## 1 Introduction  
Many of the intriguing features of blood originate from its cellular nature. These cells are immersed in blood plasma, an incompressible fluid. Of these cells, red blood cells (RBCs) are the most numerous, having a biconcave disc shape with a diameter of 7.82 \(\upmu\)m and a thickness of approximately 2 \(\upmu\)m, making up about 45% of the blood volume. Platelets (PLTs) are the second most numerous cell type with approximately one platelet for every ten RBCs [1]. They are significantly smaller (\(\approx\)2.5 \(\upmu\)m diameter) and less deformable in their unactivated form. Due to a majority in cell count and volume ratio, the transport mechanics of the whole blood are mainly dictated by RBCs. The cytoplasmic fluid that resides inside the RBC has a higher viscosity than that of the surrounding blood plasma [2] mainly due to hemoglobin. This contrast is known to affect the type of motion that a red blood cell exhibits [3], as well as affecting other transport properties such as the lift velocity [4] or the diffusion [5] of RBCs. Furthermore, there are several diseases which are known to influence the structure of a RBC, altering its viscosity and deformability, such as malaria [6] or sickle cell disease [7]. Some of the interesting phenomena arising from this cellular nature include shear-thinning [8], the appearance of a cell-free layer in which no red blood cell resides [9; 10], the Fahraeus effect [11] and the Fahraeus-Lindqvist effect [12]. Although much research has been done to investigate the rheological properties of blood for an overview, see [PERSON] et al. [13]), many of the underlying mechanics are still not understood well enough to provide a complete mathematical analysis [14; 15; 16]. Obtaining a better understanding of the transport behaviour is, however, essential as it can help to further improve medical devices and treatments of diseases. In-silico cellular models of blood are invaluable to gain this understanding since many properties that blood exhibits are difficult to measure through experiments. Many numerical investigations have been carried out in the literature lately that target cellular blood flows (e.g., [17; 18; 19; 20; 21; 22; 23; 24; 25]). A detailed overview of the methods can be found in the work of [PERSON] [26]. These express the mechanical behaviour of RBCs and PLTs based on constitutive models, such as the energy model of [PERSON] [27], the spectrin-link model in [28], or its coarse-grained version [29], or the improved spectrin-link model of [PERSON] et al. [25], which is applied in the current work as well. One important advantage of the latter model is its increased numerical stability under high shear rate flows. The RBC cytoplasm is a dense mixture of protein complexes [30] which contributes to its increased viscosity. The effects of cytoplasmic viscosity on the transport characteristics of blood has not yet been fully explored. [PERSON] et al. implemented viscosity contrast in their lattice Boltzmann method (LBM) based model by tuning the relaxation time of the flow field [31; 32] but a detailed investigation was not made to quantify the effects of this addition. [PERSON] et al. carried out membrane fluctuation simulations [33] in their dissipativ particle dynamics (DPD) based model with a viscosity contrast of 5, however, they did not include this contrast in any other of their cases. More expansive investigation on the effects of added viscosity contrast was done for two-dimensional models of vesicles [34] and red blood cells [35] where the authors found that it does indeed affect the deformability and motion of cells but the two-dimensional nature of the models prevented quantitative comparison of the obtained results. The current work focused on the effects of the viscosity contrast between the interior fluid of a red blood cell and the exterior suspending fluid. We extended an existing model developed for three-dimensional blood flows based on the open-source framework HemoCell [25].