# Computational Study of Inertial Flows in Helical Microchannels
## 4 Results--Effects of the Simulation Parameters on the Cell's Trajectory
### Modification of the Helical Microchannel Geometry: Curvature Radius  
The modification of the helix curvature radius has an opposite impact to the cell trajectories compared to the modification of the helix pitch. In Figure 9, we can see that the higher values of the curvature radius lead to a new stabilised position in the lower part of the cross section for the larger cell. The lower stabilised position of the smaller cell stays in the lower part of the channel, and the convergence area is larger. With the decreasing curvature radius, we can make a similar observation as for the increasing helix pitch--the stabilized position (if it exists) vanishes, and the stabilised position in upper part of the cross-section moves towards the centre of the cross-section.  
The curvature radius and the helix pitch are two parameters that altogether influence the trajectory and the stabilised position of the cells in very similar way as we already saw in the case of fluid velocity and fluid viscosity.  
With the increasing value of \(R_{c}\), the local geometry of the helix becomes more similar to a torus geometry--the pitch value is less important in comparison with \(R_{c}\). Therefore, the trajectory of the cells is more similar to a trajectory observable in torus, copying two Dean vortices. This effect is noticeable also in our results. With larger curvature radius, we can see that the lower part of the circular cross-section enclose a new stabilised position in case of the larger cell. In the case of the smaller cell, the existing separation line between two stabilised positions moves closer to the centre of the cross-section.  
From (10) and (11), the lift force over the Dean force ratio changes with \(\sim\)\(R_{c}^{1}\). Increasing the curvature radius makes the Dean force less important compared to the total lift force. The increasing of curvature radius yields to adding another stabilised position (in the case that there was only one), or to increasing of cross-section area linked to the lower stabilised  
Figure 8: The trajectory of cells with modification of the helix pitch. Cross markers denote the extrapolated stabilized positions. Negative values on the x-axis are for the inner wall of the cross-section, and positive values are for the outer wall of the cross-section. (**a**) The cell with a radius of 3.91 \(\upmu\)m. (**b**) The cell with a radius of 2 \(\upmu\)m.  
position (in the case of two stabilised positions). From this, we can again draw similar conclusion as with increasing the fluid velocity or decreasing the pitch: The increase of the curvature radius enables differentiation between the cells according to their size.  
Curvature Radius Influences the Transversal Speed of Cells  
Decreasing \(R_{c}\) increases the moment of inertia, and this affects the transversal speed of cells. To illustrate this observation, we simulated a fixed time of 10 ms for different \(R_{c}\). For a curvature radius of 150 \(\upmu\)m, the cell passed approximately 17 \(\upmu\)m within the perpendicular cross-section during 10 ms of the simulation. With a curvature radius of 75 \(\upmu\)m, the cell passed approximately 113 \(\upmu\)m during the same time, and for a curvature radius of 37 \(\upmu\)m, the cell passed approximately 47 \(\upmu\)m.  
For smaller cell, it passed 101 \(\upmu\)m in the case of the smallest radius curvature, 35 \(\upmu\)m in the case of the reference radius curvature, and 13 \(\upmu\)m in the case of the largest radius curvature, all within 10 ms of simulation. The observed trajectories are depicted in Figure 10.