the action of epithelial squeezing and gravitational sliding. We then start to address the more difficult questions of the disruption of this ideal picture through the effect of external physiological parameters, particularly the boundary dilution of the microbicide gel vehicle by vaginal secretions exuded by the epithelium. Finally, to address the relevance of this biophysical research to healthcare and HIV prevention, we address the questions of overlap between biophysical properties of the gel vehicle and behavioral and social issues from the point of view of the user.