We define the volume density and basing on the Euler’s and Lagrange theorems derive the volume continuity equation. These fundamental formulae define the volume fixed frame of reference in the multicomponent, solid and liquid solutions. The volume velocity is a unique frame of reference for all processes namely, the mass diffusion, charge transport, heat flow, etc. No basic changes are obligatory in the foundations of linear irreversible thermodynamics except recognizing the need to add volume density to the usual list of extensive physical properties undergoing transport in every continuum. The volume fixed frame of reference allows the use of the Navier-Lamé equation of mechanics of solids. Proposed modifications of Navier-Lamé and energy conservation equations are self-consistent with the literature for solid-phase continua dating back to the classical experiments of Kirkendall and their interpretation by Darken. We do show that when Darken constraints are used the general formulae reduce to the Darken expression.

The paper presents a brief historical overview of the field of the measurement of diffusion in zeolites. The focus will be on macroscopic measurements, i.e. when diffusion through entire crystals is studied. While this may appear to be a simple task, we will see that there are difficulties in obtaining reliable results. Two case studies, the volumetric/piezometric experiment and the Transient Analysis of Products (TAP) apparatus are discussed and ways to improve either the experiments or the way in which the results are analyzed are presented. The author’s perspective into what are the current challenges in the field concludes the paper.

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Nuclear magnetic resonance (NMR) spectroscopy was used to study exchange of three distinctly different molecules across the membranes of human red blood cells (RBCs). In studying water, t-butanol, and dimethyl sulfoxide we exploited the marked differences in the apparent diffusion coefficients of these species inside and outside the cells in suspensions. The measurements were made with diffusion ordered spectroscopy (DOSY) with a domain of ‘diffusion times’ of 20 - 100 ms. In attempting to make the DOSY spectra quantitative we identified time domains for each of the three molecules in which the spectra showed well resolved peaks, and those in which only a single peak was evident for two of the species. The apparent mean resident times for water and t-butanol in the RBCs estimated by the methodology were ~17 ms, while the DMSO exchange was too slow, on the NMR timescale, to be quantified by this method. However, it is very clear that other methods that are based on regression analysis with a prescribed fitting function provide more reliable estimates of exchange rate constants. Also, to make the DOSY analysis more generally accessible we implemented a Laplace transform inversion method (the Post-Widder algorithm), and a procedure for enhancing the resolution of the resulting diffusion spectra by using standard functions in Mathematica.

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