The flow of blood past an axisymmetric thrombus analogue, within an in vitro geometry, is computed via solution of the discrete three-dimensional (3D) Navier-Stokes equations. Particle tracking is used to model the behaviour of thrombocytes (platelets) moving throughout the domain and to investigate behaviour with respect to the platelets. The system is explored using shear rate to quantify the effects an idealised thrombus has with respect to an undisturbed in vitro geometry over 'Poiseuille flow' shear rate conditions applicable to in vivo and in vitro experiments (1,200-10,000 s⁻¹). Local shear rate variations show peaks in shear rate greater than double that of Poiseuille flow conditions. These local shear rate variations are observed to be non-linear, despite the low Reynolds number (5.2-43.4) within the system. Topological transitions of shear rate are observed, limiting the height of peak shear rate within the system, suggesting a thrombus growth limiting behaviour. Temporal gradients of shear rate, measured with respect to individual platelets, were calculated. Multiple regions of peak shear rate gradient were observed throughout the flow, suggesting that platelet-platelet interaction may not be limited to regions near to the surface of the thrombus.