The 1 H NMR microimaging technique is applied to study water vapor sorption by the individual cylindrical silica gel and alumina pellets impregnated with hygroscopic salts. The two-dimensional images or the onedimensional profiles of the sorbed water distribution are detected sequentially to monitor the transport of water within the pellets in real time in the course of the sorption process. The results identify the propagation of the sorbed water front through the dry regions of the pellets as the rate-limiting stage of the sorption process. This propagation can be facilitated by employing the pellets with the eggshell distribution of the salt, but in such cases the salt redistributes readily in the course of the sorption process, as revealed by the relaxation weighted 1 H NMR microimaging experiments in which paramagnetic salts are used. The diffusion equation with water content dependent diffusivity is employed to model the one-dimensional radial profiles of water distribution within the pellet with appropriate correction for the relaxation weighting effects.
Mass transport of liquids which obeys the equation with liquid concentration -dependent diffusivity is considered. Numerical algorithm of solving the direct and inverse problems is presented. Water concentration profiles measured experimentally in the course of drying of water-saturated porous alumina pellets are shown to be adequately modelled assuming exponential concentration dependence of diffusivity. 336 5. /. Kabanikhin, I. V. Koptyug, K. T. Iskakov, and R. Z. Sagdeev porous solid comprises a tremendous number of structural units. To further simplify the problem additional assumptions are often introduced. For instance, drying is often treated as an isothermal process (which is not true in the general case and can only be justified for very slow drying rates). In this case the problem can be reduced to a single differential equation describing the transport of the liquid phase in the sample, with appropriate initial and boundary conditions. Strictly speaking, the transport of a liquid during drying of a porous sample is not caused by diffusion. At early stages of drying when most of the pores are still filled with the liquid and a contiguous system of liquid elements exists, the main mechanism of liquid redistribution is the capillary flow caused by capillary suction which arises due to the difference in capillary pressures over menisci of different size. However, for certain simple porous structures capillary transport of liquids has been shown to conform to the equation which is similar to the diffusion equation. Therefore the redistribution of liquid caused by capillary forces is often called "capillary diffusion".Solution of the diffusion equation provides the variation of the diffusing substance concentration in space and time. To interpret experimental results, however, the inverse problem has to be solved, i.e., one has to evaluate the diffusivity (P) provided that.the .concentration of the diffusing substance is sampled as a function of space and time. This inverse problem is generally ill-posed, and is further complicated due to the fact that the closed form solution of the diffusion equation can be obtained for a limited number of simple geometries only and under the assumption that the diffusion coefficient is concentration-independent. However, in many cases, including drying processes in natural and synthetic porous solids, the diffusion coefficient is likely to be dependent on the concentration of the diffusing substance. Thus, a numerical approach to the solution of the inverse problem is required, which should yield the concentration-dependent diSusivity pto\ r \ded that iel\ab\e experimental data on the variation of liquid concentration in space and time is available.
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