Tortuosity of Porous Particles

Multiscale adsorption and transport in hierarchical porous materials

This review presents the state-of-the-art of multiscale adsorption and transport in hierarchical porous materials.

The origin of a large apparent tortuosity factor for the Knudsen diffusion inside monoliths of a samaria–alumina aerogel catalyst: a diffusion NMR study

The contribution from surface diffusion into the apparent tortuosity factor can be separated for light gases in a porous catalyst.

Generalized modeling of spontaneous imbibition based on Hagen-Poiseuille flow in tortuous capillaries with variably shaped apertures

Spontaneous imbibition of wetting liquids in porous media is a ubiquitous natural phenomenon which has received much attention in a wide variety of fields over several decades. Many traditional and recently presented capillary-driven flow models are derived based on Hagen-Poiseuille (H-P) flow in cylindrical capillaries. However, some limitations of these models have motivated modifications by taking into account different geometrical factors. In this work, a more generalized spontaneous imbibition model is developed by considering the different sizes and shapes of pores, the tortuosity of imbibition streamlines in random porous media, and the initial wetting-phase saturation. The interrelationships of accumulated imbibition weight, imbibition rate and gas recovery and the properties of the porous media, wetting liquids, and their interactions are derived analytically. A theoretical analysis and comparison denote that the presented equations can generalize several traditional and newly developed models from the literature. The proposed model was evaluated using previously published data for spontaneous imbibition measured in various natural and engineered materials including different rock types, fibrous materials, and silica glass. The test results show that the generalized model can be used to characterize the spontaneous imbibition behavior of many different porous media and that pore shape cannot always be assumed to be cylindrical.

How particle shape affects the flow through granular materials

Flow through the pores of granular materials has many instances in practice. Therefore, it is interesting to realize how some parameters, such as the shape of the particles affect the passing flow. Following the recent mathematical theory proposed by the authors, this paper deals with the issue of how tortuosity and permeability are influenced by the particle shape. Comparison of the results with the experimental data reveals the competency of the theory in predicting the impact of particle geometry.

Iontophoresis from a micropipet into a porous medium depends on the ζ-potential of the medium

Iontophoresis uses electricity to deliver solutes into living tissue. Often, iontophoretic ejections from micropipets into brain tissue are confined to millisecond pulses for highly localized delivery, but longer pulses are common. As hippocampal tissue has a ζ-potential of approximately -22 mV, we hypothesized that, in the presence of the electric field resulting from the iontophoretic current, electroosmotic flow in the tissue would carry solutes considerably farther than diffusion alone. A steady state solution to this mass transport problem predicts a spherically symmetrical solute concentration profile with the characteristic distance of the profile depending on the ζ-potential of the medium, the current density at the tip, the tip size, and the solute electrophoretic mobility and diffusion coefficient. Of course, the ζ-potential of the tissue is defined by immobilized components of the extracellular matrix as well as cell-surface functional groups. As such, it cannot be changed at will. Therefore, the effect of the ζ-potential of the porous medium on ejections is examined using poly(acrylamide-co-acrylic acid) hydrogels with various magnitudes of ζ-potential, including that similar to hippocampal brain tissue. We demonstrated that nearly neutral fluorescent dextran (3 and 70 kD) solute penetration distance in the hydrogels and OHSCs depends on the magnitude of the applied current, solute properties, and, in the case of the hydrogels, the ζ-potential of the matrix. Steady state solute ejection profiles in gels and cultures of hippocampus can be predicted semiquantitatively.

Analytical derivation of tortuosity and permeability of monosized spheres: a volume averaging approach

Macroscopic properties of granular materials are important in modeling a variety of flow and transport phenomena in many fields of science. Determination of these parameters has always been an issue among both researchers and engineers, mainly in view of tortuosity and permeability. This paper presents analytical functions for the tortuosity and permeability of monosized sphere arrays based on a volume averaging approach and eliminates some ambiguities by modification of the original representative elementary volume model. Veracity of the proposed formulations has been illustrated through comparisons with the latest available results on the subject. Good agreement is found.

Characterization of pore structure of a strong anion-exchange membrane adsorbent under different buffer and salt concentration conditions

The quantitative characterization of pore structure of Sartobind Q, a strongly basic membrane anion exchanger that is formed by cross-linked cellulose support and a hydrogel layer on its pore surface, was made combining the results obtained by several experimental techniques: liquid impregnation, batch size-exclusion, inverse size-exclusion chromatography, and permeability. Mercury intrusion and nitrogen sorption porosimetry were carried out for a dry cellulose support membrane in order to get additional information for building a model of the bimodal pore structure. The model incorporated the distribution of the total pore volume between transport and gel-layer pores and the partitioning of solutes of different molecular weights was expressed through the cylindrical pore model for the transport pores and random plane model for the gel layer. The effect of composition of liquid phase on the pore structure was investigated in redistilled water, phosphate and Tris-HCl buffers containing up to 1M NaCl. Evident differences in the bimodal pore structure were observed here when both the specific volume and size of the hydrogel layer pores significantly decreased with the ionic strength of liquid phase.

Tortuosity-porosity relation in porous media flow

We study numerically the tortuosity-porosity relation in a microscopic model of a porous medium arranged as a collection of freely overlapping squares. It is demonstrated that the finite-size, slow relaxation and discretization errors, which were ignored in previous studies, may cause significant underestimation of tortuosity. The simple tortuosity calculation method proposed here eliminates the need for using complicated, weighted averages. The numerical results presented here are in good agreement with an empirical relation between tortuosity (T) and porosity (varphi) given by T-1 proportional, variantlnvarphi , that was found by others experimentally in granule packings and sediments. This relation can be also written as T-1 proportional, variantRSvarphi with R and S denoting the hydraulic radius of granules and the specific surface area, respectively. Applicability of these relations appears to be restricted to porous systems of randomly distributed obstacles of equal shape and size.