## 3 Results
### Platelet-RBC Collisions  
In physiological blood flows, due to the non-zero shear rate, cells collide with each other, resulting in displacements. In particular, these repeated collisions create a shear dependent diffusivity and influence the distribution of the cells. This effect spans from affecting the haematocrit distribution to creating phenomena such as platelet margination. In the latter, the collision between a platelet and an RBC creates displacement in the platelet trajectory. Since collisions typically happen on a ms time-scale, they might be significantly influenced by the increase of inner cytoplasmic viscosity. To investigate the effects of such viscosity contrast on platelet trajectories during a collision, we positioned a RBC and platelet 16 \(\upmu\)m apart in Couette flow where the distance between the centre points of the particles perpendicular to the shear plane (denoted \(y\) direction) is \(h=2\)\(\upmu\)m. Each of the simulations is performed with and without the cytoplasmic viscosity contrast for the internal fluid of the RBC at shear rates of 400 s\({}^{-1}\) and 4000 s\({}^{-1}\). As the orientation angle of the RBC and platelet can vary in blood flow, we performed each simulation 16 times, varying the starting orientation of the platelet and the RBC with respect to each other in each simulation to sample the possible orientations, after which the results of these simulations were averaged. Figure 7 shows the average displacement of the cell centre of a platelet in the \(y\)-direction after a single collision. Due to the asymmetry of the cells and the deformability of the RBC, this flow is not reversible. According to our expectations, we can see a higher displacement in the platelet trajectories for the \(\Lambda=1\) cases. This is due to the short (few milliseconds) time-scale of the collisions where the viscous effects can significantly modify the deformability. The symmetry breaking is higher in the case of higher deformability, which corresponds to the cases with no viscosity contrast. This also implies that the application of cytoplasmic viscosity contrast might influence (i.e., decrease) the shear-induced diffusivity and the intensity of the margination of platelets. Figure 7: Average \(y\)-position of the platelet cell centre for different shear rates after a single collision event with a red blood cell. The shaded regions represent the variations of the trajectories due to the different incoming cell orientations: (**Left**) \(\dot{\gamma}=4000\) s\({}^{-1}\); and (**Right**) \(\dot{\gamma}=400\) s\({}^{-1}\). Using periodic boundary conditions, we also simulate continuous subsequent collisions. The results of these repeated collisions are shown in Figure 8. The effect of added viscosity contrast accumulates over the repeated collisions and produces significantly smaller displacements. This effect is more notable for the simulations of higher shear rate \(\dot{\gamma}=4000\) s\({}^{-1}\) where the deformations are faster as the collisions happen on a shorter time scale. This indicates that taking inner viscosity into account is important for high shear-rate cases. As the distance between the cells grow after each subsequent collision event, in this periodic setup, the effect of the collision distance \(h\) can be depicted. The platelet displacements after every collision are shown in Figure 9. In accordance with the previous results, the larger difference corresponds to the smaller incoming collision distance which also translates to larger RBC deformation during the collision. A similar curve was reported in the experimental work of [PERSON] et al. [53], however, contrary to our results, they found no significant difference due to the viscosity contrast. The most probable reason for this is the much lower shear rates (1-40 s\({}^{-1}\)) in their experiments. In our simulations, the \(\dot{\gamma}=400\) s\({}^{-1}\) case (right side of Figure 9) already displays much less difference than the higher \(\dot{\gamma}=4000\) s\({}^{-1}\) case (left side of Figure 9).