“…Since our gradients were generated in seconds to minutes, their evolution fell in the early to intermediate dispersion regime. Approximate theoretical descriptions valid for early, intermediate, and late times exist for many geometries, including rectangular channels,[26, 27] cylindrical tubes,[28] and channels with smooth cross-sections. [12, 23] We define the gradient length Δ as the length of the transition zone between 10% and 90% of the maximum concentration, which captures the most linear, and therefore usable, portion of the concentration profile.…”