# 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: Helix Pitch  
In the following sections, we discuss the trajectory modification induced by changes in the channel geometry. The first examined parameter is the helix pitch, which is the distance between centres of two adjacent helical loops. The reference pitch was already relatively small and difficult to decrease: with a radius of cross-section 25 and pitch 60, there is only 10 left of free space between the edges of two adjacent loops. Therefore, we tested only values of the helix pitch that were larger than the reference one.  
There was an evident impact of helical pitch in both cases--for the larger and for the smaller cell; Figure 8. In the case of the larger cell, the increase in the helix pitch changes the final location of the stabilised position, while with a smaller pitch of 60, the stabilised position is in approximately in the upper 2/3 of the cross-section. With the pitch of 240, it is closer to the centre of the cross-section. We can see a similar shift in the case of the smaller cell. The pitch of 60 leads to two different stabilised positions, a lower one and an upper one. With an increase in the pitch, the lower stabilised position (if it exists) vanishes, and the upper stabilised position becomes closer to the centre of the cross-section.  
Figure 6: The trajectory of cells with modification of the curvature radius (CR) or tube radius (TR) of the channel, for the cell with a radius of 2. 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. The outer circle stands for the circumference of the the 25 cross-section, and the inner circle is for the circumference of the 20 cross-section.  
Figure 7: The trajectory of cells with modification of the fluid velocity. 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. (**b**) The cell with a radius of 2.  
Reaching the stabilised position takes a longer time in channels with higher values of the pitch. This is reasonable if we consider a helical channel as an intermediate channel between two extremes--a torus and a perfectly straight channel. In a torus, the particles would follow the flow induced by Dean vortices; therefore, they will flow in circular-like trajectories (as we already saw in other helices that are more similar to a torus in their pitch). In a perfectly straight channel, the particles would slowly change their position within the cross-section and focus in a specified distance between the centre of the tube and its circumference. Eventually, they would create a set of focusing positions as a circumscribed circle (Segre-Silberberg effect). In a helix, the particles would flow in circular-like trajectories, and their initial position as a distance from the centre of the cross-section would change only slowly.  
We notice that the decreasing of the pitch may lead 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 position (in the case of two stabilised positions). From this, we can draw similar conclusion as with increasing the fluid velocity: The decreasing the pitch enables differentiation between the cells according to their size.