Abstract:

Heil, M. & Hazel, A. L. (2003) Mass transfer from a finite strip near an oscillating stagnation point --- implications for atherogenesis. Journal of Engineering Mathematics 47 315-334.

We consider the mass transfer from a finite-length strip near a two-dimensional, oscillating stagnation-point flow in an incompressible, Newtonian fluid. The problem is investigated using a combination of asymptotic and numerical methods. The aim of the study is to determine the effect of the location of the strip, relative to the time-averaged position of the stagnation point, on the mass transfer into the fluid. The study is motivated by the problem of mass transfer from an injured region of the arterial wall into the blood, a process that may be of considerable importance in atherogenesis. For physiologically realistic parameter values, we find that the fluid flow is quasi-steady, but the mass transfer exhibits genuine time-dependence and a high-frequency asymptotic solution provides an accurate prediction of the time-average mass transfer. In this regime, there is a significant reduction in mass transfer when the centre of the strip is located at the point of zero time-averaged wall shear rate, or equivalently wall shear stress, which may serve to explain, at least partially, the correlation between arterial disease and regions of low wall shear stress.