DIFFUSIONAL MODEL WITH AND WITHOUT SHRINKAGE DURING SALTED FISH MUSCLE DRYING

Abstract

The drying process of salted pieces of shark muscle (Carckarhinus limbatus) was accomplished using three air conditions (20 ^°C -40 %RH; 30 ^°C - 30 %RH; 40 ^°C - 45 %RH) and two air velocities (0.5 m/s; 3.0 m/s). Shrinkage of material during drying was correlated as a linear function between linear dimension and moisture content. The experimental drying data were obtained using both the diffusional model with moisture content parameter (considering no shrinkage) and the diffusional model with moisture concentration parameter (considering shrinkage). The values of effective diffusivity varied between 1.50×l0^?10m²/s and 2 85×l0^?10m²/s for drying process considering no shrinkage and between 0.87×l0^?10m²/s and 1.61×l0^?10m²/s for process considering shrinkage. The activation energy was calculated assuming an Arrhenius' type equation. The values were 17.94 KJ/mol with the air velocity of 0.5 m/s and 21.94 kJ/mol with the air velocity of 3,0 m/s for effective diffusivity without shrinkage. The values were 2.04 kJ/mol with the air velocity of 0.5 m/s and 16.12 kJ/mol with the air velocity of 3.0 m/s for effective diffusivity with shrinkage. These low activation energy values, calculated considering the shrinking effect, show that the side effects during drying reduces the effective diffusivity dependence on temperature     

Drying and Heat Transfer Characteristics for a Novel Fluidized Bed Dryer

Abstract

The use of a fluidized bed dryer with a lateral air flow and mechanical agitation to the drying of sludge from a wastewater treatment plant was investigated. Experimental curves of moisture content vs. drying time, as well as heat transfer coefficients and the size characteristics of the products, were determined at temperatures between 80°C and 110°C, a stirring rate of 55 rpm and air velocity of 0.9 m/s for 3 kg sludge batches with initial moisture contents of 0.55 and 0.65 (d.b.). Experimental drying kinetics were compared with values derived from three models based on Fick's second law, namely: the constant diffusivity model, the simplified variable diffusivity model, and the modified quasi-stationary model.     

Effect of Adsorption Conditions on Effective Diffusivity and Textural Property of Dry Banana Foam Mat

Foamed banana product, a crispy snack, can quickly adsorb the moisture from the moist air, leading to loss of textural property. The main purpose of this research was therefore to study moisture adsorption kinetics of dry banana foam mat and its texture quality change. The adsorption isotherm experiments were carried out with a standard static method using saturated salt solutions over a wide range of relative humidities from 32 to 82% and temperatures of 35, 40, and 45°C. Three dry banana foam densities of 0.21, 0.26, and 0.30 g/cm³ adsorbed water vapor under controlled conditions. Fick's second law coupled with an optimization technique was used to estimate the effective moisture diffusivity at sorption conditions. Empirical equations with two and three constant parameters for describing the dependence of the effective moisture diffusivity on moisture content were tested. The two constant parameters could suitably describe the variation of the effective moisture diffusivity with moisture content. The initial foam density, relative humidity, and temperature significantly affected the effective moisture diffusivity. The banana foam mats for all densities lost their crispy texture at moisture content of 0.078 kg/kg db.     

Drying Characteristics and Moisture Diffusivity of Distillers' Spent Grains Dried in Superheated Steam

Distillers' spent grain pellets were prepared from material with an initial moisture content of 25% (wb). These pellets were dried in pairs using superheated steam at 120°C in two orientations, horizontal and vertical. The drying characteristics, modeled by the Page equation, showed that there was a significant difference between orientations. The overall moisture diffusivity was calculated using a finite cylinder model based on Fick's law of diffusion accounting for a change in dimensions over the course of drying. The overall diffusivity values ranged from 4.08 × 10^?10 to 1.48 × 10^?8 m²/s.     

DETERMINATION OF MOISTURE DIFFUSIVITY AND BEHAVIOR OF TOMATO CONCENTRATE DROPLETS DURING DRYING IN AIR

ABSTRACT

The drying mechanism and diffusion coefficient of water in spherical droplets (1.73 – 2.08 mm diameter) of tomato concentrates were successfully interpreted and modelled by using Fick's law. Solids content of the initial concentrate (5–15% w/w), and drying temperature (60^° – 100^° C) were varied but the drying air was kept at constant velocity and humidity.

The effective moisture diffusivity was estimated from the drying rate curves and expressed by an Arrhenius relation. Further, it was observed that case hardening has a large effect on the diffusion process causing the effective diffusional distance and the rate of moisture accumulation in the hardened crust to vary with the moisture content, according to a sorption controlled mechanism.     

PARAMETER ESTIMATION OF FICK'S LAW DRYING EQUATION

ABSTRACT

Distributed parameter drying models such as the Fick's law diffusion model, unlike the lumped parameter model of van Meel whose parameters can be easily estimated by regression, suffer from the difficulty in estimating the parameters of the models quantitatively with accuracy. In the past they were estimated by visual inspection of the theoretical drying curves which fit the experimental drying curve best In this work, a quantitative parameter estimation technique originally suggested by Chavent, is developed by minimizing the integrated squares of error between theoretical and experimental curves over the drying lime (the criterion) subjected to the constraints that the theoretical curve is governed by the constant diffusivity Fick's taw diffusion equation (the constraint). Although the estimation of Fick's law constant diffusivity can be done by using the analytical solution developed by Crank, the use of the Fick's law model here is simply to demonstrate the utility of the proposed technique which can be used in more complex distributed models. The optimization problem is to solve for the adjoint equation for which the value of the Fick's law diffusivity minimizes the criterion. The Lagrangian derivative is solved by using a discrete derivative of the criterion. The theoretical curves are generated by using simple explicit (FSE) and modified Crank-Nicholson (FCR) algorithms The drying of oil palm kernels are used as a case study. Ii is found that the estimated diffusivities of moisture in oil palm kernels range from 0 5 to 5.0 × 10^-10 m²sol;s which are comparable with published data. It is also found that the estimated diffusivity is dependent on the initial moisture content.     

Pore Development and Moisture Transfer in Chicken Meat during Deep-Fat Frying

Abstract

Changes in the structure of food products play important role in the various mass transfer processes during deep-fat frying. The relationship between moisture loss and pore formation were investigated at frying oil temperatures of 170, 180, and 190°C and frying times up to 900 s. Porosity and pore structure were characterized by using mercury intrusion porosimetry and helium displacement pycnometer. Moisture transfer in the samples was modeled using Fick's law and effective moisture diffusivity was computed from experimental data. Pore formation changes significantly (P < 0.01) in time as modulated by frying oil temperature. A peak pore fraction of 0.283 (after 360 s of frying), 0.238 and 0.220 (after 900 s of frying) at frying temperatures 190, 180 and 170°C, respectively was observed. Effective moisture diffusivity of 5.4 to 6.9 × 10^?9 m² s^?1 and activation energy of 20 kJ/mol was obtained for the frying oil temperatures. Changes in pore structure influenced moisture diffusivity and oil uptake. Eighty-four percent of the pores are capillary pores, hence moisture transfer increased.     

Experimental modelling of infrared drying of industrial grape by-products

The thin-layer infrared drying behaviour of industrial grape by-products was experimentally investigated in the temperature range from 100 to 160 °C. The drying rate was found to increase with temperature, thus reducing the total drying time. In particular, as drying temperature was raised from 100 °C up to 160 °C, the time period needed to reduce the moisture content of the sample from 204.32% down to 38.89% by weight (dry basis) decreased from 60.5 to 21 min.Using a non-linear regression (Marquart's method) together with a multiple regression analysis, a mathematical model for the thin-layer infrared drying process of wet grape residues was proposed. The values for the diffusivity coefficients at each temperature were obtained using Fick's second law of diffusion. They varied from 11.013 × 10^?9 to 26.050 × 10^?9 m²/s along the temperature range. The temperature dependence of the effective diffusivity coefficient was expressed by an Arrhenius type relationship. Activation energy for the moisture diffusion was determined as 19.27 kJ/mol.     

An Effective Moisture Diffusivity Model Deduced from Experiment and Numerical Solution of Mass Transfer Equations for a Shrinkable Drying Slab of Microalgae Spirulina

From experimental data, Spirulina effective moisture diffusivity was analytically estimated by considering two diffusion regions and the product shrinkage. Then, the moisture diffusivity was deduced from the numerical solutions of mass transfer equations by minimizing the difference between experimental and simulated drying curves and by taking into account the slab thickness variation. The range of moisture diffusivity used for simulations was estimated from minimal and maximal values of experimental effective diffusivities and calculation started with the mean value of experimental effective diffusivities. Identified effective diffusivities ranged from 1.79 × 10^?10 to 6.73 × 10^?10 m²/s. These diffusivities increased strongly with drying temperature and decreased slightly with moisture content. A suitable model correlating effective diffusivity, temperature, and moisture content was then established. Effective diffusivities given by this model were very close to experimental ones with a relative difference ranging from 0.5 to 24%.     

DRYING OF CARROTS IN A FLUIDIZED BED. I. EFFECTS OF DRYING CONDITIONS AND MODELLING

ABSTRACT

Drying curves were determined in a mechanically agitated fluidized bed dryer, at temperatures between 70°C and 160°C, air velocities between 1.1 m/s and 2.2 m/s and stirring rates between 30 rpm and 70 rpm for batch drying of 3 kg lots of carrot slices, measuring the moisture content and shrinking of the particles in time. This was complemented by a study of the rate and degree of swelling of dried carrot particles in water between 20 and 75°C. Drying kinetics were modeled by Fick's second law, for which an optimal agreement with the experimental data was obtained when the effective diffusivity (D _e ) was determined by a correlation based on the air velocity (v), the air temperature (T) and the dimensional moisture content of the carrot particles (X/X _o ). Loss of carotenes is minimized when dehydration is carried out at about 130°C with a drying time below 12 min.     

Characterisation of industrial tomato by-products from infrared drying process

The thin-layer infrared drying behaviour of industrial tomato residues, peels and seeds, was experimentally investigated in the temperature range from 100 °C to 160 °C. The drying rate was found to increase with temperature, hence reducing the total drying time. In particular, as drying temperature was raised from 100 °C up to 160 °C, the time period needed to reduce the moisture content of the sample from 236.70 wt% down to 5.26 wt% (dry basis) was observed to decrease from 99.5 min to 35 min.Using a non-linear regression (Marquart's method) together with a multiple regression analysis, a mathematical model for the thin-layer infrared drying process of industrial tomato residues was proposed. The effective moisture diffusivity is dependent on moisture content; the average values for the diffusivity coefficients at each temperature were obtained using Fick's second law of diffusion, and varied from 5.179 × 10^?9 m²/s to 1.429 × 10^?8 m²/s over the temperature range. The temperature dependence of the effective diffusivity coefficient was described following an Arrhenius-type relationship. Activation energy for the moisture diffusion was determined as 22.23 kJ/mol.     

Determination of Moisture Diffusivity by Thermo-Gravimetric Analysis under Non-Isothermal Condition

Abstract:

In drying of solids, the diffusion model based on Fick's second law is usually applied to interpret the moisture migration within the solid. Then the temperature dependence of the moisture diffusivity, generally described by an Arrhenius-type equation, is obtained through the drying kinetics. In this article, a nonisothermal (linearly increasing temperature) procedure was used to determine the moisture diffusivity as a function of temperature with the complex optimization method, and the result was accessed by comparison with a classical isothermal procedure. All the experiments were conducted in a thermogravimetric analyzer (TGA) for accurately recording the mass loss from the sample and easily programming the heating profile.     

From Laboratory Experiments to Design of a Conveyor-Belt Dryer via Mathematical Modeling

Abstract

A conveyor-belt dryer for picrite has been modeled mathematically in this work. The necessary parameters for the system of equations were obtained from regression analysis of thin-layer drying data. The convective drying experiments were carried out at temperatures of 40, 60, 80, and 100°C and air velocities of 0.5 and 1.5 m/sec. To analyze the drying behavior, the drying curves were fitted to different semi-theoretical drying kinetics models such as those of Lewis, Page, Henderson and Pabis, Wang and Singh, and the decay models. The decay function (for second order reactions) gives better results and describes the thin layer drying curves quite well. The effective diffusivity was also determined from the integrated Fick's second law equation and correlated with temperature using an Arrhenius-type model. External heat and mass transfer coefficients were refitted to the empirical correlation using dimensionless numbers (J _h , J _D  = m · Re ⁿ ) and their new coefficients were optimized as a function of temperature. The internal mass transfer coefficient was also correlated as a function of moisture content, air temperature, and velocity.     

A Method of Determination of Concentration Dependent Effective Moisture Diffusivity

ABSTRACT

A method based on Fourier series solution to Fick's diffusion equation has been proposed to evaluate effective diffusivity (D) as a function of moisture content in agricultural materials undergoing shrinkage during drying process. The shrinkage kinetics of the particulate was used to correlate its instantaneous size (spherical equivalent diameter) as a function of material moisture content A computer program was used to evaluate D based on shrinkage kinetics and experimental drying data and relate it to moisture content. The method was used to obtain moisture diffusivity data for thin layer drying of grape and corn.     

Drying Kinetics of Apple Tissue Treated by Pulsed Electric Field

The aim of this work was to study the influence of pulsed electric field (PEF) on the drying kinetics of apple tissue. Therefore, mathematical models that are commonly used in the literature were applied to describe the process. PEF treatment of the samples was carried out at an intensity of E = 5–10 kV/cm and 10–50 pulse numbers. Subsequently, the apples were convectively dried at 70°C and air velocity of 2 m/s. Based on electrical conductivity measurement, the cell disintegration index Z _p was computed. Midilli et al.'s(Drying Technology, Vol. 20, pp. 1503–1513, 2001) model was evaluated as the most adequate to describe the moisture transfer in PEF-treated and intact samples. PEF pretreatment induced a reduction in drying time of up to 12% when 10 kV/cm and 50 pulses were applied. For instance, after 60 min of drying, the dimensionless moisture ratio for PEF-treated (10 kV/cm, 50 pulses) samples was 0.18 compared to 0.26 for the untreated apples. The effective moisture diffusivity, calculated on the basis of the Fick's second law, was 1.04 × 10^?9 m/s for intact samples and from 1.09 × 10^?9 to 1.25 × 10^?9 m²/s for PEF-treated samples at 10 pulses at 5 kV/cm and 50 pulses at 10 kV/cm, respectively.     

Drying with Chemical Reaction in Cocoa Beans

Desirable flavor qualities of cocoa are dependent on how the cocoa beans are fermented, dried, and roasted. During fermentation and drying, polyphenols such as leucocyanidin and apecatechin are oxidized by polyphenols oxidase to form o-quinone, which later react nonenzymatically with a hydroquinone in a condensation reaction to form browning products and moisture. The objective of this article is to model the cocoa beans drying together with the browning reaction. A Luikov drying model for the moisture and a simple Fick's law diffusion model combined with first-order reactions for both the enzymatic oxidation and nonenzymatic condensation reactions were constructed. Both models were used to identify moisture diffusivity coefficient and total polyphenols diffusivity in cocoa beans from experimental drying and polyphenols degradation data and published kinetic data of the reactions. The theoretical drying model fitted the experimental cocoa bean drying curves with low mean square of residuals. The polyphenols diffusion and reaction model also fitted the experimental polyphenols degradation curves with minimum mean residual squares. The rate of polyphenols degradation in the cocoa beans increases at higher temperature and higher relative humidity. This is because the increasing reaction rate of polyphenols oxidation reaction as well as higher moisture diffusion at higher relative humidity and temperature. The effective moisture diffusivity in cocoa beans is estimated to be between 8.194 × 10^?9 and 8.542 × 10^?9 m²·s^?1, which is of the same order of magnitude as published data. The effective total polyphenols diffusivity is estimated to be between 8.333 × 10^?12 to 1.000 × 10^?11 m²·s^?1 with minimum mean residual squares. It is three orders of magnitude less than the estimated moisture diffusivity because of the larger polyphenols molecules. The estimated polyphenols diffusivity is very close to those published in the literature for sorption and ultrafiltration processes.     

Vacuum dehydration kinetics of onion slices

Onion slices were dried in a single layer of thickness varying from 1 to 5 mm in the temperature range of 50-70 °C in a laboratory scale vacuum dryer. The effect of pretreatment, drying temperature and slice thickness on the drying kinetics of onion slices was studied. Four thin layer drying models namely Lewis model, logarithmic model, Page model and Fick's law model were applied on the experimental moisture loss data with respect to time to predict the drying pattern properly on the basis of coefficient of determination and standard error. The Page model showed better fit to the experimental data compared to other models. Effective moisture diffusivity of the slice was measured using Fick's second law of unsteady state diffusion. The diffusivity values were found ranging from 1.32E−10 to 1.09E−09 m²/s for untreated and 1.32E−10 to 1.09E−01 m²/s for treated onion slices. Effective moisture diffusivity showed increasing trend with increase in temperature and thickness.     

Air Drying Kinetics of Potato Cylinders

ABSTRACT

An experimental air tunnel dryer was used to investigate the kinetics of moisture transport in potato cylinders (Solanum tuberasum). Acoordingly, the experimental results, represnting only falling-rate drying behaviour and hence. dehydration completely controlled by internal mass transfer, were interpreted on the basis of Fick's diffusional model for non-stedy state radial diffusion. The effects of air velocity and temperature on the drying rate were studied. with he temperature being the principal controlling factor. Analysis of the drying curves by the method of slopes resulted in a variable effective moisture diffusivity. Shrinkage as a function of moisture content under various drying conditions was investigated. The volumetric shrinkage of the samples was affected mainly by air velocity. whilst air temperature had a negligible effect. Good agreement was obtained between the experimental apparent density data and the predicted correlation.     

Ascorbic Acid Thermal Degradation during Hot Air Drying of Camu-Camu (Myrciaria dubia [H.B.K.] McVaugh) Slices at Different Air Temperatures

Abstract

Air drying of camu-camu slices was performed in order to estimate the effect of air temperature on the kinetics of ascorbic acid thermal degradation. Moisture variation during the air drying process was monitored gravimetrically by weighing the trays at predetermined time intervals. The experimental points were adjusted by Fick's diffusion model and by the Page empirical model. The effective diffusion coefficient (D_eff) ranged from 8.48 × 10^?10 to 1.34 × 10^?9 m²/s.The ascorbic acid content was evaluated in samples taken during the drying process using Iodine titration, and the results modeled by the Weibull equation. Concerning ascorbic acid retention the best drying condition required air at 50°C. The ascorbic acid retention was 78%, when the moisture content of the product reached 10% (wet basis).