## 5 Flow Gallery
### Two-Dimensional Dynamics of Fiber Suspensions Near a Flow Constriction  
Fabrication of ordered suspensions is illustrated by two cases of different initial fiber orientation in the right panel of Figure 3d,e. In such experiments, the objective was to investigate the flow of ordered suspensions towards a constriction. The lithography mask contains respectively eleven and eight fiber shapes. It is carefully aligned on the microscope to fabricate all of the fibers inside the channel, before manually moving the stage to position the mask upstream and fabricate a new batch of fibers. The operation is repeated as many times as necessary. Fabrication was done at zero flow, then a calibrated hydrostatic pressure was imposed to start the flow. In this case, we designed the channels in such a way as not to allow fibers to flow above each other. The fiber dynamics at the approach of a constriction was investigated in both configurations (fibers all parallel or all initially perpendicular to the flow direction) [12; 23]. Figure 13 shows images of the parallel suspension at different times after the flow is applied. The initial configuration of the suspension is well organized, and when the flow is applied, the fibers in the middle of the first row experience the largest flow velocity and, thus, pass through the constriction. The two outer fibers on both sides are then blocked by the wall of the constriction. When the second row approaches, the outer fibers of the first row are pushed and rotate, allowing the fibers closest to the constriction to pass, while most outer fibers are still blocked. This mechanism is illustrated in the first column of Figure 13 where 200 ms separate the different frames. Then, the suspension disorganizes, breaking its lateral symmetry, and clogging occurs rapidly, as can be seen on the second column of Figure 13. Note that the time between frames in this column is 3 s. From that moment onwards, the flow of fibers into the constriction is drastically slowed down as shown on the third column of Figure 13 where the time between frames is 6 s.  
The bottom image of Figure 13 is a spatio-temporal representation showing the time evolution of a given area. Here, time goes from left to right, whereas the vertical axis corresponds to the pixels of a vertical line from each picture. Its position on the pictures is indicated by the thin black line on the last frame on the bottom right of Figure 13. This type of representation is very useful to obtain a global view of a time-dependent phenomena. Each elongated bright object corresponds to a fiber passing through the observed line, but the length of the object is not the fiber length, but the duration of the passage. The shorter the object, the fastest the fiber. On the spatio-temporal image, one can identify the passage and reorientation of the first row (from the beginning to the end of the yellow line). Then, in the first half of the red line, the fibers enter the constriction quickly, and the lateral symmetry starts to be broken. From this moment onwards, all horizontal objects on the spatio-temporal image are very long, meaning that the dynamics is strongly slowed down, and the constriction remains clogged. Figure 11: Time-lapse image of a fiber flowing in the channel. Two hundred milliseconds separate two successive positions. The channel width is 200 \(\upmu\)m; fiber length 290 \(\upmu\)m. The corresponding video is available in Supplementary Materials Video S4. Figure 12: Chronophotography of an elastic fiber bending during the drift flow. The observed dynamics are very different in the perpendicular configuration (shown in Figure 14). During the first period (the first column in Figure 14), the first fibers accumulate at the constriction as their orientation prevents them from passing through. Then, they start to bend slightly (as can be seen in the fifth image of this column).