Pore size distribution, survival probability, and relaxation time in random and ordered arrays of fibers

Abstract

We present a random walk based investigation of the pore size probability distribution and its moments, the survival probability and mean survival time, and the principal relaxation time, for random and ordered arrays of cylindrical fibers of various orientation distributions. The dimensionless mean survival time, principal relaxation time, mean pore size, and mean square pore size are found to increase with porosity, remain practically independent of the directionality of random fiber beds, and attain lower values for ordered arrays. Wide pore size distributions are obtained for random fiber structures and relatively narrow for ordered square arrays, all in very good agreement with theoretically predicted limiting values. Analytical results derived for the pore size probability and its lower moments for square arrays of fibers practically coincide with the corresponding simulation results. Earlier variational bounds on the mean survival time and principal relaxation time are obeyed by our numerical results in all cases, and are found to be quite sharp up to very high porosities. Dimensionless groups representing the deviation of such bounds from our simulation results vary in practically the same range as the corresponding values reported earlier for beds of spherical particles. A universal scaling expression of the literature relating the mean survival time to the mean pore size ͓S. Torquato and C. L. Y. Yeong, J. Chem. Phys. 106, 8814 ͑1997͔͒ agrees very well with our results for all types of fiber structures, thus validated for the first time for anisotropic porous media.

Electrospinning of poly(lactic acid)/polyhedral oligomeric silsesquioxane nanocomposites and their potential in chondrogenic tissue regeneration

“…Characteristic pore diameters (3) of the peg-POSS/PLLA scaffolds were calculated according to Tomadakis and Robertson [40].…”

Introducing dimensionless parameters into the correlation of NMR relaxation time to transport properties of porous media

“…It is worth noting that the pore size distribution of the investigated fiber structures is practically of monoexponential form (28,38); this makes possible for an asymptotic rate with a sufficiently large share of the magnetization decay signal to represent the system, justifying the use of the principal relaxation time, T 1p , in the above analysis. The same may not be feasible in systems where a significant part of the pore volume-hence the NMR signal-is shared by a broad range of pore sizes (such as the multiexponential pore size distributions and signals often encountered in sandstones (18,25,34)).…”

“…Consequently, the f 2 T 1p n values are derived in a straightforward manner from the corresponding T 1p D/r 2 values reported earlier (38), given the porosity (f) and fiber radius (r) of the structures. For any given values of T and M, the mean thermal speed v is a constant whose presence in the group f 2 T 1p v affects only the value of the fitting coefficient a of Eq.…”

“…Our recent numerical results on the viscous permeability, k, and principal relaxation time, T 1p , for bulk diffusion in random and ordered fiber structures (29,38) were further processed and correlated, to assess the applicability of literature k-T 1 correlations in the slow diffusion regime, and search for an improved dimensionless-group-based correlation that would account explicitly for the particle size effect. We considered random porous media consisting of cylindrical fibers randomly distributed in space with their axes parallel to a line (1-d), parallel to a plane (2-d), Figure 5 Dimensionless-group-based regression analysis results for the highly anisotropic 1-d random fiber structures, based on Eq.…”

“…It was also applied separately to pores of characteristic size i, (V pi =S pi ¼ rT 1i ), leading to the derivation of pore size distribution curves from NMR measurements (9,25). Figure 2 presents the outcome of a regression analysis of our earlier simulation results for the principal relaxation time (38) and the viscous permeability (29), for the various types of fiber structures and flow configurations investigated in this work. Specifically, the numerical data is plotted in the form ln k vs. ln (f 2 T 1p v) 2 to investigate the applicability of Eq.…”