In this talk I present two problems, linked via gravity-defying cylinders and the importance of small asymptotic regions on global outcomes.
In the first part, I discuss a problem of fundamental fluid mechanics: if one places a cylinder on a vertical belt covered in a thin layer of oil, is it possible to keep the cylinder centre at a fixed location by moving the belt upwards at a fixed speed? I will present the results of an experimental, asymptotic, and numerical study of this fluid-structure interaction, and show that the asymptotic structure is integral to understanding levitation.
In the second part, I explore a tissue engineering application that involves understanding the motion of a porous cylindrical cell scaffold in a nutrient-fluid-filled rotating bioreactor with a small aspect ratio. While this is ostensibly a problem of coupled lubrication flow, I will show how weak inertia can have a significant effect on the scaffold trajectories. Moreover, I will show how the asymptotic structure of the flow near the bulk-porous interface is key to capturing the trajectories of such scaffolds over timescales of interest.