Mean Relative Deviation Modulus Research Articles

Simplified Approach Based on Polynomial Equations to Predict the Permeability of Micro‐perforated Polymeric Films

A simplified approach to predict the mass transport properties of micro‐perforated films was presented in this work. In particular, the proposed mathematical model was based on a second‐degree polynomial function. Different types of micro‐perforated films with two thicknesses (35 and 25 µm) were tested for gas and water vapour permeability, under proper conditions. The films differed in both number of holes per unit area and hole diameter. Corresponding non‐perforated films were also tested. The experimental data obtained were used to validate the model. Moreover, the surface response plot of the interactions between hole diameter and number of holes per area relative to oxygen, water vapour and carbon dioxide permeability were determined. Results of the mean relative deviation modulus (E%) between the experimental and predicted data confirmed the ability of the proposed model to predict the permeability of micro‐perforated films. Copyright © 2016 John Wiley & Sons, Ltd.

Development of artificial intelligence based systems for prediction of hydration characteristics of wheat

Hydration characteristics (moisture content, moisture ratio and hydration rate) of wheat kernel during soaking process were studied and simulated. Hydration procedure was performed at five different experimental water temperatures (30, 40, 50, 60 and 70 (°C)) with respect to hydration time changes. Hydration characteristics of samples were modeled using one of the most popular simulation frameworks of artificial intelligence, adaptive neuro-fuzzy inference system (ANFIS). A comparison was also made between results of the best developed ANFIS model and those of the another well-known artificial intelligence technique, artificial neural network (ANN). The hydration temperature and time were used as input parameters and moisture content, moisture ratio and hydration rate were taken as output parameters of the intelligent modeling frameworks. To attain the best model with the highest predictive ability, developed models were compared based on statistical parameters of coefficient of determination, root mean square error and mean relative deviation modulus. According to the results, although the best framework of both ANFIS and ANN were able to accurately predict hydration characteristics, the best ANN simulation framework with a simple structure (2–4–3) was easier to use than the ANFIS with three different structures. ANN surface plots also illustrated that increasing the hydration temperature and time increased moisture content and decreased moisture ratio. Moreover, ANN modeling results indicated that the hydration rate increased in the initial and decreased in the middle and final phase of hydration procedure.

Measurement and modelling the effect of temperature, relative humidity and storage duration on the transpiration rate of three banana cultivars

Transpiration rate (TR) of three cultivars of banana (triplicates of each experimental run, 2 nos. present in each run) was measured at different temperatures (10, 20 and 30°C) and relative humidity (RH) (70, 80 and 90%) and storage time (2, 3 and 6days). Models based on unsteady state energy balance equation and regression equation was fitted to the TR data. Best fitting model was validated at 15°C and 70, 80 and 90% RH and on 2nd, 3rd and 6th day of storage. Using the TR data design parameters for equilibrium humidity packaging for three banana varieties had been estimated. While the TR of banana increased with rise in temperature, it decreased with rise in storage RH and with progress of storage duration. Banana Cv. Singapuri had significantly low (P<0.05) average TR (21.69g/kg-day), while the average TR of G9 (34.96g/kg-day) and Chapa (29.53g/kg-day) cultivars were similar (P>0.05), and these two varieties (G9 and Chapa) were least affected by variation in temperature and relative humidities. The energy balance model (R2=0.61–0.81) fitted the TR data better than the regression model at all RH and temperature studied. Temperature of the banana surface was determined from the model and was found to be greater than the wet bulb temperature of banana. Heat transfer from banana surface by convection was found to provide approximately 70% of the heat required for transpiration. At 15°C, the predicted TR was plotted against the experimental data corresponding to storage RH, and duration. For these two predictions the mean relative percentage deviation modulus was 10.27% and 18.35%, respectively. The required water vapour transmission rate for designing equilibrium humidity packaging of three variety of banana ranged from 172 to 618g/m2day at 10–20°C.

Analytical study of friction coefficients of pomegranate seed as essential parameters in design of post-harvest equipment

Friction coefficients (static friction coefficient (SFC) and dynamic friction coefficient (DFC)) of pomegranate seed on different structural surfaces (glass, aluminum, plywood, galvanized steel and rubber) as affected by moisture content (4–21.9% (d. b.)) and sliding velocity (1.4–16 (cm/s)) were investigated. Analysis of variance (ANOVA) was performed to determine the effect of main treatments and their interactions on SFC and DFC. Significance of single or multiple effect of the main treatments with five levels was assessed using Duncan’s multiple range test (DMRT). To predict SFC and DFC, multiple linear regression (MLR) modeling technique was applied for each type of structural surface. The goodness of fit of each MLR model was evaluated using statistical parameters: coefficient of determination, root mean square error and mean relative deviation modulus. Results showed that the minimum and maximum SFC or DFC were in minimum and maximum moisture content on glass and rubber surface, respectively. ANOVA table indicated the significant effect of main treatments and their interactions on SFC and DFC at significance level of 1% (P<0.01). According to DMRT results, SFC linearly increased as moisture content increased and DFC increased also linearly as individual or simultaneous increment of moisture content and sliding velocity occurred, for all experimental conditions. According to the obtained statistical parameters, both SFC and DFC were properly predicted by means of MLR modeling technique.

Modeling of gas transmission properties of polymeric films used for MA packaging of fruits

High value fruits namely, apple (cv. Royal Delicious), guava (cv. Baruipur) and litchi (cv. Shahi) harvested at their commercial maturity were considered for MA packaging to enhance storage life. Polymeric films namely LDPE, BOPP, PVC, PVDC of different thickness were used for MA packaging study and various film characteristics such as gas transmission rates, water vapour transmission rate, clarity, strength and durability were evaluated. Mathematical model was developed based on Arrhenius type equation to predict gas transmission rate (GTR) and the developed model was found to be very good fit with the mean relative deviation modulus value quite less than 10%. The GTR of the films increased with the increase in storage temperature and the magnitude of the increase varied with the film type and thickness. Regression models have been suitably developed to predict the oxygen transmission rate and carbon dioxide transmission rate of selected polymeric films and combined film laminates as a function of temperatures. Since, none of the individual films could meet the gas transmission requirements of MAP for selected fruits, two different films were tailored to form laminates that sufficed the requirements for prolonged storage with maintaining original quality.

Beta-glucan rich composite flour biscuits: modelling of moisture sorption isotherms and determination of sorption heat.

Moisture adsorption isotherms of beta-glucan rich composite flour biscuits were determined at 28, 37 and 45°C. Experimental data were fitted to 12 mathematical models. A nonlinear regression analysis method was used to evaluate the constants of the sorption equations. Statistical testing of sorption models was carried out using multiple criteria such as coefficient of determination (R (2) ), reduced chi-square (χ (2) ), mean relative percent deviation modulus (P) and plotting of residuals. BET (R (2) > 0.99; χ (2) < 0.09; P < 7.52; RMS% < 9.22) was found suitable for predicting the M e -a w relationship in the a w range of 0.10-0.53. However, in the a w range of 0.10-0.85, although Ferro-Fontan and GAB models were found to have high R (2) values (>0.99), Peleg model was found to meet the multiple statistical criteion (R (2) > 0.9996; χ (2) < 0.04; P < 3.97; RMS% < 7.09). Properties of sorbed water were also determined. BET, GAB and Caurie monolayer moisture contents ranged from 2.64 to 3.36, 1.29-2.66 and 1.88-3.38% d.b., respectively. Second-order regression equation was found to describe the relation between monolayer moisture content, M o and temperature, t (°C). The isosteric heat, calculated using Clausius-Clapeyron equation, was varied between 1.46 and 50.39kJg(-1)mol(-1) at moisture levels 1-12% (d.b.). An exponential relationship was observed between the isosteric heat of sorption and moisture content.

Mathematical Modelling of Convection Drying Characteristics of Artichoke (Cynara scolymus L.) Leaves

This paper presents the results of a study on mathematical modelling of convection drying of artichoke (Cynara scolymus L.) leaves. Artichoke leaves used for drying experiments were picked from the agricultural faculty experimentation fields on the campus area of Ege University. Chopped artichoke leaves were then used in the drying experiments performed in the laboratory at different air temperatures (40, 50, 60 and 70 °C) and airflow velocities (0.6, 0.9 and 1.2 m s) at constant relative humidity of 15±2%. Drying of artichoke leaves down to 10% wet based moisture content at air temperatures of 40, 50, 60 and 70 °C lasted about 4.08, 2.29, 1.32 and 0.98 h respectively at a constant drying air velocity of 0.6 m s while drying at an air velocity of 0.9 ms took about 3.83, 1.60, 0.96 and 0.75 h. Increasing the drying air velocity up to 1.2 m s at air temperatures of 40, 50, 60 and 70 °C reduced the drying time down to 3.5, 1.54, 1.04 and 0.71 h respectively. Different mathematical drying models published in the literature were used to compare based on the coefficient of multiple determination (R), root mean square error (RMSE), reduced chi-square (χ) and relative deviation modulus (P). From the study conducted, it was concluded that the Midilli et al drying model could satisfactorily explain convection drying of artichoke (Cynara scolymus L.) leaves under the conditions studied.

Osmo-convective dehydration kinetics of jackfruit (Artocarpus heterophyllus)

Osmotic dehydration is a process in which partial water is removed by immersion of water containing cellular solid in a concentrated aqueous solution of high osmotic media for a specific time and temperature. Preliminary trials were planned for finalizing the concentration of osmolyte (salt solution: 5%, 10%, 15% and 20%). The osmotically pre-treated samples were dried at 50°C which were examined using sensory parameters. On the basis of sensory parameters, 15% salt solution concentration was considered best. The osmotically pre-treated jackfruit samples of 15% salt solution were convectively dehydrated in a tray dryer at air temperatures of 50, 60 and 70°C at constant velocity of 1.5m/s air flow in perforated trays. Results indicated that drying took place in falling rate period. The sample dried at 60°C was found better in color as compared to samples at 50 and 70°C. Mathematical models were fitted to the experimental data and the performance of these models was evaluated by comparing the coefficient of determination (R2), Root mean square error (RMSE), reduced chi-square (χ2), percent mean relative deviation modulus (E%) between observed and predicted moisture ratio. The best model was chosen as one with the highest coefficient of correlation (R2); and the least χ2, RMSE and mean relative deviation modulus (E). Wang and Singh model, having χ2 and RMSE value (at 60°C) of 0.00027 and 0.01655 respectively gave the best results for describing the drying behavior of jackfruit samples.

Evaluation and Modelling of Water Absorption Characteristics of Paddy

Water absorption characteristics of paddy (PB1121) were evaluated over a temperature range 40 to 80oC. The equilibrium moisture content of the grain during water absorption varied from 48.24 to 55% (d.b.). Average critical moisture content of PB1121 for soaking during parboiling was 41.67% (d.b.). Average moisture diffusivity during water absorption process was 5.06x10-10 m2.s-1 and activation energy was 53.85 kJ.mol-1. Modelling of water absorption behaviour using Page model revealed that it fitted well at individual temperatures (R2&gt;0.9). However, the Generalized Page model provided poor performance with R2 of 0.65, MSE 0.0018 and mean relative deviation modulus (% P) 48.02, whereas multi-layer perceptron neural network model fitted well with R2 =0.99, MSE =0.0013 and P =14.69%.

Mathematical Modelling of Thin Layer Dried Cashew Kernels

In this paper mathematical models describing thin layer drying of cashew kernels in a batch dryer were presented. The range of drying air temperature was 70 – 110°C. The initial moisture content of the cashew kernels was 9.29% (d.b.) and the final moisture content was in the range of 3.5 to 4.6% dry-basis. Seven different thin layer mathematical drying models were compared according to their coefficients of determination (R 2 ) mean square error (MSE) and mean relative deviation modulus (P) to estimate drying curves. The effects of the drying air temperature and time on the drying model constants and coefficients were predicted by multiple regression analysis using linear and non-linear type models. The results have shown that among the models, the Page model was found to be the best for describing the drying behaviour of cashew kernels with R 2 , MSE and P values of 0.9830, 0.00311 and 5.046 respectively.

Physical property and resistance to airflow through bulk and thin-layer lemon fruit

Introduction Physical properties of lemon fruit are important for drying system and Kept in stock. Objective The prediction of airflow resistance is fundamental to the design of efficient drying and aeration systems for lemon fruit. Methods Using a laboratory unit, two sets of experiments were carried out, namely thick and thin layers. In the thick-layer experiments, four bed depths, 11 flow rates and four temperatures 25, 35, 45 and 55 C. In the thin layer (two kernels depth, 3 cm), the kernels were put together in three arrangements: A, B and random; five moisture contents and 11flow rates were studied. Results Results indicated that resistance to airflow through a column of lemon fruit increased with increasing bed depth and airflow rate. In the latter experiment, pressure drop decreased with a decrease in moisture content.Airflow rate was the most significant factor affecting the pressure drop of lemon fruit in both experiments. Conclusion Three applicable models (Shedd, Hukill and Ives, and Ergun) were used to evaluate the pressure drop data. The Ergun model, with higher values for coefficient of determination and lower values for sum of square error and mean relative deviation modulus, is the best model for predicting pressure drop across lemon fruit bed for the conditions studied.

Sorption of Triclosan onto Tyre Crumb Rubber

The effectiveness of using tyre crumb rubber (TCR) as an adsorbent for the removal of triclosan (TCS) from aqueous solutions was evaluated as a function of pH through controlled batch experiments. Carbon black (CB) and styrene-butadiene polymer (SBP), which are the main components in TCR, were individually evaluated and their contribution in the sorption process was assessed. At pH 3, the maximum rate of adsorption of TCS onto TCR, CB and SBP was 89, 95 and 92%, respectively. The Freundlich model provided the best fit for the experimental data obtained, as indicated by the mean relative percent deviation modulus (P). Our study results indicate that the removal of TCS using SBP follows an absorption process. Maximum desorption rate of TCS from TCR was approximately 89%. Results of sorption/desorption experiments clearly indicated the viability of TCR to be reused without any significant loss in its sorption/desorption capacity.

Temperature-dependent kinetics of grape seed phenolic compounds extraction: Experiment and model

The kinetics of a batch solid–liquid extraction of total phenolic compounds (PC) from milled grape seed (Vitis vinifera L. cv. “Frankovka”) using 50% ethanol at different extraction temperatures (25–80°C) was studied. The maximum yield of PC was 0.13kgGAE/kgdb after 200min of extraction in agitated vessel at 80°C. A new model based on the assumptions of a first order kinetics mechanism for the solid–liquid extraction and a linear equilibrium at the solid–liquid interface was developed. The model involves the concept of broken and intact cells in order to describe two successive extraction periods: a very fast surface washing process followed by slow diffusion of phenolic compounds from grape seeds to the solvent.The proposed model is suited to fit experimental data and to simulate the extraction of phenolic compounds, which was confirmed by the correlation coefficient (r⩾0.965), the root mean square error (RMSE⩽0.003kgGAE/kgdb) and the mean relative deviation modulus (E⩽2.149%). The temperature influenced both equilibrium partition coefficients of phenolic compounds and transport properties, which is manifested by a relatively high value of activation energy (23–24)kJ/mol and by values of effective diffusivity in seed particles.

Suitable drying model for far infrared drying of taegeuk ginseng

In this study we have elucidated the suitable drying model for the far infrared drying of taegeuk ginseng. Thin layer drying tests of taegeuk ginseng were conducted at 3 temperature levels of 45, 55, and 65°C, and 3 taegeuk ginseng size levels of large, medium, and small. Four thin layer drying models were used to estimate drying curves. The goodness-of-fit of the drying models were evaluated using the coefficient of determination (R2), root mean square error (RMSE), mean relative deviation modulus (Pe), and reduced chi-square (χ2). In the mean time, the influences of drying temperature and taegeuk ginseng size on drying behavior were also determined. The results revealed that the Page model, which can describe the far infrared drying behavior of taegeuk ginseng with a great accuracy, was the best model to fit adequately most of the drying conditions for the far infrared drying of taegeuk ginseng.

A new approach to predict the mass transport properties of micro-perforated films intended for food packaging applications

A new mathematical approach to predict the mass transport properties of micro-perforated films is presented in this work. In particular, 16 different types of micro-perforated films, differing in both the number of holes per unit area and the hole diameter, and the corresponding bulky film (i.e., without holes) were tested for gas and water vapor permeability. Two different models have been proposed in this work: a theoretical model derived assuming that holes permeability is constant, and an empirical model. The gas and water vapor permeability data were used to calculate the values of parameters for both models. The obtained values were used to predict the gas and water vapor permeability of tested films. The mean relative deviation modulus (E¯%) was used as a quantitative measure of the predictive ability of the models. Results suggest that the predictive goodness of the empirical model is much better than that of the theoretical one. This is mainly due to the critique assumption used to derive the theoretical model that is the hypothesis of constant holes permeability, which does not account for possible hydrodynamic flow.

Modelling perforated mediated modified atmospheric packaging of capsicum

SummaryPerforation of a film would otherwise have a low permeability is an alternative to obtain optimum oxygen and carbon dioxide concentration in modified atmosphere packages. In present study, gas exchange was studied through a macroperforated packet containing capsicum having different number of holes, 1–4, of diameter 0.3 mm at temperatures of 5 and 25 °C. A model combining the Michaelis–Menten kinetics to describe the respiration rate of the product with mass transfer equation to describe the gas transfer across the package provided a good fit to the experimental data. Its applicability was further validated in a dynamic test, subjecting a package to a variable temperature programme simulating conditions in distribution chains. Model showed good agreement between predicted and observed values for both storage conditions with constant temperatures and variable temperature conditions of distribution chain, as mean relative deviation modulus (E) value was &lt;10%.

THERMODYNAMIC ANALYSIS OF MOISTURE ADSORPTION ISOTHERMS OF RAW AND BLANCHED ALMONDS

ABSTRACTThe equilibrium moisture content of raw and blanched almonds of California grown “Carmel” variety was determined by using static gravimetric method at 25, 35 and 45C over a range of water activities (Aw) from 0.11 to 0.97. The sorption data were fitted to the Guggenheim–Anderson–de Boer (GAB) model. The goodness of fit of the model was evaluated by standard error of estimate, mean relative percentage deviation modulus and randomness of residual, which showed good fit of the GAB equation to the experimental data. The moisture adsorption isotherms of almonds exhibited type II sigmoid shape. Thermodynamic properties such as differential enthalpy and entropy were determined from moisture adsorption data by using the Clausius–Clapeyron equation. The results showed that enthalpy–entropy compensation theory was applicable for the moisture adsorption phenomena of raw and blanched almonds. The adsorption process of almond was enthalpy‐controlled.PRACTICAL APPLICATIONSOver 80% of the world almond production is grown in California and shipped to over 90 countries around the world. When exported to distant markets in the tropical regions, the physical, chemical and microbiological changes in almonds could cause the deterioration of food products due to environmental factors. Despite the large‐scale production and export of almonds, very little information on the sorption characteristics of almond varieties grown in California can be found in the literature. Reliable information on sorption isotherms is critical to designing optimum storage and shipping conditions to ensure desired levels of almond quality at consumption. This paper presents results from a comprehensive study of the sorption characteristics of one of the most important almond varieties grown in California, namely “Carmel.”

Kinetics Modeling of Mass Transfer Using Peleg’s Equation During Osmotic Dehydration of Seedless Guava (Psidium guajava L.): Effect of Process Parameters

Peleg’s equation was used to study the effect of process parameters on kinetics of mass transfer in terms of solids gain and water loss during osmotic dehydration using 30–50% (w/w) sucrose solution at 30, 40 and 50 °C. The experimental data were successfully fitted employing Peleg’s equation with the coefficient of determination (R 2) higher than 0.88, the root mean square error, and the mean relative percentage deviation modulus (E) of less than 0.003% and 6.40% for all treatments, respectively. In all cases, initial mass transfer rate parameter (K 1) decreased significantly (p 0.78). The results of this work allow estimating the kinetics of mass transfer during osmotic dehydration in order to obtain products with determined solid and water contents.

Modelling starch digestion in sweetpotato with biphasic digestograms

The kinetics of starch digestion in 20 sweetpotato samples obtained from Papua New Guinea were investigated using an in vitro procedure based on glucometry. Irrespective of the cultivars ( 3-mun, Carot kaukau, Wahgi besta, Nillgai, Baiyer kaukau, and 1-mun), provinces, farmers and locations, the samples exhibited biphasic digestograms, possibly due to initial impediments to amylolysis and/or transport of digestion products by non-starch components (e.g. plant cell walls). The biphasic digestograms were segmented into two monophasic digestograms using a second-order polynomial (average r 2 = 0.723; p < 0.001), and a modified first-order kinetic model adequately described the digestograms (average r 2 = 0.984, p < 0.001; mean relative deviation modulus, MRDM, =8). Generally, the digestion rate constants (initial, K i = 3.2–5.2 × 10 −3 min −1; final, K f = 3.8–18.4 × 10 −3 min −1) indicated faster digestion during the final segment after the initial impediments to digestion had possibly been overcome. K i was significantly ( p < 0.05) different among the samples, which did not significantly ( p < 0.05) differ in K f. A logistic model, which treated each digestogram as a single process, also adequately described the biphasic behaviours (average r 2 = 0.994, p < 0.001; mean relative deviation modulus, MRDM, =15). The digestion parameters from the segment and logistic approaches significantly ( p < 0.05) differed among the sweetpotato samples. The rate of digestion from the logistic model was significantly ( p < 0.05) related to the initial and final rates of digestion from the segment approach ( K = 3.99 K i + 0.65 K f; r 2 = 0.456; p < 0.001). Irrespective of the approach, maximum starch digestion was less than 100% in some samples to indicate the presence of resistant starch type 1, 2 or both. The present study is the first to model biphasic starch digestograms.

Frozen mirabelle plum drying: Kinetics, modelling and impact on biochemical properties

The aim of this research was to study and model the kinetics of the hot air drying of frozen mirabelle plums. Effects of temperature (50–85 °C), air velocity (0.6–1.2 m/s) and a pre-treatment (ascorbic acid + sucrose-saturated solution) were investigated. The sorption isotherm and heat of sorption of mirabelle plum were mathematically described respectively by the Guggenheim, Anderson and de Boer (GAB) model and a new one. Depending on temperature and air velocities, the effective diffusivity and the energy of activation were respectively in the range of 8–16.8 × 10 −10 m 2 s −1 and 43.7–55.14 kJ mol −1. To establish the model best adapted to describe this process the fit quality of five models (Newton, page, modified page, logarithmic and diffusion) were evaluated and compared. The diffusion model led to low values of reduced χ-square, mean square root and mean relative deviation modulus with the highest linear regression coefficient. This model was validated in a large range of operating conditions and represents an excellent tool to predict the duration of this process. The pre-treatment preserves biochemical properties of the dried mirabelle plums (reducing sugar content, total phenolic compounds and anti-oxidant activity).