This paper presents, on the basis of high Peclet number, a mathematical model for the activation and initial adhesion of flowing platelets onto a surface. In contrast to past work, the model is applicable to general 2D and axi-symmetric flows where the wall shear stress is known a priori. Results indicate that for high activation reaction rates there exist two layers, one containing only activated platelets and the other both activated and non-activated platelets. Fundamental relationships are proposed between the adhesion rate of platelets to the surface and the characteristic parameters of Peclet number and Reynolds number. Activation in the bulk fluid (blood) is characterised by the Damkohler number, which is a function of activation rate and the free-stream velocity. It is shown that, as the free-stream velocity varies, there exists a maximum of activated platelet flux to the wall for particular values of the velocity. These values, at which the maximum occur, are themselves functions of the platelet activation rate. As the free-stream velocity increases the activation of platelets ceases altogether and adhesion is reduced to a very small value strengthening the hypothesis of the correlation between atherogenesis/thrombogenesis and areas of low shear.