Characteristic Drying Curves of Cocoa Beans

ABSTRACT

The characteristic drying curves of cocoa beans are determined by using a tunnel drier where conditioned air passes a single cocoa berm suspended from an electronic balance in the test section. Weight loss, and temperatures of air, testa and nib of the cocoa bean is monitored on personal computers. The nornmalised drying rate versus the normalised moisture content is regressed by least square method to fit a new polynomial model for the penetration falling rate period and a linear model for the regular regime falling rate period. It can be concluded that there are three drying periods for cocoa beans namely the constant drying rate period, the penetration falling rate period and the regular regime falling rate period. The polynomial model estimates the penetration period quite well whereas the linear model estimates the regular regime quite well as well. There is no observable influence of relative humidity and air temperature on the characteristic drying curve of cocoa beans. However, the air velocity seems to have some influence on the curve.     

A Simple Data Processing Approach for Drying Kinetics Experiments

A simple mathematical approach is proposed to be applied to drying kinetics raw data processing. The data collected in a drying experiment of powder cork under constant air drying conditions served as case study to present the methodology. Two functions (linear and third-degree polynomial) were used to fit solid moisture content in the constant drying rate and the falling rate periods. The drying rate curve was obtained by differentiation and the time at which the drying rate period's transition occurs was determined iteratively until virtually continuous functions were achieved. The critical moisture content was easily identified and two falling drying rate periods were detected.

The powder cork moisture decrease was also used to test several semiempirical models available in the literature. The Logarithmic, Midilli, and Page Modified I models were the ones that revealed the best correlations performance. When the methodology proposed was applied using these models, the critical moisture content was underpredicted.

The effective moisture diffusivity and the activation energy were also obtained for powder cork after the proposed mathematical approach has been applied on the raw data obtained in experiments performed at different air drying temperatures.     

A New Variable Diffusion Drying Model for the Second Falling Rate Period of Paddy Dried in a Rapid Bin Dryer

The objectives of this article is to propose a new drying model for the second falling rate period known as the variable diffusion controlled period that follows after the first falling rate period and to propose a new method to determine the second critical moisture content that separates these two periods. Experimental work on paddy drying at minimum fluidization velocity was carried out in a rapid bin dryer. The effects of operating temperatures (60-120°C) and bed depths (2-6 cm) on the paddy drying characteristics were investigated. It was found that the normalized drying rate of paddy was proportional to the normalized moisture content in the first falling rate period but in the second falling rate period, the normalized drying rate of the material varies exponentially with the normalized moisture content. The different relationship between the normalized drying rate and the normalized moisture content in the first and second falling rate periods indicate that two different mechanism of moisture transport are at work. The new exponential model of the second falling rate period and the linear model of the first falling rate period were found to fit the experimental data very well. Derivation from variable diffusion equation shows that the linear model is the result of constant diffusion coefficient whereas the new exponential model is the result of linear diffusion coefficient. This also implies that the first falling rate period is a constant diffusion controlled period and the second falling rate period is a variable diffusion controlled period. In addition, drying kinetics data of a drying process that fits the exponential model over a very slow drying period will show that the drying process is under the effect of a linear diffusion coefficient. It was also found that the proposed new method to determine the second critical moisture content that distinguishes between the first and second falling rate periods by using a sudden change in the value of the drying rate gradient to a much lower value at that point is more rigorous and yet simpler than the method of determining the specific location of the receding drying boundary since it is based on the behavior of the actual drying kinetic data.     

Drying Kinetics of Sludge from a Wastewater Treatment Plant

Drying kinetics of sludge from a municipal sewage treatment plant were determined in a laboratory drying tunnel with parallel airflow at different temperatures and air velocities. The constant drying rate period was identified followed by two falling rate periods. Drying kinetics in these falling rate periods were then satisfactorily modeled using the modified quasi-stationary method and the Fick's second law. The two-period model was used, however, to describe drying kinetics over the entire drying process, and the equation for a generalized drying curve was proposed. The effective diffusivity was also determined from the integrated Fick's equation, and correlated with temperature by an Arrhenius type equation.     

Effects of air drying properties on drying kinetics and stability of cactus/brewer's grains mixture fermented with lactic acid bacteria

The present work examined the effect of air drying conditions on drying kinetics of cactus/brewer's grains mixture fermented with Lactobacillus plantarum HG328248. The drying kinetics was performed in a convective dryer for three air temperatures (40, 50 and 60 °C) and three air velocities (0.7, 1.0 and 1.3 m/s). Four mathematical models were tested to fit the drying curves. The Page model seemed the most appropriate to describe experimental data. The experimental drying curves showed two periods: that at constant rate and that of falling rate. The air temperature was the main factor in controlling the drying rate. The characteristic drying curve equation was determined.The influence of air drying conditions on color, water activity and microbiological quality of the fermented product was also studied. The temperature affected these parameters more significantly than air velocity. All dehydrated products had a satisfactory microbiological quality and consequently could be introduced in ruminant feed.     

EVAPORATION FROM POROUS MEDIA: A CAPILLARY MODEL OF A PENETRATING FRONT

A capillary tube model was solved to investigate the influence of mass transfer coefficient, temperature, and front depth on the evaporation rate during the penetrating-front period of water-filled porous media dried in hot air. The results show that increasing the flow rate of the drying air is not so efficient as increasing the sample temperature. Due to attenuating diffusion rate, the rate of liquid front migration decreases with time. The calculations explain the falling rate period behavior of sandstone heated at 121°C. Trends depicted by the model may be useful for the design of heating conditions for drying processes.     

Drying of fluidized materials in a centrifugal fluidized bed

Drying characteristics of the fluidized food materials such as rice, potato and carrot have been investigated in a centrifugal fluidized bed whose effective length and diameter have been 0.2 m and 0.1 m, respectively. The effects of air velocity and initial moisture content on the hydrodynamics and drying rate have been determined. The pressure drop has exhibited a maximum in the relatively thicker bed, while it has showed a plateau in the relatively thinner bed, with an increase in the air velocity. The drying rate has been increased with increases in the initial moisture content of the materials and air velocity. The variation of drying rate with respect to the moisture content has been almost linear at the falling rate period, and it has been well correlated by means of the rotational power acting on the bed.     

Microwave-Vacuum Drying of Wood: Model Formulation and Verification

Based on the mechanism of moisture and heat transfer in wood during microwave-vacuum drying (MVD), a one-dimensional mathematical model to describe the process of wood MVD was established and verified by experiments in this research. The results showed that the process of MVD of wood experienced three distinct periods: (1) accelerating rate with rapid warming-up drying period, (2) a constant temperature and constant rate drying period, and (3) a heating-up with falling rate drying period. Compared with conventional hot air drying, the total drying process is almost governed by a constant rate period in vacuum-microwave drying of wood. The predicted temperature and moisture content in wood match well with the experimental data, the square of the relevant coefficient of the values of simulation and test is above 0.9, and the simulation precision of the change rule of the moisture is higher than that of the temperature.     

An Experimental Test of the Concept of the Characteristic Drying Curve Using the Thin-Layer Method

The drying behaviour of paticles ( purolit and silica gel) was studied using the thin-layer method described by Langrish et al ( 1). The experiments covered inlet air temperatures between 100 and 150°C, inlet air humidities from 0.02 to 0.052 kgkg¹ superficial air velocities between 3.8 and 10.8 ms^-1, with layer thicknem of 2 - 10mm. No constant mle period war observed. Characteristic drying curves were found to fall within a narrow band fur these ranges of process variables, for material of uniform size and shape and with relative moisture content defined in terms of the end of the induction period. Small changes in panicle shape, particle size distribution and uniformity of particle layers had negligible infuence on the drying kinetics. However, reduction in particle size from 5.2mm diameter to 0.86mm had a marked effect: the normalised drying rate at a given relative moisture content became larger as the particle size became smaller. This phenomenon is attributed to an increase in available contact area per unit volume with diminishing particle size. The thin-layer technique thus appears to be a useful and robust way of obtaining a general characteristic drying curve for a given particulate material. A review of various works ( Keey, 2) has shown that the concept ofa characteristic drying curve may be used to describe the drying kinetics of paniculate materials below 20mm in size for modest changes in process variables ( air temperature, humidity and velocity). This concept has found to be very useful to help model drying processes of a wide variety of particulates, cross-circulated slabs, heaped loaw fabric fibres, hygroscopic ceramic cylinders and discrete vermiculite particles. The drying of a single particle has been related lo the drying kinetics of a fluidized bed by the use of this ida. ( Tsotsas, 7). A grater understanding of the properties of the characteristic drying curve will provide a greater confidence in applying thir concept more generally to process design and the analysis of industrial drying equipment. The goal of this study was to examine further the experimental and theoretical foundations of the characteristic drying curve, using thin-layer methods.     

An Experimental Test of the Concept of the Characteristic Drying Curve Using the Thin-Layer Method

ABSTRACT

The drying behaviour of paticles ( purolit and silica gel) was studied using the thin-layer method described by Langrish et al ( 1). The experiments covered inlet air temperatures between 100 and 150°C, inlet air humidities from 0.02 to 0.052 kgkg¹ superficial air velocities between 3.8 and 10.8 ms^-1, with layer thicknem of 2 – 10mm. No constant mle period war observed. Characteristic drying curves were found to fall within a narrow band fur these ranges of process variables, for material of uniform size and shape and with relative moisture content defined in terms of the end of the induction period. Small changes in panicle shape, particle size distribution and uniformity of particle layers had negligible infuence on the drying kinetics. However, reduction in particle size from 5.2mm diameter to 0.86mm had a marked effect: the normalised drying rate at a given relative moisture content became larger as the particle size became smaller. This phenomenon is attributed to an increase in available contact area per unit volume with diminishing particle size. The thin-layer technique thus appears to be a useful and robust way of obtaining a general characteristic drying curve for a given particulate material. A review of various works ( Keey, 2) has shown that the concept ofa characteristic drying curve may be used to describe the drying kinetics of paniculate materials below 20mm in size for modest changes in process variables ( air temperature, humidity and velocity). This concept has found to be very useful to help model drying processes of a wide variety of particulates, cross-circulated slabs, heaped loaw fabric fibres, hygroscopic ceramic cylinders and discrete vermiculite particles. The drying of a single particle has been related lo the drying kinetics of a fluidized bed by the use of this ida. ( Tsotsas, 7). A grater understanding of the properties of the characteristic drying curve will provide a greater confidence in applying thir concept more generally to process design and the analysis of industrial drying equipment. The goal of this study was to examine further the experimental and theoretical foundations of the characteristic drying curve, using thin-layer methods.     

Modeling of Mass Transfer During Hot-Smoking of Fish Fillets

This work aims at evaluating the mass reduction of traditionally hot-smoked catfish ( Arius heudelotii ) during hot-air drying unit operation. Drying kinetics of fish fillets are proposed from experimental investigations, taking into account the relative contributions of water evaporation and water and fat drips. The influence of the air temperature (50 to 80 ^° C), air velocity (1 to 3 m/s) and relative humidity (15 to 40%) on drying rate functions is analyzed from a Doehlert experimental design. Based on the identification of characteristic drying rate curves, a drying model is defined and proves to be quite accurate regarding the prediction of evaporation rate during the falling rate period.     

Microwave-convective drying characteristics of pharmaceutical powders

Common pharmaceutical excipients and active ingredients, wetted with specific solvents, were dried in a combined microwave-convective system (2.45 GHz, 90 W). The drying curves showed a constant drying rate period, followed by two falling rate periods. Cross-flow air velocity had little effect on solvent evaporation rate in the initial stages; however, an increase in drying rate was observed during the falling rate period. Increasing air temperature increased the drying rate throughout the entire process, with reductions in drying time of up to 78% being observed. Average and maximum sample temperatures were found to decrease on addition of air-flow, the extent of which was dependent on material and operating conditions.     

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.     

Characterization of the First Falling Rate Period During Drying of a Porous Material

This study deals with the evolution of the surface state and its influence on the drying of porous media. Surface temperature and saturation values are obtained using optical metrology. Analysis of the experimental results allows discussion of the apparition of constant drying rate period and to characterize the transition to the falling rate period. A mathematical model is developed to account for these observations and experimental results for some physical properties of a model material. It allows determination of the internal profile of moisture and the penetration of the drying front during the falling rate period.     

Modeling of Banana Convective Drying by the Drying Characteristic Curve (DCC) Method

Experimental convective drying tests of banana have been carried out for different air conditions to show the influence of air temperature, absolute humidity and speed on the drying rate. The analysis of the drying rate evolution as a function of product water content enables the identification of fourth drying phases: temperature rising (phase 1), exponentially decreasing drying rate (phase 2), linearly decreasing drying rate (phase 3) and very low drying rate (phase 4). The temperature rising phase 1 being very short and the last phase 4 being not reached during typical drying, the drying characteristic curve (DCC) has been represented by two different mathematical functions fitting phases 2 and 3. Their parameters have been determined by minimization of the quadratic errors between experimental and theoretical curves. It leads to a unique curve (the DCC) representing all air drying conditions the integration of which enables the calculation of the product water content with a maximum error of 0.09 between experimental and simulated values.     

Modeling the Drying of Grass Seeds (Brachiaria brizantha) in Fluidized Beds

A modified three-phase model is developed to simulate the drying of Brachiaria brizantha in fluidized beds. In this new model, the constitutive equation of drying kinetics is formulated including both the constant rate and the falling rate mechanisms; the seed shrinkage is taken into account during all drying operation and the transition between bubbling to slugging regime is delineated for estimating the bubble velocity and size. Such modifications improve the mathematical model to better simulate the drying of coarse particles in fluidized beds. The best estimation of the five adjustable model parameters, which are required to define heat and mass transfer mechanisms between interstitial gas and seed particles and to specify the heat loss from dryer walls to ambient air, is attained by incorporating an optimization routine into the computer model program. Having been specially designed to supply data for this model, experiments are performed in a bath laboratory-scale fluidized bed. Additional data are generated to validate the model and program routines. Results show a good agreement between simulated and experimental data, validating the approach used to describe drying kinetics and particle shrinkage.     

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.     

Interpretation of the hydrodynamic behaviour in a conical fluidized bed dryer

Wet batches of placebo pharmaceutical granule were dried at inlet superficial gas velocities of 0.64 and 1.3 m/s in a Glatt GPCG-1 fluidized bed. Using pressure fluctuation analysis, the hydrodynamic behaviour indicates a transition from a multiple bubbling regime to a coalescence dominated regime as drying proceeds. The transitional fluidization behaviour is linked to the physical mechanisms associated with the constant and falling rate periods of drying porous materials. Excess surface moisture present during the constant rate period increases interparticle forces through liquid bridging. These liquid bridges stabilize the bed structure which limits bubble formation in the bed. Once the falling rate period is reached, the liquid bridges cannot be maintained and bubble coalescence increases. The resulting bubbling bed hydrodynamics can be explained using the simple two-phase model proposed by Toomey and Johnstone [1952. Gas fluidization of solid particles. Chemical Engineering Progress 48, 220-226] using the full support velocity and bed voidage characteristics of the granule at varying moisture contents.