Transport Phenomena: Computational Models for Convective and Diffusive Transport in Capillaries and Tissue - Multiscale Modeling in Biomechanics and Mechanobiology - page 134

Fig. 7.3 Representation of diffusion within confined space. a Trajectories of diffusing molecules
( dark spheres ) within a nanochannel illustrate surface effect which reduces diffusivity of molecules
at proximity to surface; b Diffusion within nannochannel with bulk domain (free diffusion) and
diffusion domain affected by interaction with surface in case of nanochannel of (nano) height h ; c
A porous medium with bulk diffusion domain and surface influence domain

Periodic boundary conditions were applied in all directions. The whole model was
minimized, equilibrated and later production simulation executed over 20 ns using
2 fs integration step.
Diffusion was analyzed studying center-of-mass displacement of target molecules
(glucose, Rhodamine 6G) and calculating diffusivity dependence on proximity to
the fiber or silica wall like in [ 42 , 63 ]. Diffusion coefficients were calculated from
trajectories by using the mean square displacement r 2

:

r 2 = 2d Dt (7.14)

where the factor d = 1, 2, 3 depends on the dimensionality of the space, and t is time.
The diffusivity along the surface normal was evaluated from the surface of the fiber
or silica wall to distances at which the diffusivity value saturates. The time window
t for r 2 was chosen as 20 ps, which is small enough to catch local displacements

within 0.5 nm thick slabs. Values of r 2

were collected to bins according to the
center of mass of molecules and their initial position. Molecules could leave the bin in
which

r 2

is computed in order to avoid restricted ensembles. The diffusivity results