3.5 Comunicación de resultados
3.5.1 Informe de auditoría de gestión
R. Olivas-Vargas, F.J. Molina-Corral, A. Pérez-Hernández, and E. Ortega-Rivas
CONTENTS
11.1 Introduction
11.2 Materials and Methods 11.3 Results and Discussion 11.4 Conclusions
Nomenclature Acknowledgments References
11.1 INTRODUCTION
Drying is a physical separation process that has the objective of removing a liquid from a solid phase by means of thermal energy. The liquid is generally water and is liberated by vaporization rather than by breaking chemical bonds between the liquid and the solid; i.e., the liquid is not chemically bound to the solid. In most industrial drying applications, it is neither necessary nor economically feasible to remove every vestige of water from the solid; thus, commercially dry solids will usually contain a certain amount of residual moisture, the amount of which is determined by a compro-mise between product quality and economic factors. In food and biological materials, low moisture levels are necessary to stop or slow the growth of spoilage microorgan-isms, as well as the occurrence of undesirable biochemical and enzymatic reactions.
The fundamental principles underlying drying processes are, in general, those typical of the science of heat and mass transfer. Drying, as a unit operation in food and chemical engineering, is characterized by the separation, usually partial, of a
11
liquid contained within a solid by the process of vaporization of the liquid into a gas phase. The mechanism of the drying process, as controlled by the principle of heat and mass transfer, consists of the transport of mass from the interior of the solid to the surface, the vaporization of the liquid at or near the surface, and the transport of the vapor into the bulk gas phase. Simultaneously, heat is transferred from the bulk gas phase to the solid phase, where all or a portion of it provides for vaporization, and the remainder accumulates in the solid as a sensible heat. The overall rate by which the above sequence of steps takes place defines the drying rate and is inversely related to the drying time.
Regardless of how heat is provided, the drying cycle generally consists of three steps:
1. Before any evaporation takes place, sensible heat must be added to the drying mass until the boiling point of the liquid under the given operating conditions is reached.
2. Once the boiling point is reached, evaporation takes place at a rate related to the moisture level in the solid, and this rate is normally constant over a certain moisture range.
3. At some condition, a critical moisture point is reached and the drying rate begins to fall.
Constant rate drying is the first stage, in which drying occurs at or near the boiling point of the liquid. There is no resistance to vaporization, since the moisture appears on the surface of the solid, completely wetting the outer surface. The constant drying rate is proportional to the difference between the vapor pressure of the liquid covering the surface of the solid and that of the vapor surrounding the wetted solid.
It has been found that the vapor pressure of the wetting liquid is very close to that of the pure liquid at the same temperature.
At the critical moisture content of the solid, the drying rate begins to fall because there is not enough moisture to completely cover the solid surface. The reduced amount of moisture being evaporated comes from the interstices of the solid through the porous structure. Falling rate drying is controlled by the physical properties of the liquid and solid. The rates of movement of the liquid and its vapor depend on capillary size, glazing of the solid, pressure gradients between trapped liquid and vapor, and the environs of the solid, as well as on cracking, checking, etc. At the same time, the heat transfer rate to the interior of the solid is being slowed because of the receding boundary of the liquid-wetted portion of the particle. This boundary movement increases the resistance to heat flow because it reduces the thermal conductivity within the solid. Cracking and checking disrupt the paths of heat transfer, further reducing the rate.
Moisture migration during drying has been explained by different models. Four mechanisms are recognized: capillarity, concentration gradient diffusion, vapor dif-fusion by pressure difference, and layer difdif-fusion across solid–fluid interfaces (Bren-nan, 1994). Capillary forces are responsible for water retention in porous solids or those of rigid construction, while osmotic pressure is responsible in aggregates of fine powders and on the surface of the solid (Toei, 1983). It has been reported that
moisture migration by diffusion is the predominant mechanism in drying of many food products, such as vegetables (Geankoplis, 1983).
Drying data are usually expressed as total weight of the material as a function of time during the drying process. These data can also be expressed in terms of drying rate by recalculation of some values. The moisture content is defined as the ratio of the amount of water in the food to the amount of dry solids, i.e.,:
(11.1)
where Xt is the moisture expressed as weight of water/weight of dry solids, Wt is the total weight of the material at time t, and Fs is the weight of the dry solids. An additional important quantity used in designing drying processes is the free moisture content X, which can be evaluated considering the equilibrium moisture content Xeq, by the simple relation:
(11.2) As previously mentioned, moisture contents can be recalculated to obtain drying rates. The rate of drying R can be expressed proportional to the change in moisture content as a function of time t, by the following relationship:
(11.3)
Individual values of dX/dt as a function of time t can be obtained from tangent lines drawn to the curve of X vs. t. Replacing the proportionality condition in Equation (11.3) by Fs/A, the drying rate can be represented by:
(11.4)
where A is the drying surface area.
Drying of fruits and vegetables follows conventional dehydration theory, which was adapted from drying of inorganic materials and other raw materials in the chemical processing industry (Sarvacos and Charm, 1962). The advantages of reducing moisture content below 5% in biological materials are well known: microbial and enzyme activity are practically stopped, and transport costs are greatly reduced. However, fruits and vegetables can also suffer undesired changes due to the drying process. Shrinkage, case hardening, texture damage, and reconstitution difficulty can be caused by drying (Brennan, 1994). Dehydrated vegetables, when reconstituted, cannot match the original texture even if precautions are taken during the entire drying process.
The large scale of industrial drying makes the analysis of the process difficult.
Operators and process engineers often have only a few variables to use in formulating
X W F
t F
t s
s
= −
X=Xt−Xeq
R dX
∝ dt
R F
A dX
dt
= − s
any changes needed to control the operation. Typically, the feed rate is held constant and the controlling variable is the drying medium temperature. The operator may use exaggerated safety factors to prevent product build-up or over-drying. Mathe-matical modeling may be considered an efficient tool to overcome inefficiencies of drying plants such as damaged product, wasted energy, wear on the dryer, or decreased throughput.
Models to describe dehydration of foods are necessary for process design, improvement, and minimization of energy while keeping quality as unimpaired as possible. Development of mathematical models to describe drying of porous solids has been the topic of many research studies for many years. Heat and mass transfer take place in a porous solid when it contains moisture and is subjected to any or all of the gradients of concentration, partial vapor pressure, temperature, total pressure, and external force fields. There has been no general agreement among researchers on which driving forces predominate, considering different materials or media and external drying conditions. More and more sophisticated drying models are becom-ing available based on either a mechanistic classical approach or on nonequilibrium thermodynamics. However, a major question that still remains is the determination of the best driving forces and assumptions to be made for drying model formulation.
Another concern should be the determination of the coefficients and parameters used in the model. The measurement or determination of the necessary coefficients should be feasible and practical for general applicability of a drying model.
The research described here was directed towards developing a predictive math-ematical model of jalapeño pepper drying and thermal damage, due to the economic importance of this commodity, as well as its potential commercialization value as a processed product.
11.2 MATERIALS AND METHODS
Fresh green jalapeño peppers (Capsicum annuum L.) obtained from local markets were used for the experiments. They were selected manually in order to obtain peppers in good condition of uniform size (6–7 cm), and then sliced to an approx-imate thickness of 5 mm using an electrical cutting machine (S.A. Bertuzzi; Brugh-erio, Milano, Italy). The jalapeño slices were washed to remove seeds and allowed to drain for 10 min. Samples of 180 g were placed over nine trays of a locally manufactured dryer, diagrammatically illustrated in Figure 11.1. Air was heated by a gas burner model HP225B LP (Adams Manufacturing Company; Cleveland, OH) and directed in parallel direction towards the peppers at 5 m/sec and temperatures of 60, 70, and 80°C. The drying time was 150 min. Dry bulb temperatures were recorded using thermometers located at different positions, as shown in Figure 11.1.
Air velocity was measured using a Pitot tube (Dwyer Instruments, Inc.; Michigan City, IN) connected to a differential inclined manometer according to ASTM (1995) norm D3154. Moisture changes were determined by weight difference according to AOAC (1990) method 6.004. To determine a rehydration ratio, samples of 5 g dried slices were immersed in 400 ml water baths. The water baths were set at 75°C, and the immersion time was 6 min.
The results obtained were used to derive drying and rehydration kinetics pre-dictive models by means of regression analysis, using the Statistica 5.5 software (StatSoft, Inc., Tulsa, OK).
11.3 RESULTS AND DISCUSSION
In fundamental drying research of food materials, ideally a model would contain a minimum of restrictive assumptions, and all material property values needed for the model would be obtained. The prediction of the drying characteristics based on knowledge of composition and structure is complex due to the nature of solid structures and the limited understanding of the moisture transport mechanism. An alternative is the identification of the relevant driving forces and the use of independent experimental tests that isolate the different driving forces to determine the necessary model coefficients. The model should have the most possible theo-retical meaning and require the minimum of experimental tests to determine the coefficients.
The model developed in this work was derived according to the characteristics described above. Drying kinetics were determined and the data were handled in a mathematical way to evaluate the best fitting equations describing the drying curves.
To achieve this, drying conditions had to be controlled very carefully to ensure constant velocity, constant moisture content, and constant temperature of the flowing air. When these conditions were set, it was assumed that the drying rate represented by Equation (11.4) could also be established entirely in terms of the moisture gradient FIGURE 11.1 Schematic diagram of the tray dryer used for the experiments.
Trays Thermometers
Air valve
Burner Exhaust
64 cm 83.5 cm 49.5 cm
198 cm
206 cm
between the sample and the surrounding drying air, i.e.,
(11.5)
where XR is the moisture content on a dry basis of the vegetable, Ky is a coefficient governing the mass transfer, and Xeis the moisture content of the air.
To give the model a generalized characteristic, the moisture content was nor-malized using the following dimensionless relation:
(11.6)
where X0 is the moisture content of the material at the initial time, i.e., t = 0.
It can be demonstrated (Molina-Corral, 1988) that Equation (11.5) can be rear-ranged by incorporating the normalized moisture content described by Equation (11.6), to give the following relationship:
(11.7)
The normalized moisture content Θ can be made explicit and transposed to give:
(11.8)
Integrating Equation (11.8), the following relationship is therefore obtained:
(11.9) where C is the integration constant.
Taking natural logarithms on both sides of Equation (11.9) transforms it into the following exponential expression:
(11.10) Using logarithm’s laws it can be demonstrated (Molina-Corral, 1988) that Equation (11.10) simply becomes the one presented below, which relates the variation of moisture content of the material Θ as a function of time t and temperature T, i.e.,
(11.11)
Equation (11.11) represents a one-exponential model known as the thin film drying model. Such a model basically states that the drying constant, Ky in this case, is a combination of the transport properties involved in drying and describes with reasonable accuracy the drying kinetics of hygroscopic materials. When the previ-ously mentioned constant conditions of velocity, moisture, and temperature of the drying air are ensured, the transport properties most influential in drying of vegeta-bles are time and temperature. The correlation exercises practiced in accordance with the experimental data demonstrated that the best fitting model for the coefficient governing the mass transfer Kywas a quadratic one expressed as:
(11.12) where the parameters β1,β2,…,β6 are those presented inTable 11.1.
The model for predicting moisture content as a function of time and temperature was therefore given by:
(11.13) Figure 11.2 shows the experimental drying curves contrasted with the corre-spondinc correspondent ones obtained using Equation (11.13) above at the three temperatures tested. As can be seen, the mathematical model fit the experimental data very well, judging by the high given values of the coefficient of determination R2. As stated earlier, moisture migration by diffusion is the predominant mass transfer mechanism in drying of fruits and vegetables. It has also been reported (Toledo, 1991) that diffusivity may be constant if cells do not collapse and pack together. This behavior would be identified in firm solids such as grains, or in high moisture products such as fruits and vegetables when physical changes such as water removal are minimal. As shown in Figure 11.3, the presence of only a falling rate period for all the conditions tested was confirmed. This trend was in agreement with the work reported by Turhan
TABLE 11.1
Regression Parameter Values for the Dehydration and Rehydration Models from Experimental Data
Parameter Dehydration Model Rehydration Model β1 5.209× 10−1 −7.3340 × 10−2 β2 3.730× 10−2 1.6000× 10−5 β3 1.550× 10−2 2.5004× 10−3
β4 0.0 0.0
β5 1.000× 10−4 −2.4360 × 10−5
β6 6.000× 10−4 0.0
Ky= +β β1 2t+β3T+β4t +βT +β tT
2 5
2 6
Θ =e(β β1+2t+β3T+β4t2+β5T2+β6tT t)
FIGURE 11.2 Experimental (䉱) and calculated (—) drying curves for 60 (A), 70 (B), and 80°C (C) dehydration temperatures.
0 0.2 0.4 0.6 0.8 1
0 30 60 90 120 150
0 0.2 0.4 0.6 0.8 1
0 30 60 90 120 150
0 0.2 0.4 0.6 0.8 1
0 30 60 90 120 150
S = 0.031 R2 = 0.99
S = 0.020 R2 = 0.99 S = 0.023 R2 = 0.99
(a)
(b)
(c)
Moisture content
Time (minutes)
and Turhan (1997), who found that peppers dehydrated without previous blanching presented only a falling rate period in their drying kinetics.
The drying curves presented in Figure 11.2 also show the difference in drying velocities according to the applied temperature. It can be observed that drying FIGURE 11.3 Experimental drying rate curves for 60 (A), 70 (B), and 80°C (C) dehydration temperatures.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
0 0.2 0.4 0.6 0.8 1
0 0.5 1 1.5 2
0 0.2 0.4 0.6 0.8 1
0 0.4 0.8 1.2 1.6 2 2.4
0 0.2 0.4 0.6 0.8 1
Moisture content Drying rate (kg/h·m2)
(a)
(b)
(c)
kinetics were higher, with a similar trend, for the processes carried out at 70 and 80°C, but slower for the minimum temperature of 60°C. Thus, it can be argued that drying kinetics were optimal at any of the higher temperatures, and that these levels of heat were moderate enough to prevent undesirable phenomena such as case hardening. It has been observed that in drying of some fruits, vegetables, meat, and fish, as drying temperatures approach the water boiling range, a hard and imperme-able film develops on the surface (Brennan et al., 1979). Case hardening can be more severe during final stages of drying, where more than one falling rate period is presented. Since there was only one falling rate period in this study, case hardening was not a problem and drying kinetics developed quite well. However, as more undesirable phenomena can be caused by high drying temperatures, it would be advisable to use 70°C as the dehydration processing temperature in further applica-tions, as drying behavior was similar at either 70 or 80°C.
In addition to case hardening, shrinkage and texture damage can be caused by drying of vegetables, resulting in poor appearance and loss of some sensory attributes. The amount of thermal damage in drying of vegetables is difficult to evaluate, but it may be related in some way to structural alteration of the tissues due to excessive heat. The degree to which a dehydrated sample will rehydrate is influ-enced by such structural and chemical changes. Rehydration is maximized when cellular and structural disruption is minimized. Several measures can be taken to minimize structural alterations in order to improve the reconstitutability of dried food products. The drying method and adjustment of drying conditions can result in a product with good rehydration properties. For example, it has been reported that freeze-drying causes fewer structural changes than any other method, with minimal changes to the product’s hydrophilic properties (Heldman and Singh, 1981).
This procedure results in obtaining food pieces with an open pore structure that will absorb water easily when reconstituted. However, freeze-drying is an expensive form of dehydration for foods due to the slowness of the drying rate and the use of vacuum.
Since the vapor pressure of ice is very small, freeze-drying requires very low pressures or very high vacuum.
For this reason, it is more feasible to try to obtain food products with good recon-stitution properties by manipulating the operating variables of dryers. One possibility is to partially dehydrate fruits by immersion in sugar solutions to promote water migra-tion by osmotic pressure difference, then give them a gentle drying cycle in order to obtain crisp products that rehydrate easily (Beltrán-Reyes et al., 1996). Also, the blanch-ing method and dryblanch-ing temperatures can have an effect on reconstitution properties of vegetables (Ortega-Rivas et al., 1997).
In this work, the amount of damage produced by the different drying conditions was determined by estimating the rehydration ratio RR using the following relation:
(11.14)
where w0 is the weight of the dry sample and wf is the weight of the rehydrated sample.
RR w
wf
= 0
Rehydration rates, estimated by Equation (11.14), are shown in Figure 11.4. The best fitting model for the rehydration ratio, obtained using a procedure similar to that in deriving Equation (11.13), was:
(11.15) The parameters β1,β2,…,β6 are given in Table 11.1.
As can be observed in Figure 11.4, rehydration kinetics showed a trend opposite to that of the drying process, i.e., the dried peppers rehydrated better at the lower drying temperature and at the shorter treatment times. In general terms, the worst rehydration characteristics were demonstrated by the peppers dried at 80°C. This behavior could be due to the extent of tissue damage, which is expected to be more severe at higher drying temperatures. It has been reported (Charm, 1971) that excessive thermal damage, due to high drying temperatures, may be responsible for poor appearance and loss of texture of dehydrated biological materials.
11.4 CONCLUSIONS
A mathematical model to describe dehydration of jalapeño pepper at normal oper-ating conditions was developed. The model describes the drying process in terms of the moisture migration as a function of time at different temperatures. The effect of thermal damage as a function of rehydration capacity is also included. The regression equations describing the model were highly correlated. The model can be used to opt for the best compromise between drying capability and product quality.
Application of the model to a material similar to the one tested in the experiments would indicate that the use of relatively high temperatures would make a product
Application of the model to a material similar to the one tested in the experiments would indicate that the use of relatively high temperatures would make a product