MOISTURE DIFFUSIVITY, SHRINKAGE, AND APPARENT DENSITY VARIATION DURING DRYING OF LEAVES AT HIGH TEMPERATURES

Abstract

The variation of moisture diffusivity, apparent density, and shrinkage during drying of yerba maté leaves at high temperatures were studied. A simple mathematical model that describes the variation of the temperature and moisture content into the leaf during drying was developed. Temperatures of air varied between 100 and 130°C when the experiments were carried out in a convective cross-flow air dryer. Thickness and apparent density varied greatly with moisture content, but this variation does not depend on drying temperature. Moisture diffusivity varied from 2.3 × 10⁻¹¹ to 2.5 × 10⁻¹⁰ m²/s, and activation energy values are in the range of other foodstuffs. A great dependence of moisture diffusivity on moisture content was also found.

NOMENCLATURE

B	=	constant
Cp	=	specific heat capacity (J/kg °C)
D	=	moisture diffusivity (m2/s)
D0	=	constant (m2/s)
E	=	activation energy (kJ/mol)
h	=	convective heat transfer coefficient (J/s m2°C)
ka	=	thermal conductivity of air (J/s m °C)
L	=	leaf thickness (m)
n	=	number of experimental values
R	=	constant of ideal gases, J/kmol °K
Re	=	Reynold number
T	=	temperature (°C)
T∞	=	air temperature (°C)
V	=	volume (m3)
X	=	moisture content (% dry basis)
y	=	moisture content (wet basis)

Greek Symbols
Δ t	=	time step (s)
λ	=	latent heat of water (J/kg)
ρ	=	apparent density (kg/m3)

Subscripts
calc	=	calculated
e	=	equilibrium
exp	=	experimental
o	=	initial
t	=	time

INTRODUCTION

Drying is a process that involves simultaneous heat and mass transfer, and therefore, depends on a material's properties and air transfer properties (thermal conductivity, moisture diffusivity, and convective heat and mass transfer). When air velocity is high, moisture diffusivity has an important role during drying (Zogzas and Maroulis, 1996).

During drying, heat is used to warm the material and evaporate water, generating thermal gradient. Loss of water in material surface generates an important moisture gradient in the solid. The higher the drying temperature, the higher the heat and mass transfer and sharper the moisture and temperature profiles in the material. However, when the material has a very small length characteristic, like leaf thickness, internal moisture and thermal profiles are planes, and drying modeling could be made considering global values of the properties depending on this two variables (Kreith and Bohn, 1997; Zogzas and Maroulis, 1996).

The material considered in this study is yerba maté leaves (Ilex paraguariensis Saint Hilaire). With these leaves, a very popular infusion in Latin American is made. Industrial processing has a very high heat treatment. In the first stage the material is in contact with gases from burning wood at 300–350°C, for 2 or 3 minutes, to inactivate enzymes that produce browning and partially dry it. Because of high moisture content and heat treatment, several physical and chemical changes, such as color, vitamins, apparent density, and thickness are produced in this step (Ramallo et al., 1998; Schmalko et al., 1996; Schmalko et al., 1997).

The objective of this research is to study the change of apparent density, thickness, and moisture diffusivity during drying as a function of temperature and moisture content. A simple mathematical model was developed during drying of yerba maté leaves at high temperatures.

MATHEMATICAL MODEL

In the differential equations that describe drying process, a series of material properties that depend on moisture content and temperature are involved. This relation shows that heat and mass balance equations are interdependent and analytical solutions are not applicable. This problem is solved using numerical methods (Hoffman, 1992).

If the material has a small thickness, absence of temperature profile may be considered. With these criteria, the mathematical model that describes drying of leaves at high temperatures makes the following assumptions:

•	absence of thermal profile in the material,
•	material properties depend on mean moisture content,
•	for a small time step, physics properties, moisture content, and temperature in the material remain constants,
•	integrated Fick's second law for a plane plate can be used for a small time step

With these assumptions, moisture content and temperature of the leaf can be estimated using the following equations:

MATERIALS AND METHODS

Material

Yerba maté leaves (Ilex paraguariensis Saint Hilaire) from a local producer and before processing were used as the test material. Thickness was measured with an automatically operated dead weight type micrometer (model 549M micrometer from Testing Machines, Inc.) provided with a flat ground circular movable face with an area of 200 ± 5 mm² with an accuracy of ± 2.54 × 10⁻⁶ m (± 1 × 10⁻⁴ inches). Leaves were sorted according to their thickness, varying between 2.79 and 4.57 × 10⁻⁴ m, in a range of ± 2.54 × 10⁻⁵ m. Four measures of each leaf were made, and those ones that fit the measures in the range of ± 2.54 × 10⁻⁵ m were used (Tappi, 1997).

Apparent Density and Shrinkage

To determine apparent density and thickness at different moisture contents and drying temperatures, the following procedure was used: once leaves with a determined thickness were selected, the area of the leaves was measured by drawing them on a paper, and then cutting and weighing the paper (Mantovani, 1999). These samples were divided into fractions and were partially dried at different temperatures and for different times and then were placed in a tightly closed flask and maintained in it during 3 days to equilibrate water in the sample. Finally, thickness, mass, and moisture content were determined. These experiences were carried out for different thickness and for four different drying temperatures (100, 110, 120 and 130°C). Apparent density was determined as the relation between the mass and volume of the leaves (the volume was calculated by multiplying the area plus the mean thickness). Shrinkage coefficient is defined as the relation between the volume and the initial volume (Lozano et al., 1983); but when the area of the material remains constant during drying, it can be considered as the relation between the thickness and the initial thickness of the leaf (L/L_o ).

Moisture Content

Moisture content was determined by drying the sample in an oven at 103 ± 2°C until constant mass was reached. This took about 6 h of drying.

Drying Kinetics—Experimental Procedure

Drying curves were obtained with a thin-layer of leaves in a cross-flow dryer at constant conditions. Air velocity was fixed at 2.5 m/s and temperature varied between 100 and 130°C. The leaves were put in a basket and they were weighed every 2 minutes until constant. Mass loss and final moisture content determined moisture content for each time.

Moisture Diffusivity Determination

Moisture diffusivity was the parameter used to fit the model to experimental data. It was considered depending on temperature and moisture content, according to Equation 3 (Zogzas et al., 1996).

In a first step, values of D_o , B and E are assumed to calculate D according to Equation 3. The other parameters used in Equations 1 and 2 (X_e , L, C_p , ρ, h and λ) are evaluated at X_t and T_t . Then values of temperature and moisture content were estimated for the next step time with Equations 1 and 2. This procedure is repeated until weighing time is reached. At this time, experimental and calculated values of moisture content were compared for each experience. The values that minimized the mean percent error (MPE) calculated with Equation 4, were considered the best.

RESULTS AND DISCUSSION

Apparent Density and Shrinkage

Experiments were carried out using four temperatures (between 100 and 130°C) and at five different initial thickness of leaves. Data were analyzed using linear regression and with the following two considerations:

1.	L/Lo vs X/Xo , and
2.	L vs X

The influence of temperature was analyzed comparing the slope and intercept of the linear regression of L vs X for each temperature. There were no difference between slopes and intercepts as a function of temperature (p < 05). Similar results were observed by Statgraphics (1993). The data of 94 measurement at different temperature were fitted as:

The MPE is 10.05%. Figure 1 shows the agreement between the experimental and predicted values of thickness vs. moisture content. Apparent density for different moisture contents was determined from data of leaves thickness, area and mass. Like thickness, apparent density was independent of drying temperature. This result was obtained comparing the slope and intercept of the regression line of apparent density vs. moisture content for each temperature. According to this result, all data of densities were adjusted to only one equation, resulting:

with p < 10⁻⁵ and MPE = 10.75%. In the literature it has been identified that the apparent density of food depends on moisture content (Lozano et al., 1983; Krokida and Maroulis, 1997; Schmalko et al., 1997; Wang and Brennan, 1995). In this study, linear model was used because apparent density values are more congruent when values of moisture contents approach zero.

Figure 1. Experimental and predicted values of thickness versus moisture content.

Drying Kinetics

Thirty-four experiments between 100 and 130°C were carried out for drying kinetics. In these experiment values of moisture contents varied from 300 and 5% (dry basis) and drying times varied from 10 and 20 minutes.

Moisture Diffusivity

The parameters used in Equations 1 and 2 to calculate X _t+1 and T _t+1 were evaluated as follows:

•	thickness was calculated with Equation 5
•	apparent density was calculated with Equation 6
•	specific heat capacity was calculated with the equation: Cp = 1.79 × 103 + 2.36 × 103 X (Schmalko et al., 1997)
•	equilibrium moisture content for T ≥ 100 was considered zero, and for T < 100 was obtained from the data of Kanzig et al. (1987)
•	latent heat of water evaporation was obtained from Perry and Green (1983) and
•	convective heat transfer coefficient was calculated from Equation 7 (Kreith and Bohn, 1997)

Parameter D_o , B and E of Equation 3 were found from the best fitting of the data as:

The MPE was 25.72%. The values of D, D_o , B and E obtained in this work were in the range of those obtained for other foodstuffs (Zogzas et al., 1996). Values of D varied between 2.3 × 10⁻¹¹ and 2.5 × 10⁻¹⁰ m²/s, while in other published articles it varied between 10⁻¹⁴ and 10⁻⁶ m²/s. The value of E = 31.04 KJ/mol obtained was in the range of reported values for other foodstuffs (15–95 KJ/mol). Figure 2 shows experimental and calculated values of moisture content using moisture diffusivity of Equation 8 and calculated temperature from Equation 2 for one experiment carried out at leaf thickness of 0.000394 m and drying temperature of 110°C.

Figure 2. Experimental and calculated values of moisture content and calculated values of temperatures for an experience carried out with leaves 0.000394 m thick and dried at 110°C.

CONCLUSIONS

Thickness and density of yerba maté leaves vary in a linear form with moisture content when they are being dried at high temperatures (100–130°C). These variations were statistically independent of drying temperature. A simple mathematical model that describes the variations of moisture content and temperature of leaves during drying was developed. This model considers these two variables that depend only on time and physical properties that depend on temperature and average moisture content of the material.

Acknowledgments