We investigate a connection between random walks and nonlinear diffusion equations within the framework proposed by Einstein to explain the Brownian motion. We show here how to properly modify that ...framework in order to handle different physical scenarios. We obtain solutions for nonlinear diffusion equations that emerge from the random walk approach and analyse possible connections with a generalized thermostatistics formalism. Finally, we conclude that fractal and fractional derivatives may emerge in the context of nonlinear diffusion equations, depending on the choice of distribution functions related to the spreading of systems.
In this work, laser-induced Thermal Lens Temperature Scanning technique (TL-TS) is applied to evaluate oxidative stability and time of transesterification during biodiesel synthesis. Samples ...collected at different time intervals during the transesterification process of sunflower (SF) and soybean (SB) oils were submitted to fast oxidation through temperature scanning (between 22 and 190°C), and simultaneously measured with the TL-TS technique. Temperature dependence of Thermal Lens effect amplitude showed the occurrence of oxidation, with the onset (Tonset) changing with the transesterification stages from 149 to 169°C for sunflower and from 120 to 142°C for soybean samples. The characteristic evolution of Tonset with reaction duration was estimated to be ∼7min for sunflower and ∼10min for soybean samples. The thermal diffusivity values were shown to be sensitive to rapid changes at transition temperatures, which could be related to molecular ruptures. Additional measurements were performed with DSC, TG and FTIR, to validate the information obtained by the TL-TS technique. In conclusion, the results showed the TL-TS technique as a promising tool for oxidative stability evaluation and determination of both chosen working temperature and minimal time interval for the solution to reach an optimized transesterification stage, thus contributing for reduction of costs, quality control and consequently for certification of biodiesel fuels.
We investigate possible connections between two different implementations of the Poisson–Nernst–Planck (PNP) anomalous models used to analyze the electrical response of electrolytic cells. One of ...them is built in the framework of the fractional calculus and considers integro-differential boundary conditions also formulated by using fractional derivatives; the other one is an extension of the standard PNP model presented by Barsoukov and Macdonald, which can also be related to equivalent circuits containing constant phase elements (CPEs). Both extensions may be related to an anomalous diffusion with subdiffusive characteristics through the electrical conductivity and are able to describe the experimental data presented here. Furthermore, we apply the Bayesian inversion method to extract the parameter of interest in the analytical formulas of impedance. To resolve the corresponding inverse problem, we use the delayed-rejection adaptive-Metropolis algorithm (DRAM) in the context of Markov-chain Monte Carlo (MCMC) algorithms to find the posterior distributions of the parameter and the corresponding confidence intervals.
Diffusion—Reaction processes on a backbone structure Marin, D.; Guilherme, L.M.S.; Lenzi, M.K. ...
Communications in nonlinear science & numerical simulation,
June 2020, 2020-06-00, 20200601, Letnik:
85
Journal Article
Recenzirano
•Diffusion on a backbone structure with reaction.•Irreversible and reversible reaction processes and comb-model.•Solutions for a reaction processes in a comb-model.•Anomalous diffusion and reaction ...processes on backbone structure.
We analyze the diffusion of a system on a backbone structure, by considering the presence of reaction terms. We start our analysis by considering an irreversible reaction process, where the particles are removed from the system. After, we consider the diffusion subjected to a reversible reaction process. The behavior for the system in this scenario depends on the relative rates of diffusion and reaction. For these cases, we obtain exact solutions in terms of the Green function approach and show a rich class of behavior which can be related to anomalous diffusion.
We report on an extensive characterization of the cracking noise produced by charcoal samples when dampened with ethanol. We argue that the evaporation of ethanol causes transient and irregularly ...distributed internal stresses that promote the fragmentation of the samples and mimic some situations found in mining processes. The results show that, in general, the most fundamental seismic laws ruling earthquakes (the Gutenberg-Richter law, the unified scaling law for the recurrence times, Omori's law, the productivity law, and Båth's law) hold under the conditions of the experiment. Some discrepancies were also identified (a smaller exponent in the Gutenberg-Richter law, a stationary behavior in the aftershock rates for long times, and a double power-law relationship in the productivity law) and are related to the different loading conditions. Our results thus corroborate and elucidate the parallel between the seismic laws and fracture experiments caused by a more complex loading condition that also occurs in natural and induced seismicity (such as long-term fluid injection and gas-rock outbursts in mining processes).
We investigate the influence of the surface effects on a diffusive process by considering that the particles may be sorbed or desorbed or undergo a reaction process on the surface with the production ...of a different substance. Our analysis considers a semi-infinite medium, where the particles may diffuse in contact with a surface with active sites. For the surface effects, we consider integrodifferential boundary conditions coupled with a kinetic equation which takes non-Debye relation process into account, allowing the analysis of a broad class of processes. We also consider the presence of the fractional derivatives in the bulk equations. In this scenario, we obtain solutions for the particles in the bulk and on the surface.
•Solutions for a fractional reaction diffusion equation.•Different regimes and Interplay.•Anomalous spreading and long tailed distributions.
We investigate the behavior of a mass transfer process ...governed by a set of fractional diffusion equations coupled by appropriate reaction terms. The presence of memory effects in the diffusive term is also considered. For this set of equations, we obtain solutions and analyze the influence of the reaction terms on the spreading of these solutions. Particularly, we observe that for reversible reaction processes the reaction terms play an important role for intermediate times and for long times the processes are essentially governed by the bulk equations. These results show a rich class of behaviors which can be connected to sub- or superdiffusive regime.
In this study, we argue that ion motion in electrolytic cells containing Milli-Q water, weak electrolytes, or liquid crystals may exhibit unusual diffusive regimes that deviate from the expected ...behavior, leading the system to present an anomalous diffusion. Our arguments lie on the investigation of the electrical conductivity and its relationship with the mean square displacement, which may be used to characterize the ionic motion. In our analysis, the Poisson–Nernst–Planck diffusional model is used with extended boundary conditions to simulate the charge transfer, accumulation, and/or adsorption–desorption at the electrode surfaces.
We present a theoretical analysis of the current–voltage characteristics of electrolytic cells using their electrical impedance response to a simple periodic external voltage of small amplitude. The ...examined cell is a thin-film electrolyte (solid, liquid, or gel) sandwiched between flat electrodes at which Ohmic conduction or adsorption–desorption phenomena occur. The basic equations of the Poisson–Nernst–Planck (PNP) model are analytically solved for the case of two diffusing mobile ions (ambipolar diffusion), yielding the charge densities in thermal equilibrium and the profile of the electric potential across the sample. Proper boundary conditions permit us to explore the influence of blocking, Ohmic and adsorbing-desorbing electrodes on the final I(V) curves. Remarkable, it is possible to establish an equivalence between the Ohmic and adsorption–desorption boundary conditions for a general set of physically relevant values of the parameters characterizing the electrodes. This equivalence is a natural way to further incorporate a frequency dispersion caused by the surfaces on the whole response of the cell. This makes the approach well-tailored to investigate the role of the different diffusion coefficients for cations and anions as well as the surface effects on the voltammetry measurements in insulators containing ionic impurities.
•A generalized model for adsorption-desorption in confined systems.•Bulk dynamics affected by extended surface reach, such as found in porous media.•Model allows different adsorption ...mechanisms.•Non-usual diffusive regimes are found.•Potential for applications in several separation and industrial processes.
The adsorption-desorption phenomena play a pivotal role in several industrial and scientific processes, deserving attention from research groups across several fields of knowledge. In this article, we study adsorption-desorption of neutral particles scattered in a confined liquid when memory effects are present in both processes, the adsorption and desorption phenomenon. On contrary to previous studies, in which kernels representing memory effects were added to kinetic equations in the desorption term, resulting in considerable change in the dynamics of adsorbed particles, in this work we study the insertion of memory effects on the adsorption process. Such memory means that the preceding state of the particle in the bulk is relevant to the adsorption process, thus heavily affecting how particles are distributed in the bulk and making the reach of the surfaces far greater than when these effects are not considered. We firstly study a case where memory effect occurs only on the adsorption case, and then we analyze situations in which memory effects are included on both adsorption and desorption, and the distinct diffusion regimes in these systems. Our results could be potentially applied and easily adapted to model systems with complex geometries where diffusion and adsorption are present, such as occurs in slit pores.
PDF
