The necessary information extracted from the simulations is the diffusion profile, along the centerline of the capillary (including the tapered ends) in the 𝑥 direction (specifically at the lattice node indices 𝑥 = 1 -1500, 𝑦 = 31, and 𝑧 = 31) as time progresses. This 2D data, simplified from 3D simulations, has been shown to be far superior to results derived from 1D and 2D approaches. The comparative analysis, as shown in Figure , indicates that the 1D analytical solution of the diffusion equation and the 2D diffusion process on a cross-section of the capillary both significantly deviate from the full 3D simulation results. Figure illustrates the temporal progression of the concentration profile at the centerline, with a selected diffusion coefficient 𝐷 of