Natural additives with antioxidant properties can be used as biodegradable and sustainable alternatives to synthetic products, because they can inhibit the biodiesel oxidation reaction, increasing oxidative stability and extending its storage period. This research evaluated the efficiency of jabuticaba peels, gabiroba leaves, and hibiscus flowers in ethanolic extracts, analyzing through the simplex-centroid design, the induction periods (IP) and rate constants (k) of the biodiesel oxidation reaction at 110 °C. Antioxidant activity was observed in all extracts, either decreasing k or increasing the IP. The mathematical models obtained showed coefficients of determination greater than 0.9400, a non-significant lack of fit at the 5% level, and low dispersion between predicted and experimental data, indicating that the 1st order reaction fit was appropriate and can be used for predictive purposes. In this work, the optimization was performed with maximization of IP and minimization of k showing that the mixture containing 25% of jabuticaba peels extract and 75% of gabiroba leaves extract was the most suitable, because proportionally increased the IP and decreased k of the biodiesel oxidation reaction. It is possible to suggest the use of jabuticaba peels extract or gabiroba leaves extract as well as various combinations between them as antioxidant additives.

The objective of the present work was to apply self-organizing feature maps (SOFM) and multilayer perceptron (MLP) to evaluate the protective capacity of tert-butylhydroquinone (TBHQ), butylhydroxyanisole (BHA), and butylhydroxytoluene (BHT) antioxidants against the biodiesel oxidation reaction. For this, the antioxidant concentration and the biodiesel compliance parameters were used as continuous input variables and the type of antioxidant as a categorical. The SOFM proved to be an adequate tool for the classification of biodiesel samples containing antioxidants. The performance of the 5 most active networks of the model ranged from 89 to 99% for training, testing, and validation with an error below 1.42 × 10-4. Statistical tests applied to validate the model showed no significant difference between predicted and experimental values. The global sensitivity analysis showed that the relative protection factor (RPF) contributed with 34.89%, the antioxidant with 31.49%, the induction period with 10.69%, the water content with 6.00%, and the others all together with 16.93% in the construction of the regression models by MLP.

The simultaneous diffusion of inorganic components in the olive pulp in wet brine was modeled based on Fick’s generalized 2nd Law and simulated using the finite element method. The main and crossed diffusion coefficients, the film coefficient and the Biot number were determined, with the application of the simplex optimization method, through the minimization of the percentage errors. The errors between the simulated and experimental data were 5.35% for NaCl and 4.77% for KCl and the adjusted main diffusion coefficients were 0.4358 × 10-12 m2 s-1 for NaCl and 0.5408 × 10-12 m2 s-1 for KCl. The system developed to simulate diffusion allows the control and modulation of the salts content that diffuses through the olive pulp.

Olive samples were subjected to the salting process in brine containing 1196 mol m−3 of NaCl and 402 mol m−3 of KCl. Samples were collected during 60 h and salt concentration values were determined. With the finite element method (FEM) and the minimization of the errors percentage between the simulated and experimental values, the mass transfer coefficients in the film (hm) were obtained, being 1.0072 × 10−8 and 1.2499 × 10−8 for NaCl and KCl, respectively. The salts concentration at the olive/brine interface was simulated by FEM and analyzed via SOFM. A network with 4 × 4 topology and 10000 training epochs was used. It was observed that the influence of the stationary film formed on the surface of the olives during the salting process depends on the position, the salt involved in the diffusion and that the concentration of the salts, at each point, varies according to the immersion time.

Biodiesel is capable of replacing diesel because it has similar physicochemical properties, but this biofuel is susceptible to oxidation, which makes the application of antioxidant substances necessary. For this study, alcoholic extracts of senna leaves, hibiscus flowers, and blackberry were used. Biodiesel samples were submitted to physicochemical analysis to evaluate interference in the volume of these alcoholic extracts with antioxidant properties. The data obtained were processed using the neural network of the multilayer perceptron type (MLP). For the network’s training, 200 epochs were used. The samples were randomly divided into three groups, with 70% used for training, 15% for testing, and 15% for validation. The type of extract was considered as a categorical variable, the extract volume as a target variable, and the other ones as input variables. Among the 200 networks trained, with 5 to 20 hidden layers, the 5 with the best performance were highlighted. The Tukey test applied to the means showed no significant difference at the 5% level, between the value of the added volume and the means value predicted by the networks. The sensitive analysis showed that the most important input variable for the construction of the model was the type of extract.

Sodium chloride is used in the cheese salting process as it promotes sensory changes and food preservation. However, in excess can cause hypertension problems, and for this reason, it has been partially replaced by potassium chloride. In the present work, Prato cheese was subjected to joint diffusion of NaCl and KCl by immersion in static and stirred brine. The salt concentration values on the cheese surface were determined as a function of time. They were tabulated and presented to the self-organizing map (SOM)-type neural networks and the multilayer perceptron (MLP) for analysis and modeling of the film formed on the surface of the cheese during static and dynamic salting. The SOM network showed that the behavior of the diffusive process, on the surface of the cheese, depends on the analyzed position and that the points in which occupy similar positions, concerning the distance from the edge, have similar behavior. Regression models for NaCl and KCl were significant at the 5% level and can be used for predictive purposes.

The influence of the film formed during the salting of champignon mushrooms with brine containing NaCl and KCl was modeled using the finite elements method (FEM). It was verified that the film formed on the mushroom surface had a greater influence in the static salting since the diffusion of the ions was 7.5-fold smaller in this system than in the stirred salting. The application of self-organizing maps showed that the ions diffusion along the surface of the solid presented a heterogeneous occurrence and depended on the region for both static and stirred salting. A direct relation was observed among the mushroom surface morphology, the salts diffusion behavior, and the film formation. In addition, the film was not completely extinguished in the stirred system, although it has a minimal influence as the film formation is also dependent on the biosolid surface.

The NaCl and KCl diffusion in the film formed on the cheese surface during salting was simulated by the finite element method. The time and salts concentration values on the cheese surface were determined, tabulated, and presented to the multilayer perceptron neural network (MLP) for the regression modeling. The samples were divided into 70, 15 and 15% for training, testing, and validation, respectively. The networks with the best performance showed 5 to 12 hidden layers. The Tukey’s test showed that there was no significant difference, at the 5% level, between the time value used and the mean value modeled for training, testing, and validation for the NaCl. For the KCl, a significant difference was observed only for 2 training samples and 1 test sample. Sensitivity analysis showed that the discrete variable Z, which represents the static and dynamic systems, was the most important in the models’ construction.

Biodiesel contains unsaturated methyl esters making it susceptible to oxidation reaction. Among the factors that cause oxidative instability is the contamination by transition metal ions that in small quantities catalyze the oxidation reaction. The objective of this work was to evaluate the relative protection factor of rosemary extract, in biodiesel, in the presence of transition metal ions. Chromatographic analysis and characterization of biodiesel were performed as well as the quantification of total phenolic compounds and extract activity. The ions Cr3+, Co2+ and Fe2+, at a concentration of 3.95 x 10-3 mol L-1, were added to the biodiesel with and without rosemary extract. The samples were submitted to the Rancimat test and to infrared region analyses. The infrared region spectra of the samples with Cr3+ are in accordance with the least catalytic power of this ion under the biodiesel oxidation. Samples with Co2+ ions, without extract, presented bands of aldehydes, and samples with Fe2+ ions show the formation of peroxide radicals, without rosemary extract at 48h. The antioxidant effect of the extract in biodiesel is observed by the reduction of the induction period of the samples. The relative protection factor proved to be a good tool to evaluate its efficiency.

Biodiesel contains esters in its composition which make it susceptible to oxidation. Among the factors that cause this reaction is the contamination with metal ions. In the present work, it was analyzed biodiesel samples obtained from a mixture containing 39.0% m/m soybean oil, 22.0% m/m beef tallow and 39.0% m/m poultry fat using a methyl route. Copper ions were added to the biodiesel to evaluate its catalytic action in the oxidation reaction, in the presence and absence of rosemary extract. During 192 h of assay, samples containing copper, without extract, showed shorter induction periods, higher rate constants and lower activation energy, when compared to samples containing extract, at the same assay temperature. Copper ions presented a strong catalytic action causing linearity deviations showing a super-Arrhenius behavior, while rosemary extract delayed the oxidative process and showed no linearity deviations.

The champignon mushroom has no antinutritional factors that can affect iron bioavailability. It is considered a functional food and can provide health benefits by presenting bioactive components. The simultaneous transfer of Na+, K+ and Fe2+ in the pre-cooked mushroom (Agaricus bisporus) was modeled and simulated by the finite element method (FEM). The Biot number, cross and main diffusion coefficients were determined by the super modified simplex optimization method by minimizing the percentage errors. The errors between experimental and simulated data were 5.66% for NaCl, 5.36% for KCl and 8.26% for Fe2+ in the static brine and 3.11% for NaCl, 3.30% for KCl and 15.34% for Fe2+ in stirred brine. With the obtained model, it was possible to verify the influence of the film formed on the surface of the mushroom during the diffusion of ions, as well as the increase of ferrous ion adsorption when using the salting system with stirring.

The use of biodiesel as fuel has been presented as a viable alternative in the search for renewable energies. It can be produced from the transesterification reaction of vegetable oils with methanol in the presence of sodium or potassium hydroxide as catalysts. In the present research, the transesterification reaction of soybean oil was modeled considering the three steps of the direct and reverse reactions following a second order general kinetics by the finite element method using the COMSOL Multiphysics® software. The values of rate constants were determined using the simplex optimization method coupled with the desirability functions. The optimized rate constants for the forward reactions were 0.250 × 10−6 (k1f), 1.137 × 10−6 (k2f) and 3.134 × 10−6 (k3f); and for the reverse reactions were 0.202 × 10−6 (k1r), 0.884 × 10−6 (k2r) and 0.219 × 10−6 (k3r) all in m3mol−1s−1. The kinetic model proposed for the reaction can be simulated by the finite element method (FEM) under realistic conditions.

The purpose of this research was to evaluate the influence of metallic alloys and copper in the degradation of biodiesel in mixture with blackberry extract. Biodiesel is formed by unsaturated esters highly susceptible to the oxidation reaction. The initial induction period (IP) of the control sample was 9.53 h and, after 208 days, the IP reduced to 5.74 h. However, with the addition of the antioxidant, the final IP was 6.27 h. The assays involving carbon steel, stainless steel, silver steel and copper showed final IP of 3.78, 4.43, 1.59 and 0.09 h, respectively. This behavior indicates that the reaction was catalyzed in the presence of metal. The addition of the blackberries extract favored the increase of the induction period and the decrease of the reaction rate constant values, aside from the carbon steel that presented a final IP of 1.22 h. The highest rate constant was 7.41 h obtained for biodiesel in contact with copper, as well as the highest IP. The acid number ranged from 0.34 to 0.60 mgKOH g-1. It was possible to observe in the oxidation reactions the presence of the linearity deviation proposed by Arrhenius.

A influência da temperatura sobre a oxidação de biodiesel foi avaliada pelos parâmetros cinéticos e termodinâmicos do biocombustível de óleo de soja e gordura suína com antioxidantes sintéticos: 3-terc-butil-4-hidroxianisol (BHA), 3,5-di-terc-butil-hidroxitolueno (BHT), 2-terc-butil-hidroquinona (TBHQ) e galato de propila (PG), de acordo com delineamento de mistura simplex-centróide. Os parâmetros cinéticos foram determinados considerando-se reação de primeira ordem e aplicando a equação de Arrhenius. A adição de antioxidantes promoveu o aumento da energia de ativação (Ea), sendo TBHQ e PG os mais eficientes, apresentando efeito sinérgico. BHT e BHA foram os menos eficientes, assim como suas misturas. Os parâmetros termodinâmicos de ativação, avaliados pela equação de Eyring, não indicaram processos espontâneos (∆G‡ > 0) com valores de ∆H‡ positivos, e ∆S‡ positivos e negativos. O delineamento simplex-centróide indicou valor otimizado de 174,46 kJ mol-1 para a mistura contendo 33,33 e 66,67% de TBHQ e PG, respectivamente.

Temperature's influence on biodiesel oxidation was evaluated by kinetic and thermodynamic data in biofuel from soybean oil and lard with synthetic antioxidants: butylatedhydroxyanisol (BHA), butylatedhydroxytoluene (BHT), tert-butylhydroquinone (TBHQ), and propylgallate (PG) by simplex centroid mixture design. The kinetic parameters ware obtained by Arrhenius equation and showed that addition of antioxidants in all tests increased activation energy (Ea) and that TBHQ and PG were more efficient and presented synergistic effect. BHT and BHA were the least efficient, as well as their mixtures. The thermodynamic activation parameters of the reactions, evaluated by the Eyring equation and based on the theory of the activated complex (ACT), indicated no spontaneous processes (∆G‡ > 0) with positive ∆H‡ values and positive and negative ∆S‡ values. The application of simplex centroid mixture design, using Ea as response, showed the optimised value of 174.46 kJ mol-1 for a mixture containing 33.33 and 66.67% of TBHQ and PG, respectively.

A transferência de um soluto (cloreto de sódio), através de uma matriz sólida tridimensional (queijo) foi estudada aplicando-se o método de elementos finitos. A formulação variacional (Galerkin) do problema diferencial (modelo de difusão) teve como base teórica a 2ª lei de Fick. Os procedimentos para integração no tempo foram o de Crank-Nicolson e o de Euler-modificado, que foram escolhidos por apresentarem estabilidade incondicional. O programa computacional desenvolvido mostrou-se versátil para resolver situações de amostragem em condições mais realistas e pode ser aplicado para geometrias complexas. O modelo proposto permitiu uma boa estimativa do ganho de sal no queijo, usando um coeficiente de difusão cujo valor pode ser obtido por extrapolação de dados experimentais. A aplicação do método numérico (MEF), com o esquema de Crank-Nicolson, na simulação da difusão do cloreto de sódio na salga de queijos, mostrou boa aproximação quando os resultados foram comparados com os valores experimentais encontrados na literatura especializada.

Solute (sodium chloride) transference through a three-dimensional matrix (cheese) was studied applying the finite element method (MEF). The variational formulation (Galerkin) of the differential problem (diffusion model) had as the theoretical basis Fick’s second law. The methods for time integration were developed according to Crank-Nicolson (central difference), and modified Euler (backward difference), which presented unconditional stability. The computational program proved to be versatile in solving sampling situations in realistic condition and can be used in complex geometry. The proposed method gave good estimation of salt gain in the cheese when using a diffusion coefficient which value can be calculated by extrapolation of experimental data. The application of numeric method (MEF), with Crank-Nicolson scheme, in the simulation of diffusion of sodium chloride in the brining showed to be close to the values published in specialized literature.