Thin films of transversely isotropic fluid: applications to collagen gels
Mathematical Biosciences Institute (MBI), The Ohio State University
(March 26, 2009 2:30 PM - 3:30 PM)
Biological gels (such as collagen gels) used in tissue engineering have a fibrous microstructure which affects the way forces are transmitted through the material, and in turn affects cell migration and other behaviours. In order to understand the effects of mechanical interactions between the cells and the matrix on tissue architecture, we need to understand the mechanics of the gels themselves. In this talk, I will present a simple continuum model of gel mechanics, based on treating them as transversely isotropic viscous materials. Two simple canonical problems are considered involving thin two-dimensional films: extensional flow, and squeezing flow of the fluid between two rigid plates. Neglecting inertia, gravity and surface tension, in each regime we can exploit the thin geometry to obtain a leading-order problem which is sufficiently tractable to allow the use of analytic methods. Special cases in which the solution may be determined explicitly are considered and the physical interpretation of the results is discussed.