Localized Re and Radial Position Predicts Particle Flux at Microvascular Sized Branch Points
Authors: Frame Mary (Molly) , Darvishi Samira 
Published: November 2023

Non‐Newtonian 2‐phase viscous driven flow describes blood flow deep within the nutrient flow paths of small arterioles (< 100μm). Current flow theories do not predict the mismatch of flux distribution of red blood cells (RBC) vs flow at branch points, and yet understanding this seemingly simple phenomenon is crucial to understanding oxygen delivery to the tissues, as well as the ability for rapid dynamic changes in oxygen delivery as tone modifies the bifurcation shape, and lack of uniform delivery (shunting) in inflammatory states where bifurcation shape remains somewhat fixed. We have previously identified a ‘stagnation zone’ in microchannel bifurcations (25μm diameter) where the trajectory of RBCs is shifted across flow paths, resulting in flux distribution affected by the branch angle, the radius of curvature, and the bulk Re number. However, these properties did not completely explain the discrepancy between flux and bulk flow distribution. To better understand particle behavior within the stagnation zone, we used spherical particles 1μm (particle:tube diameter ratio, 25:1) and 6μm (6:1) in PDMS microchannels (photolithography). The channels were 25μm square and T‐shaped with a feed (F) that split into two channels (feed continuation, FC and branch, B). Three bifurcation angles (45°, 90°, 135°) and three radius of curvatures (0.5d, 1d and 2d, where d is the tube diameter) were tested. Particle distribution was measured as a function of bulk Re in F, ranging three orders of magnitude from 0.0005 to 0.4. Mass balance (velocity) was confirmed with 1μm particles. Moreover, distribution of the 1μm indicates they are more likely to continue on their corresponding streamlines (flow path) downstream at the bifurcation region, as predicted by their radial position in F. The larger, 6μm, instead show that the trajectory close to the stagnation point is influenced by the bifurcation angle, the radius of curvature, and the bulk Re number. Larger stagnation areas were seen with lower bulk Re (in F), and larger bifurcation cross‐sectional areas. As with RBC, fewer 6μm particles pass to the branch in bifurcations with 90° angles vs. the obtuse and acute angles (compared to mass flow). This has been attributed to a restriction‐size effect that prevents some larger particles from entering the side branch, i.e., decreased cross‐sectional area of the branch opening with 90° vs. 45° or 135° angles. To a lesser degree, 1μm particles were restricted as well from entering the 90° branch, indicating that the size restriction effect is not a simple function of cross‐sectional area of the branch opening. To understand this behavior the effective Re along a flow path (localized Re) was compared to the radial position of the flow path in F vs FC or B. Particles that enter the stagnation zone were identified by both their radial position within F and localized Re. Thus, flux of individual particles in microvascular sized bifurcations is more predictable within branch points with smaller stagnation areas, which occur in bifurcations with smaller cross‐sectional areas, and higher Re.