Figure 2.

(A) Optimal design of the flow channel for the PDFS. The blue semi-annulus shaped regions represent the inflow tubes and the hollow cylinder in the center represents the outside of the fiber. The lines that partition the channel in quarters indicate the symmetry planes of the geometry and show that the channel can be partitioned into four equal parts. The development length that is considered for mesh refinement is indicated with the lines around the outside of the flow channel. Compared to the existing experimental design, shown in Figures 1A,C, all dimensions are decreased: the fiber radius here is 0.25mm, the flow channel radius is 1.1mm, the length of the device is still 2.5cm and the fiber is placed concentrically in the flow channel. Detailed dimensions can be found in the Supplementary Material. (B) The mesh that is used to compute the velocity profile numerically in the optimal geometry. Only the first 8mm of the region near the inlet is shown here; the mesh is similar near the outlet. The blue region indicates the domain near the fiber where the mesh is refined. Note that to speed up computation only a quarter of the device is meshed, exploiting the symmetries in the system. To retrieve the full velocity profile in the PDFS, we could then mirror our solution. (C) Concentric cylinders with inner radius R₂, outer radius R₁, and length L. The unit vectors $(ẑ,\widehat{r},\widehat{\varphi })$ in cylindrical coordinates are depicted at a point between the cylinders, where the fluid will flow in the ẑ direction. The inner cylinder represents the outside of the cell layer. This geometry is used to approximate the PDFS; a comparison in terms of shear stress between the two geometries is described in section 3.4.