Self-diffusion in a periodic porous medium: A comparison of different approaches

Bergman, David J.; Dunn, Keh‐Jim; Schwartz, Lawrence M.; Mitra, Partha P.

doi:10.1103/physreve.51.3393

Cited by 84 publications

(50 citation statements)

References 9 publications

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“…In these papers, relaxation occurs only at the solid surfaces and in an uniform way. Bergman et al [21] compared the random walk approach to another one based on an explicit calculation of the diffusion eigenstates using a Fourier series expansion of the diffusion equation. Toumelin et al [22] took into account relaxation not only at the solid boundaries, but also in the bulk fluid far from the boundaries due to the presence of a constant magnetic field gradient.…”

Section: Introductionmentioning

confidence: 99%

Nuclear magnetic resonance diffusion with surface relaxation in porous media

Valfouskaya

Adler

Thovert³

et al. 2006

Journal of Colloid and Interface Science

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Section: Introductionmentioning

confidence: 99%

Nuclear magnetic resonance diffusion with surface relaxation in porous media

Valfouskaya

Adler

Thovert³

et al. 2006

Journal of Colloid and Interface Science

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“…In this section we will show explicitly that a random walk algorithm (Wilkinson et al 1991, Mitra et al 1993, Mendelson 1990, 1993, Bergman et al 1990, Toumelin et al 2002 gives rise to the diffusion equation (1), with the appropriate boundary condition given in Eq. 2, when the number of grid points approaches infinity.…”

Section: Numerical Algorithm-random Walkmentioning

confidence: 99%

NMR for equilateral triangular geometry under conditions of surface relaxivity—analytical and random walk solution

et al. 2006

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We consider analytical and numerical solution of NMR relaxation under the condition of surface relaxation in an equilateral triangular geometry. We present an analytical expression for the Green's function in this geometry. We calculate the transverse magnetic relaxation without magnetic gradients present, single-phase, both analytically and numerically. There is a very good match between the analytical and numerical results. We also show that the magnetic signal from an equilateral triangular geometry is qualitatively different from the known solution: plate, cylinder, and sphere, in the case of a nonuniform initial magnetization. Nonuniform magnetization close to the sharp corners makes the magnetic signal very fast multiexponential. This type of initial configuration fits qualitatively with the experimental results by Song (Phys.

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“…Exploiting the strong and constant field gradient generated by unilateral NMR sensor, diffusion measurements were carried out to obtain the average surface-to-volume ratio of pores and the degree of pores interconnection in untreated and treated tuffs. [36,37] All specimens were also characterized by morphological and colorimetric analyses. The protective efficiency of treatments was evaluated through conventional techniques, such as water capillary absorption tests, water vapor permeability (WVP), and drying index (DI) tests.…”

Section: Introductionmentioning

confidence: 99%

Unilateral NMR investigation of multifunctional treatments on stones based on colloidal inorganic and organic nanoparticles

Tullio

Cocca

Avolio

et al. 2014

Magnetic Reson in Chemistry

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Consolidation and protection are among the most important treatments usually carried out in conservation of stone artifacts and monuments. In this paper, portable unilateral NMR and conventional techniques were used for investigating new multifunctional treatments based on tetraethoxysilane, silica, and polytetrafluoroethylene nanoparticles. The study was carried out on a very complex and heterogeneous porous stone such as tuff. NMR study allowed to obtain detailed information on the penetration depth of treatments, the hydrophobic effect, and changes in the open porosity caused by treatments. Physical and chemical inhomogeneities between the impregnated layers of tuff and the layers underneath were also detected. The average pores radius and pores interconnection obtained from NMR diffusion measurements were used for the first time to compare effects of different consolidating and/or protective treatments on stone. Because unilateral NMR technique is neither destructive nor invasive, investigation of treatments can be also carried out and optimized directly on buildings and monuments of interest for Cultural Heritage.

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Self-diffusion in a periodic porous medium: A comparison of different approaches

Cited by 84 publications

References 9 publications

Nuclear magnetic resonance diffusion with surface relaxation in porous media

Nuclear magnetic resonance diffusion with surface relaxation in porous media

NMR for equilateral triangular geometry under conditions of surface relaxivity—analytical and random walk solution

Unilateral NMR investigation of multifunctional treatments on stones based on colloidal inorganic and organic nanoparticles

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