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.     

Characteristic Drying Curves of Cocoa Beans

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.     

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.     

Prediction of Microwave Drying Behavior of Pharmaceutical Powders Using Thin-Layer Models

Common pharmaceutical excipients and active ingredients, wetted with specific solvents, were dried under selected continuous power microwave and pulsed power microwave-vacuum conditions in an experimental system. Irrespective of the drying technique, a typical drying profile, with a constant drying rate stage followed by two falling rate periods, was exhibited. The experimental moisture loss data were fitted to semi-theoretical and empirical thin-layer drying equations and the models compared on the basis of three statistical parameters. The drying characteristics were satisfactorily described by the Lewis, Page, Logarithmic, Chavez-Mendez et al., and Midilli et al. models, with the latter providing the best representation of the data.     

Prediction of Microwave Drying Behavior of Pharmaceutical Powders Using Thin-Layer Models

Common pharmaceutical excipients and active ingredients, wetted with specific solvents, were dried under selected continuous power microwave and pulsed power microwave-vacuum conditions in an experimental system. Irrespective of the drying technique, a typical drying profile, with a constant drying rate stage followed by two falling rate periods, was exhibited. The experimental moisture loss data were fitted to semi-theoretical and empirical thin-layer drying equations and the models compared on the basis of three statistical parameters. The drying characteristics were satisfactorily described by the Lewis, Page, Logarithmic, Chavez-Mendez et al., and Midilli et al. models, with the latter providing the best representation of the data.     

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.     

Evaluation of Thin-Layer Models for Mushroom (Agaricus bisporus) Drying

In the present research, seven well-known mathematical thin-layer drying models were fitted to mushroom (Agaricus bisporus) drying experimental data, implementing nonlinear regression analysis techniques. The experiments were conducted in two laboratory-scale dryers. A range of temperatures 50–65°C and air velocities 1.0–5.0 m/s were tested. The statistical analysis concluded that the best model in terms of fitting performance was the logarithmic model. Correlations expressing this model parameter dependence with the drying air coefficients are also reported.     

Evaluation of Thin-Layer Models for Mushroom (Agaricus bisporus) Drying

In the present research, seven well-known mathematical thin-layer drying models were fitted to mushroom (Agaricus bisporus) drying experimental data, implementing nonlinear regression analysis techniques. The experiments were conducted in two laboratory-scale dryers. A range of temperatures 50-65°C and air velocities 1.0-5.0 m/s were tested. The statistical analysis concluded that the best model in terms of fitting performance was the logarithmic model. Correlations expressing this model parameter dependence with the drying air coefficients are also reported.     

Thin-Layer Drying of Flax Fiber: I. Analysis of Modeling Using Fick's Second Law of Diffusion

Thin-layer drying of moist flax fiber was performed at four temperatures of 30, 50, 70, and 100°C with a constant absolute humidity of 0.0065 kg water per kg dry air. The coefficients of diffusion of the fiber at different drying conditions were estimated by modeling the drying process using the one- to five-term solutions of the second Fick's law of diffusion. The models underestimated the drying process during the initial stages of drying and overestimated this process during the final stages. The estimated coefficient of diffusions ranged from 5.11 × 10^?9 to 1.92 × 10^?8 m²/s and linearly increased with the drying air temperature.     

Thin-Layer Drying of Flax Fiber: I. Analysis of Modeling Using Fick's Second Law of Diffusion

Thin-layer drying of moist flax fiber was performed at four temperatures of 30, 50, 70, and 100°C with a constant absolute humidity of 0.0065 kg water per kg dry air. The coefficients of diffusion of the fiber at different drying conditions were estimated by modeling the drying process using the one- to five-term solutions of the second Fick's law of diffusion. The models underestimated the drying process during the initial stages of drying and overestimated this process during the final stages. The estimated coefficient of diffusions ranged from 5.11 × 10^-9 to 1.92 × 10^-8 m²/s and linearly increased with the drying air temperature.     

A Test of Lumped-Parameter Methods for the Drying Rate in Fluidized Bed Driers for Bioproducts

ABSTRACT

For batch fluidized bed drying of bioproducts the distributed parameter model is presented, in which the internal diffusion equation is coupled to the air balance equations. In practice a large part of the process takes place at high relative humidity of the drying air, equivalent to low driving forces. The results of a number of lumped-parameter methods for the estimation of drying times are compared with those of the full model for the case of constant external conditions around a particle. For low relative humidity of the drying air predictions of drying times with the Regular Regime Power Law method correspond well with the full solution, for higher ambient RH large deviations occur. The other methods are shown to give large deviations in all cases.     

Thin-Layer Drying of Flax Fiber: II. Modeling Drying Process Using Semi-Theoretical and Empirical Models

Thin-layer drying experiments were performed for drying flax fiber under four different drying conditions. In all drying treatments the absolute humidity of drying air was 0.0065 kg of water per kg of dry air, but the drying temperature were 30, 50, 70, and 100°C. The drying process was modeled using the drying data and five semi?theoretical and empirical models cited in different literatures. From the five tested models, the Page model gave the best fitting for experimental data with R ² equal to 0.99, for all treatments. The estimated drying constants at different drying temperatures were highly correlated with drying air temperature. The drying constants were also highly correlated with the calculated coefficient of diffusions.     

Thin-Layer Drying of Flax Fiber: II. Modeling Drying Process Using Semi-Theoretical and Empirical Models

Thin-layer drying experiments were performed for drying flax fiber under four different drying conditions. In all drying treatments the absolute humidity of drying air was 0.0065 kg of water per kg of dry air, but the drying temperature were 30, 50, 70, and 100°C. The drying process was modeled using the drying data and five semi-theoretical and empirical models cited in different literatures. From the five tested models, the Page model gave the best fitting for experimental data with R² equal to 0.99, for all treatments. The estimated drying constants at different drying temperatures were highly correlated with drying air temperature. The drying constants were also highly correlated with the calculated coefficient of diffusions.     

Thin-Layer Drying of Green Peas and Selection of a Suitable Thin-Layer Drying Model

The thin-layer drying of three varieties of green peas was carried out in hot air-drying chamber using an automatic weighing system at five temperatures (55–75°C) and air velocity of 100 m/min. The green peas were blanched and sulphited before drying. The variety Pb-87 dried at 60°C was judged to be best for quality on the basis of sensory evaluation and rehydration ratio. The Thomson model was found to represent thin-layer drying kinetics within 99.9% accuracy. The effective diffusivity was determined to be 3.95 × 10^?10 to 6.23 × 10^?10 m²/s in the temperature range of 55 to 75°C. The activation energy for diffusion was calculated to be 22.48 kJ/mol. The variation in shrinkage exhibited a linear relationship with moisture content of the product during drying. The Dincer number at drying air temperature 60°C and drying air velocity 100 m/min was determined to be 2,838,087. The difference between temperatures of drying air and that of green pea kernels was found to decrease with drying time for all the drying temperatures taken for investigation.     

Microwave Drying Kinetics of a Thin-Layer Liquorice Root

Liquorice root (LR) (Glycyrrize glabra) is known as a sweetener and medicine plant. Drying kinetics of LR with initial moisture content of 49.5% (wet basis (w.b)) were experimentally investigated in a microwave drying system. The drying experiments were carried out at different drying temperatures (40, 45, 50, and 55°C) and microwave power levels (250, 500 and 750 W). Several models from literature were selected to fit the experimental data. The fit quality of models was evaluated using the coefficient of determination (R²), sum square error (SSE), and root mean square error (RMSE). A new model has been proposed for LR drying in the microwave drying. This new model best describes the experimental data for LRs. The activation energy was calculated to be 46.807 kJ/mol and effective diffusivity ranged from 2.9 × 10^?9 to 5.41 × 10^?9 m²/s, depending on drying temperatures at constant microwave power level.     

Thin-Layer Drying of Flax Fiber: III. Influence of Layer Thickness on Drying Parameters

Wet flax fiber was dried after rinsing at four layer thicknesses of 5, 10, 15, and 20 mm using four drying air temperatures of 30, 50, 70, and 100°C. The coefficients of diffusion of flax fiber at different drying conditions were estimated using a three-term series solution of Fick's second law of diffusion. The Page model was used to model the drying characteristic curves. The estimated coefficient of diffusion of the flax fiber and the drying constant of the Page model were both linearly proportional to drying air temperature and increased exponentially with the thickness of the drying layer.     

Thin-Layer Drying of Flax Fiber: III. Influence of Layer Thickness on Drying Parameters

Wet flax fiber was dried after rinsing at four layer thicknesses of 5, 10, 15, and 20 mm using four drying air temperatures of 30, 50, 70, and 100°C. The coefficients of diffusion of flax fiber at different drying conditions were estimated using a three-term series solution of Fick's second law of diffusion. The Page model was used to model the drying characteristic curves. The estimated coefficient of diffusion of the flax fiber and the drying constant of the Page model were both linearly proportional to drying air temperature and increased exponentially with the thickness of the drying layer.     

Modeling of Thin-Layer Drying on an Inert Sphere

A semi-empirical model was developed for the drying of press cake on an inert sphere in the spout region of a dryer. The coefficients for the Lewis and Page (for the prediction of moisture ratio) and the Chung-Pfost (for the prediction of equilibrium moisture content) models were determined experimentally. The predicted temperature of the press cake was validated using three trials conducted at drying conditions (temperature, relative humidity): 55°C, 55%; 65°C, 45%; and 75°C, 43%. Predicted temperatures were within ～10% of the experimental temperatures. Improved prediction accuracy was achieved as press cake temperature approached air temperature.     

组合式同向旋转双螺杆特性曲线分析

应用有限元分析软件ANSYS对同向旋转双螺杆挤出机螺纹输送元件中的三维非牛顿流动进行了模拟，计算出在一定转速和挤出量等工艺条件下螺纹元件的建压能力，确立了一定导程螺纹元件的特性曲线。在此基础上，对组合式同向旋转双螺杆挤出机工作特性进行了分析，并对双螺杆计量段充满长度和排气段脱挥长度的确定作了初步探讨。     

Measuring the Drying Rate of Liquid Film Coatings Using Heat Flux Method

We propose a simple method of determining solvent drying rates from heat flux measurements across thin liquid films. The theory is based on quasi-steady conductive heat transport through coatings, combined with simultaneous heat and mass transfer in the gas phase. The measured evaporation rates well reproduce conventional gravimetric measurements with an uncertainty of less than 5%. Drying experiments also revealed that the proposed method is robust in systems with high levels of fluctuation and thus provides an alternative tool for monitoring drying kinetics in forced air flows.