Platelet deposition in stagnation point flow: an analytical and computational simulation

A mathematical and numerical model is developed for the adhesion of platelets in stagnation point flow. The model provides for a correct representation of the axi-symmetric flow and explicitly uses shear rate to characterise not only the convective transport but also the simple surface reaction mechanism used to model platelet adhesion at the wall surface. Excellent agreement exists between the analytical solution and that obtained by the numerical integration of the full Navier--Stokes equations and decoupled conservation of species equations. It has been shown that for a constant wall reaction rate modelling platelet adhesion the maximum platelet flux occurs at the stagnation point streamline. This is in direct contrast to that found in experiment where the maximum platelet deposition occurs at some distance downstream of the stagnation point. However, if the wall reaction rate is chosen to be dependent on the wall shear stress then the analysis shows that the maximum platelet flux occurs downstream of the stagnation point, providing a more realistic model of experimental evidence. The analytical formulation is applicable to a large number of two-dimensional and axi-symmetrical surface reaction flows where the wall shear stress is known a priori.