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We apply an extension of dual-phase-lag in thermal systems to predict the photoacoustic signal for transmission configuration and characteristics of the open photoacoustic cell technique. For this, we consider a particular case from Jeffrey's equation as an extension of the generalized Cattaneo equations. In this context, we obtain the temperature distribution under the effects of fractional differential operators, allowing the calculation of the Photoacoustic signal for the transmission set-up. The results show a rich class of behaviors related to the anomalous diffusion connected to these fractional operators. [ABSTRACT FROM AUTHOR]

In this work, we investigate the effect of the number of available adsorption sites for diffusing particles in a liquid confined between walls where the adsorption (desorption) phenomena occur. We formulate and numerically solve a model for particles governed by Fickian's law of diffusion, where the dynamics at the surfaces obey the Langmuir kinetic equation. The ratio between the available number of adsorption sites and the number of total particles are used as a control parameter. The investigation is carried out in terms of characteristic times of the system for different initial configurations, as well as the cases of identical or non-identical surfaces. We calculate the bulk and surface densities dynamics, as well as the variance of the system, and demonstrate that the number of sites affects the bulk, surface distributions, and diffusive regimes. [ABSTRACT FROM AUTHOR]

The use of mathematical models has been longly recognized as a fundamental step for in-depth process studies. Aimed at process control applications, the use of transfer functions identified from plant data represents an interesting modeling approach when compared to the derivation of first-principles-based models. Thermal systems are widely present in scientific and industrial scenarios, with applications in different fields, representing an important component of a cost operation. Towards this, the development of low-cost thermal systems has been reported aimed at understanding basic phenomena and validating modeling and control strategies. In the first part of the work, open loop identification was performed, leading to a fractional order transfer function, with order α=0.838±0.009. In the second part, a classical closed loop identification, using an integer order PI (proportional-integral) controlled, was used to identify an integer order transfer function. In the third part, the closed loop identified transfer function was employed to successfully preview the experimental closed loop behavior of the controlled and manipulated variables using different PI controllers. [ABSTRACT FROM AUTHOR]

In this study presents a theoretical and experimental approach to the diffusion of ions and conductometry of ionic solutions. The bases used the related theory of mass transfer, diffusion, of ionic solutions and ionic conductometry. Potassium acetate and tribasic sodium citrate salts at different temperatures (20°C;25°C;35°C) were used to study the mobility of ions. The results indicated a different electrical response that means a distinct behavior of ions when in aqueous solutions of pure salts or mixtures. The study verifies that the mixture of solutions and the temperature directly influenced the conductivity. For the temperature of 20°C the result of the sequence for the conductivity as a function of time was: 10% ethyl acetate - 90% citrate > 90% ethyl acetate - 10% citrate > 50% citrate - 50% acetate > citrate > acetate; to a temperature of 25°C to approximately sequence is: citrate > acetate > 50% ethyl acetate - 50% citrate > 90% ethyl acetate - 10% citrate > 10% ethyl acetate - 90% citrate (up to 10 min) and 35°C conductivity versus time was the following: 10% ethyl acetate - 90% citrate > 50% citrate - 50% acetate > citrate > 90% acetate - 10% citrate > acetate. Moreover, the experimental data obtained were adjusted to the model proposed by Drude. [ABSTRACT FROM AUTHOR]

Fractional order PI control and multivariable systems applied to the binary distillation model of Wood and Berry (1973) were studied. Genetic algorithms were implemented for controller tuning based on the minimization of ITAE of all loops, considering a set-point change in the top and in the bottom compositions. Simulations considered decentralized controllers, random measurement errors in controlled variables, and the presence of decoupling systems, the latter with the purpose of minimizing interaction between control loops A unique set of parameters for the fractional controller, able of handling different real operating situations, was obtained. The fractional PI controller significantly improved the performance of the multivariable control system when compared to the integer order PI controller. The use of fractional control led to a reduction of the ITAE value by 53.6% for a change of set-point of the bottom composition, when compared to the ITAE value obtained with the integer PI controller. Also in regard to the ITAE value, 58.9% of improvement was achieved when comparing systems with and without the loop decouplers. The fractional controllers were stable with errors of up to 10% of the value of the measured variable. [ABSTRACT FROM AUTHOR]

Particulate and granular materials are found in different chemical processes. Measuring and characterizing the mixing degree remains a challenge, s it is an important variable for process performance. The availability of reliable sensors for real time control is still incipient or expensive, an alternative remains on the development of mathematical models for mixing prediction. The most commonly used approach for solid mixing concern on either diffusive or advective/convective processes. Fractional calculus represents a novel approach and a growing research field for process modeling, being based on derivates of arbitrary order. Therefore, it represents an important and alternative tool for mixing process modeling. This work study the use of a fractional diffusion model to describe granular mixing in a rotary cylinder, considering finite type of boundary conditions. Experimental data previously reported were used for validation purposes. The proposed approach could successfully describe the experimental data, thus, can be used as an alternative tool for mixing evaluation. [ABSTRACT FROM AUTHOR]

Lead is a heavy metal effluent pollutant, which can be generated by different chemical plants. Literature reports different approaches for lead removal, however, great attention has been given to water hyacinths. Mathematical modeling of heavy metal sorption represents an important tool for in-depth process studies. This work proposes a new approach for modeling heavy metal isotherm sorption by using fractional calculus formalism. A novel isotherm based on Mittag-Leffler function is developed for lead sorption experimental data equilibrium modeling, in order to provide more accurate equilibrium information for sorption dynamic modeling. Experimental data were obtained using Eicchorniacrassipes as the hyacinth. Simulation results were compared to classical equilibrium sorption models. It was shown that the proposed isotherm, Epslon, provides better results when compared to classical models. [ABSTRACT FROM AUTHOR]

Tilapia (Oreochromis sp.) is the most important and abundant fish species in Brazil due to its adaptability to different environments. The development of tilapia-based products could be an alternative in order to aggregate value and increase fish meat consumption. However, there is little information available on fish burger freezing and cooking in the literature. In this work, the mathematical modeling of the fish burger baking was studied. Previously to the baking process, the fish burgers were assembled in cylindrical shape of height equal to 8 mm and diameter 100 mm and then baked in an electrical oven with forced heat convection at 150 °C. A T-type thermocouple was inserted in the burger to obtain its temperature profile at the central position. In order to describe the temperature of the burger during the baking process, lumped-parameter models of integer and fractional order and also a non-linear model due to heat capacity temperature dependence were considered. The burger physical properties were obtained from the literature. After proper parameter estimation tasks and statistical validation, the fractional order model could better describe the experimental temperature behavior, a value of 0.91 ± 0.02 was obtained for the fractional order of the system with correlation coefficient of 0.99. Therefore, with the better temperature prediction, process control, and economic optimization studies of the baking process can be conducted. [ABSTRACT FROM AUTHOR]

We investigate an intermittent process obtained from the combination of a nonlinear diffusion equation and pauses. We consider the porous media equation with reaction terms related to the rate of switching the particles from the diffusive mode to the resting mode or switching them from the resting to the movement. The results show that in the asymptotic limit of small and long times, the spreading of the system is essentially governed by the diffusive term. The behavior exhibited for intermediate times depends on the rates present in the reaction terms. In this scenario, we show that, in the asymptotic limits, the distributions for this process are given by in terms of power laws which may be related to the q-exponential present in the Tsallis statistics. Furthermore, we also analyze a situation characterized by different diffusive regimes, which emerges when the diffusive term is a mixing of linear and nonlinear terms. [ABSTRACT FROM AUTHOR]

The solutions for a dimensional system with radial symmetry and governed by a fractional diffusion equation have been investigated. More specifically, a spherical system was considered, being defined in the semi-infinity interval [R, ∞) and subjected to surface effects described in terms of integro-differential boundary conditions which has many practical applications. The analytical solutions were obtained by using the Green function approach, showing a broad range of different behaviors which can be related to anomalous diffusion. The analyses also considered the influence of the parameters of the analytical solution in order to describe a more realistic scenario. [ABSTRACT FROM AUTHOR]

We investigate solutions of a generalized diffusion equation that contains nonlinear terms in the presence of external forces and reaction terms. The solutions found here can have a compact or long tail behavior and can be expressed in terms of the q-exponential functions present in the Tsallis framework. In the case of the long-tailed behavior, in the asymptotic limit, these solutions can also be connected with the Lévy distributions. In addition, from the results presented here, a rich class of diffusive processes, including normal and anomalous ones, can be obtained. [ABSTRACT FROM AUTHOR]

Particulate and granular materials are found in different chemical processes. Measuring and characterizing the mixing degree remains a challenge, s it is an important variable for process performance. The availability of reliable sensors for real time control is still incipient or expensive, an alternative remains on the development of mathematical models for mixing prediction. The most commonly used approach for solid mixing concern on either diffusive or advective/convective processes. Fractional calculus represents a novel approach and a growing research field for process modeling, being based on derivates of arbitrary order. Therefore, it represents an important and alternative tool for mixing process modeling. This work study the use of a fractional diffusion model to describe granular mixing in a rotary cylinder, considering finite type of boundary conditions. Experimental data previously reported were used for validation purposes. The proposed approach could successfully describe the experimental data, thus, can be used as an alternative tool for mixing evaluation. [ABSTRACT FROM AUTHOR]