The total artificial heart (TAH) is a bi-ventricular mechanical circulatory support device that replaces the heart in patients with end-stage congestive heart failure. The device acts as blood pump via pneumatic activation of diaphragms altering the volume of the ventricular chambers. Flow in and out of the ventricles is controlled by mechanical heart valves. The aim of this study is to evaluate the flow regime in the TAH and to estimate the thrombogenic potential during systole. Toward that goal, three numerical models of TAHs of differing sizes, that include the deforming diaphragm and the blood flow from the left chamber to the aorta, are introduced. A multiphase model with injection of platelet particles is employed to calculate their trajectories. The shear stress accumulation in the three models are calculated along the platelets trajectories and their probability density functions, which represent the 'thrombogenic footprint' of the device are compared. The calculated flow regime successfully captures the mitral regurgitation and the flows that open and close the aortic valve during systole. Physiological velocity magnitudes are found in all three models, with higher velocities and increased stress accumulation predicted for smaller devices.