The fractal mobile–immobile model (MIM) is intermediate between advection–dispersion (ADE) and fractal Fokker–Planck (FFKPE) equations. It involves two time derivatives, whose orders are 1 and γ (between 0 and 1) on the left-hand side, whereas all mentioned equations have identical right-hand sides. The fractal MIM model accounts for non-Fickian effects that occur when tracers spread in media because of through-flow, and can get trapped by immobile sites. The solid matrix of a porous material may contain such sites, so that non-Fickian spread is actually observed. Within the context of the fractal MIM model, we present a mapping that allows the computation of fluxes on the basis of the density of spreading particles. The mapping behaves as Fickian flux at early times, and tends to a fractional derivative at late times. By means of this mapping, we recast the fractal MIM model into conservative form, which is suitable to deal with sources and bounded domains. Mathematical proofs are illustrated by comparing the discretized fractal p.d.e. with Monte Carlo simulations.

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The IVIDIL (Influence of VIbrations on DIffusion in Liquids) experiment was aimed at utilizing the International Space Station for investigating the effects of vibrations on liquid diffusion and thermodiffusion. The SODI-IVIDIL project of ESA is gathering together European, Canadian and Russian researchers with complementary skills to prepare and carry out the experiment, to process the raw data and perform numerical modeling of the phenomena. The experiment IVIDIL started on the October 5, 2009. In total 55 experimental runs were successfully completed by 20 January, 2010. A general description of the ISS facility related to the diffusion experiments and accessible for European researchers is briefly presented and some details about IVIDIL instrument are given. The scientific interest of this short article is focused on one of the objectives of the experiment: performing precise measurements of diffusion and thermodiffusion coefficients for binary mixtures in the absence of gravity. We demonstrate possibility of the experimental environment and report on the first results related to measurements of mass transport coefficients in the mixture with the negative Soret effect: 10% isopropanol (IPA)-90% water.

Double-diffusive and vibrational convection with the Soret effect is considered in a cubic rigid cell filled with water ͑90%͒ and isopropanol ͑10%͒, subjected to a temperature difference between opposite lateral walls. Numerical simulations are carried out for g-jitter induced flow. The direction of g-jitter is the same as the residual gravity vector, which is perpendicular to the applied temperature gradient. Along with various combinations of static and oscillatory components, vibrations with two different frequencies are examined: ͑a͒ when the period of oscillations is smaller than any characteristic time ͑viscous, thermal, and diffusion͒, f = 0.2 Hz; ͑b͒ when the period of oscillations is comparable with viscous time, f = 0.01 Hz. Component separation due to the Soret effect under these driving actions is analyzed. The concept of time-averaged models is applied for the explanation of the high-frequency results. The interplay between the mean and fluctuating motions is discussed. Three research groups performed a benchmark of numerical solutions of three-dimensional Navier-Stokes, energy, and concentration equations using the true physical parameters for a future Space experiment. The objective of this paper is twofold: ͑i͒ to carry out an accurate study of heat and mass transfer in a binary liquid with the Soret effect in the presence of steady residual gravity and its oscillatory component; ͑ii͒ to carry out a benchmark of numerical solutions.

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