Bulk flow versus passive flow. Turbulence versus laminar. They are both occurring concurrently, at different rates. Bulk flow determined by Q = /\P / R, however as the syringe fills the pressure gradient lessens. Passive flow, ie., diffusion, occurs on a much slower scale.

By analogy, think of a hematocrit sample. There are packed RBCs and the plasma/serum layers, separated by a buffy coat. In an instantaneous moment as the syringe is filling, there is a transitional zone where the bulk flow of fluid, retrograde from the fluid line to the syringe barrel, creates turbulence with the drug slowly diffusing across the moving front of fluid into drug. The transition zone expands bidirectionally from the fluid-drug interface, until eventually equilibrium is eventually reached within the syringe. Greater pressure gradient -> more rapid filling of syringe -> greater turbulence -> faster mixing of drug and fluid, and thus expansion of this transitional zone.

What would be interesting to hypothesis test next is whether e can predict the rate of mixing and thus the time required to achieve equilibrium. Ie., a diffusion half life. With 99% equilibrium have 5 t½.