Supplementary information: Experimental and model investigation of the time-dependent 2-dimensional distribution of binding in a herringbone microchannel

The model results for the velocity field of the herringbone microchannel (Figure 1) indicate that the velocity of the fluid within the herringbone was significantly lower than the 10 velocity in the base microchannel. The velocity profile in the base microchannel closely resembles the parabolic velocity profile in the straight microchannel. However, unlike the uni-directional parabolic velocity profile in a straight microchannel, the velocity profile in a herringbone 15 microchannel will have components in three dimensions (x-, y-, and z-dimensions instead of only the y-dimension). To understand the contribution of each component to the velocity field, the velocity fields in the x-, y-, and z-dimensions are shown for two different channel depths in Figure 2. The 20 velocity profile near the binding surface is of particular importance to the surface binding profile of streptavidin. In the herringbone microchannel, the fluid travels upward (x-dimension) to fill the herringbone microstructure and is then pushed downward toward the binding surface at the 25 termination of the herringbone microstructure. This gives rise to an up and down motion in the velocity field (x-velocity profile in Figure 2). When the fluid first encounters the herringbone at the midline of the channel (z=250 microns), it moves rapidly into the herringbone microstructure (a positive 30 velocity indicated in red) and away from the binding surface. At the terminus of the herringbone near the sidewalls of the microchannel, the fluid is pushed out of the herringbone and toward the binding surface (a negative velocity indicated in blue). In the rest of the microchannel, the x-velocity is 35 minimal (near zero as indicated in turquoise). The x-velocity showed similar behavior near the binding surface (x=30 microns) and within the herringbone (x=110 microns). The y-velocity profile near the binding surface (x=30 microns in Figure 2) varies down the length of the 40 herringbone microchannel. The presence of the herringbone microstructures serves to increase the depth of the microchannel and therefore reduces the y-velocity in those locations (Figure 2; x=30 microns at locations demarked by the black arrows on the side of the microchannel). Within the 45 herringbone microstructures (x=110 microns in Figure 2), the magnitude of the maximum y-velocity was ~4 times smaller than the velocity at x=30 microns (1.75 ×10-4 m/s versus 4.15×10-5 m/s). This is not unexpected as the general velocity field (Figure 1) indicates that the overall velocity is much 50 lower within the herringbone microstructures than …