This article describes central features of the mass transport during the coagulation in water of cellulose-1-ethyl-3-methylimidazoium acetate ([C2mim][OAc]) solutions, namely, that the diffusivities are mainly affected by the relative concentrations of water and [C2mim][OAc], that the concentration of cellulose does not affect diffusivities and coagulation rates, that the diffusivities of low-Mw compounds are similar to those in aqueous [C2mim][OAc] solutions without macromolecules, that the polymer concentration is diluted by the large influx of coagulant causing a positive net mass gain, NMG, from diffusive fluxes, and that such NMG, although observed only as a function in time, is also a function in space that has local peaks significantly higher than the mean NMG value. The conclusion from the first three findings was that the diffusion advances through a liquid phase which possesses a continuous pore network and most of the volume. The precipitated cellulose is concentrated into fibrils whose inhibitive effect on the diffusion of small molecules through the surrounding phase is marginal. This key understanding about mass transport during coagulation also simplifies numerical modeling significantly.