Volume 30, Issue 4

In this paper, we explore some aspects of the formation of tree-like structures (dendrites) with branching and ramifications in Zn electrodeposition systems. A special cell is designed wherein dendrites are grown between two parallel electrodes. All measurements are carried out at fixed voltage (9.5 V). As the concentration is varied at that fixed potential, the fractal box-count dimension is exactly anti-correlated with the pattern density. The latter is measured by the fraction covered by the electrodeposits, of a total area delimited by the cathode and the farthest dendritic tip. At relatively high concentration, the obtuse angle of lateral branching and the box dimension show a good correlation. The pattern density decreases with interelectrode distance, thus displaying a perfect correlation with the dependence of the current on the latter parameter. The time evolution of the pattern density exhibits an interesting oscillation caused by the preferential growth of individualized trees.

The Soret coefficient of water–ethanol mixtures at one atmosphere and temperatures ranging from 20°C to 40°C has been studied in detail. Comparisons between the experimental data and predictions of existing theoretical models showed satisfactory agreement only for certain conditions. In order to properly model the behavior of water in the mixture, the thermodynamic properties of water–ethanol mixtures were calculated using the Cubic Plus Association (CPA) equation of state. Compared to the theoretical models of Haase, Kempers, Dougherty and Drickamer, the Firoozabadi model was found to perform much better in predicting the thermal diusion phenomena for water–alcohol mixtures.

The thermal diusion phenomena, also known as the Soret eect, is important for the study of compositional variation in hydrocarbon reservoirs. Several theoretical models have been developed over the years to predict the thermodiusion coefficient of an organic mixture. Firoozabadi et al. [1] developed an analytical relationship between the thermal, molecular, and pressure diusion coefficients based on the approach of Dougherty and Drickamer [2]. The distinctive feature of Firoozabadi's model is its ability to be used not only for binary mixtures but also for multicomponent mixtures. The verification of Firoozabadi's model by numerical simulations was limited to binary mixtures only because of a lack of experimental data on thermodiusion coefficients in multicomponent hydrocarbon mixtures. However, Platten et al. [3] were able to measure the thermodiusion coefficients of a ternary hydrocarbon mixture experimentally by utilizing the thermogravitational column technique, hence making it possible to verify the theoretical model. This paper will compare the density, thermodiusion, and molecular diusion coefficients obtained with the Fontainebleau benchmark values for binary mixtures of n -dodecane, isobutylbenzene, and tetrahydronaphtalene. The accuracy of the numerical results from the Firoozabadi's model for ternary hydrocarbon mixtures is investigated. Results reveal a positive agreement between experimental and numerical data.

Heat conduction close-to-Fourier means that we look for a minimal extension of heat conduction theory using the usual Fourier expression of the heat flux density and modifying that of the internal energy as minimally as possible by choosing the minimal state space. Applying Liu's procedure results in the class of materials and a dierential equation both belonging to the close-to-Fourier case of heat conduction.

In a ternary mixture of dodecane, isobutylbenzene, and 1,2,3,4-tetrahydronaphtalene, we succeeded in measuring the two thermodiusion factors using the thermogravitational column technique, and applying the Furry–Jones–Onsager theory. We suggest correlating the thermodiusion factors in the ternary system with those in the three binaries.

The mesoscopic concept is applied to the theory of mixtures. The aim is to investigate the diusion phenomenon from a mesoscopic point of view. The domain of the field quantities is extended by the set of mesoscopic variables, here the velocities of the components. Balance equations on this enlarged space are the equations of motion for the mesoscopic fields. Moreover, local distribution functions of the velocities are introduced as a statistical element, and an equation of motion for this distribution function is derived. From this equation of motion, dierential equations for the diusion fluxes and also for higher order fluxes are obtained. These equations are of balance type, as it is postulated in extended thermodynamics. The resulting evolution equation for the diusion flux generalizes Fick's law.