- Research Note -
Why is the Grape PuffTM Puffy? An Analysis of MIVAC Temperature Curves
by
Matthew Yen and Carter D. Clary
CATI Publication #951101
© Copyright October 1994, all rights reserved
INTRODUCTION
Microwave vacuum dehydration was first used for concentration of citrus juice in France (Decareau, 1985). It was later applied to dry grain (McKinney et al., 1977) and rice (Wear, 1982). The technology was adapted to grapes by McKinney et al. (1983) for production of Grape Puffs™. The process was patented by McKinney et al. (1987) and described by Petrucci and Clary (1989).
Proper temperature control is critical to the microwave vacuum (MIVAC) dehydration system. An understanding of the temperature history during the process in relation to the physical aspects of product changes is essential for better process controls. Temperature curves in MIVAC heating vary according to products, microwave power, product load, and many other factors. Generally, the temperature curve follows a pattern similar to that of heating water beyond the boiling point (see Figure 1).
A typical temperature curve consists of three stages: 1st stage - the temperature rises linearly to a point where phase change may take place; 2nd stage - temperature ceases to rise appreciably; it may remain flat or even decrease slightly; 3rd stage - temperature again rises linearly but at a rate which is different from that of the first stage.
This bulletin describes an analysis of each stage based on the principle of energy conservation or the first law of thermodynamics. Sample calculations are shown based on existing MIVAC data with some explanations of their implications. The ramifications of this analysis are further discussed in view of MIVAC process control.
ANALYSIS
First Stage - Temperature Rises Linearly
Microwave energy is absorbed by the product. The temperature of the product increases due to internal heating. The temperature rises along a straight line until a point where the rate of increase slows down. As it is in the case of a single substance, the slope of this straight line is a measure of the specific heat of the material being heated. It is directly proportional to the applied microwave power. From the principle of energy conservation:
The rate of product temperature change, or, the rate of internal energy change = microwave energy absorbed by the product
This relationship can be mathematically expressed as:
mc(dT/dt) = Kw (1)
whereM = mass of the product, in gm
This is a greatly simplified description of what takes place during heating. Despite its simplicity, it provides some valuable insights into the heating mechanism. It is useful to characterize the process by evaluating parameters such as coupling coefficient, specific heat, transition temperatures, and so on.
C = specific heat of the product, in J/gm- °C
dT/dt = rate of temperature change, or, slope of the rising temperature line, in degrees C/sec
K = a coupling factor between the forward microwave energy and the product, dimensionless
w = microwave power in W (watt or J/sec)
As an example, grapes have a composite structure which consists of the skin, internal tissue cells and juice. Microwave energy will be absorbed more by water and sugar solution than by the grape's solid constituents. As a result, the temperature of the fluid constituent rises faster than that of the solid parts. Therefore, the temperature distribution inside the berry may not be uniform nor stationary. Figure 2 shows a hypothetical progression of temperature distribution throughout the berry. The abscissa (x-axis) is the radial distance measured from the centroid of a grape berry. The centroid is assigned a value of 0.0. This distance is normalized so that the skin has a value of 1.0. The coordinate (y-axis) is the temperature in degrees Fahrenheit. Three curves represent temperature distributions at three instants in this stage. They are designated as t1, t2 and t3, respectively with t1 < t2 < t3.
For illustration purposes, peripheral heating is assumed during this stage as opposed to "core" heating. Assumptions for all three stages include the following: (i) berry material is homogeneous; (ii) the berry is perfectly spherical; and (iii) angular temperature variation is negligible. It should be noted that such hypothetical temperature distributions are employed strictly for discussion purpose. It is necessary to establish the actual temperature progression both theoretically and experimentally.
Since the water molecule is polarized and the specific heat of water is greater than that of solid mass, water absorbs the most microwave energy. Use of the specific heat of pure water should suffice for practical calculations. Accurate values of the specific heat of the constituents, i.e., skin, internal tissue cells and juice, may be desired, but most likely they are not readily available. The effects of this simplification need to be evaluated and adjusted according to their significance in the future.
It is expected that the coupling factor, K, has a value less than one and is a strong function of the product constituents, such as sugar content (Brix) or moisture content, etc. Also, it may vary appreciably throughout the heating process.
Second Stage - Temperature Remains Constant
In the case where water under microwave heating is not confined, its temperature can only be raised to a point at which the liquid begins to vaporize. Energy is expended as latent heat to transform liquid into vapor. If the pressure is held as a constant, the system temperature does not increase until all the liquid is evaporated. For a different pressure, the temperature at which liquid evaporates is also different. This temperature and pressure relationship is known as the saturated liquid line (Figure 3).
On the other hand, if water is confined in a space, such as in a berry, pressure will increase as long as the confining structure can hold it. Once moisture is heated to a saturation temperature, the temperature will continue to rise with the pressure along the saturated liquid line. Such a temperature and pressure increase is also associated with a volume expansion that eventually causes the confining structure, e.g., membrane, skin, etc., to yield or rupture. If the rate of vaporization is controlled by the level of microwave energy applied, a puffed character can be achieved.
Moisture may undergo two possible processes: (i) It may be drawn to the product surface and vaporized through the diffusion mechanism; or (ii) It may be pooled with adjacent moisture and start to expand and vaporize, pushing weak tissue aside to develop pores. The porous structure is evidenced by a scanning electronic microscope (SEM) image as shown in Figure 4. For grapes, this rupturing process starts near the surface and "propagates" into the interior in a fashion similar to that of peeling an onion. This rupturing and poring phenomenon explains why the Grape Puff™ is puffy. It should be noted that this dehydration process is significantly different from that of a sun-dried raisin. In the later case, the temperature profile is monotonic without a peak, and moisture is transported mainly through the diffusion process.
A hypothetical temperature progression during this stage is shown in Figure 5. The three instances depicted for this stage are designated as t4, t5 and t6 (here t4 < t5 < t6). The three temperature distributions are shown with different forms to reflect the development of pores and the radial propagation of the peak temperature, which remains nearly a constant throughout this stage.
Theoretically speaking, if the measured product temperature is an accurate estimate of the aforementioned saturation temperature, the pressure differential between the product interior and the chamber vacuum can be used to calculate the rupture strength of the product. This rupture strength would be a good indicator of the product's textural strength. It should be noted that "taste" includes this textural strength in addition to the chemical flavor. For example, we often classify products as chunky, chewy, or mushy in addition to sweet, flat or salty. Quantifying the textural strength could eventually explain why some of the pre-treatments, e.g., blanching, are needed before the MIVAC treatment. Further evaluation of the textural strength may lead to more innovative processing prior to the MIVAC treatment.
Since vaporization is taking place in the second stage, the energy equation must be re-written as:
rate of product internal energy change
Mathematically, it is expressed as:
+ latent heat of vaporized moisture
+ rupture work
= applied microwave energy
MC(dT/dt) + h(dM/dt) + R = Kw (2)
where M, C, dT/dt, K, w are defined as in equation (1), and
h = heat of vaporization or latent heat dM/dt = rate of vaporization R = work done to rupture the confining tissue
It should be noted that the first term during this is nearly zero because the overall temperature is almost constant during this stage. Assuming the rupture work, R, is negligible during most of the time, equation (2) can be simplified as:
h(dM/dt) = Kw (3)
This equation can be used in several ways: (i) if dM/dt, K and w are known, it can be used to verify the latent heat at a given vacuum; (ii) if dM/dt, h and w are known, it can be used to check the consistency of the coupling factor, K; or (iii) the equation can be used to predict the dehydration rate for a given condition.
Furthermore, all the absorbed energy is expended in the rupture work at the beginning of this stage, therefore,
R = Kw (4)
This result can be used to estimate the textural strength of the product.
Third Stage - Temperature Rise Resumes
Once most of the moisture is driven out of the system, vaporization ceases to dominate and the product temperature starts to rise again. The temperature distribution during this stage is hypothetically depicted in Figure 6. The three instants during this final stage are denoted as t7, t8 and t9, with t7 < t8 < t9. It is likely that the temperature distributions are rather uniform in this stage. The energy balance equation is the same as the first stage, that is:
mc(dT/dt) = Kw (5)
where c is the specific heat of the residual mass m. Lower case m and c are used to denote the mass and specific heat after the dehydration stage. Note that m < M and c < C.
Since the dielectric constant, the specific heat and the coupling coefficient are functions of grape temperature, it would be of interest to evaluate the ratio of the final moisture content (FMC) to the initial moisture content (IMC) and the rates of temperature rise, e.g.:
FMC/IMC = (mc/MC)(dT/dt)3/(dT/dt)1 (6)
where mc and MC are the values of mass and specific heat at the final stage and the first stage, respectively. These results might be useful for predicting the final moisture content or correlating with other process parameters, such as power level, coupling coefficients, etc.
SAMPLE CALCULATIONS
Sample calculations based on the above analysis were performed for the heating of Thompson Seedless grapes. The temperature-rise profiles in fixed power MIVAC treatment are given in Figures 7 and 8. The grapes in Figure 7 were heated for 30 minutes and in Figure 8 for 60 minutes. Microwave power values were set at 500, 750, 1000 and 1250 watts for both treatments. An additional value of 1500 watts was also applied to the 30-minute run. The products obtained from these experiments varied from chewy, wrinkled, and puffed, to burnt.
Since these experiments were conducted prior to this analysis and it was determined that applying variable power can provide more satisfactory results, no attempts were made to correlate such analysis with the product character in this study. Due to the reduction of moisture content as well as the berry structural changes, it is more practical to apply a decreasing power schedule to achieve optimal results.
I. First stage
Major heating characteristics of these experiments are summarized in Table 1. The first column is the heating rate of the first stage. In both cases, 500 watts of power resulted in relatively fast temperature rise in comparison with 750 watts and 1000 watts. This is a rather interesting result which contradicts the intuition, e.g., higher power will drive the temperature up faster. More recent tests have shown that the heating rate indeed rises faster for higher power levels. The apparent lower heating rates might have resulted from not enough data points being taken for the first stage. It should also be noted that this produces a significantly higher coupling factor, i.e., 0.4 vs 0.08.
II. Second stage
The second column is the average temperatures when active dehydration is taking place. Based on the analysis this temperature should be the same as the saturation temperatures at the recorded vacuum. The saturation temperatures are listed in the third column. It can be seen that the average temperatures are much higher than the saturation temperatures. The possible explanations for this discrepancy are (i) inaccurate temperature readings; (ii) inaccurate pressure measurements; (iii) vaporization under high pressure due to confined product structure; or (iv) combination of the three.
Since temperatures cannot be directly measured accurately without being affected by the microwave, and it was done with an infrared temperature detector, the likelihood of measurement errors is much higher than in the case of measuring pressure. But the differences between the measured temperatures and the saturation temperatures at the recorded pressures are in the magnitude of 10 to 40 degrees, which are way beyond the measurement errors, e.g., five degrees at most. This observation leads to the third explanation, that is, vaporization takes place at much higher pressure than the recorded pressure level.
Dissections of the Grape Puff have shown porous structures both to the bare eye and underneath a microscope. This fact is an indication of the presence of moderately pressurized water vapor or gas prior to it being released. This is the consequence of the microwave energy being absorbed by water molecules which are confined in the solid berry constituents. This "energy trapping" phenomenon is very similar to that of the "greenhouse effect" except it is manifested on a miniature scale. The larger the pressure differential is, the larger the pore size would be. It is these porous structures that give the Grape Puff™ a puffy appearance instead of being collapsed and wrinkled as sun-dried raisins.
Based on the prior analysis and assuming the recorded data are accurate, this pressure differential is estimated in the range of 0.5 to 1.0 psi. The actual value could be much higher. This is based on the high values of coupling coefficient at the second stage, i.e., 0.70 - 1.00. Further research on this pressure differential is needed and it may provide useful information about the textural strength of various products. In turn, such information can be a useful guide for designing processes or "engineering" recipes for better taste.
III. Third stage
Since moisture is the primary substance removed from the product, it is plausible that the ratio of the final moisture content to the initial moisture content should be very close to the ratio of the final weight to the initial weight. Results of such calculations are given in the fifth and sixth columns. The ratio of the third stage heating rate to the first stage heating rate is also given in column seven.
Though column 5 and column 6 correlate fairly well, it is apparent that these ratios decrease as the applied microwave power increases. On the other hand, the ratio in column 7 increases. This is a clear indication of larger temperature gradient when higher powers are applied. High temperature nearby the berry skin results in significant increase of berry permitivity. Consequently, it "absorbs" more microwave energy and causes a faster heating rate or "thermal run away."
III. Third stage
Columns 8, 9 and 10 summarize the coupling coefficients for the first stage, the second stage and the third stage, respectively. It is notable that the values for the third stage are a magnitude smaller than that of the first stage. Even in the case of high power levels, the heating rate for the third stage is about the same as that of the first stage. This can be explained by the "thermal run-away" of the third stage, which is taking place near the berry skin as a surface phenomenon, while the energy coupling is more of a volumetric phenomenon for the first stage.
It is also interesting to observe significant large values for the second stage (Column 9). This could be explained by the fact that once the grape berry is ruptured, free water will in effect absorb the microwave energy. These values are comparable with some of the published values which are in the range of 50% to 90% (Onress, 1968).
CONCLUSION
An analysis was performed with the temperature rise profile of the MIVAC process. The analysis provides a new tool for examining the test data in relation to the transport mechanisms. By analyzing temperature profiles at the three stages of the heating process, it leads to insights about the actual formation of the structure of the Grape Puff™ and can be used to predict results prior to the MIVAC treatment. It could also serve as a useful tool for the design of future MIVAC units.
Microwave-heated moisture may either evaporate into the vacuum or expand volumetrically to form pores or cause the berry to rupture. For grapes, this rupturing process may start near the surface and "propagate" into the interior in a fashion similar to that of peeling an onion. This rupturing and poring phenomenon explains why the Grape Puff™ is puffy. It should be noted that this dehydration process is significantly different from that of a sun-dried raisin. In the latter case, the temperature profile is monotonic and moisture is transported mainly through the diffusion process.
Specific calculations were carried out for Thompson Seedless Grape Puffs™. For the second stage sample calculations, the discrepancy between measured temperatures and the saturation temperatures led to the explanation of why the Grape Puff™ is puffy. Berry textural strength emerged as a critical factor. Sample calculations of the third stage data have shown clear correlation between the two ratios of moisture content and product weight.
Recommendations for future research are (i) to perform controlled experiments to verify trends and anomalies observed in this study; (ii) to develop theoretical values of the coupling factor of water and berry mass under moderate pressures; (iii) to design experiments to correlate product taste with textural strength; (iv) to study the microstructure in relation to the reconstitution rate; and (v) to extend such analysis to include MIVAC treatments with variable power levels.
REFERENCES
Clary, C.D. "Use of Microwave Vacuum for Dehydration of Thompson Seedless Grapes." California Agricultural Technology Institute Research Bulletin #950405. California State University, Fresno, 1995.
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Bureau of Census. October 1991. Country business patterns, 1989 - California. Economic and Statistics Administration, Department of Commerce (CBP-89-6).
Clary, C. D. "Application of Microwave Vacuum and Liquid Media Dehydration for the Production of Dried Grapes." Ph.D. Dissertation, Michigan State University. 1993.
Copson, D.A. Microwave Heating, The AVI Publishing Company Inc., 1975.
Decareau, R.V. Microwaves in the Food Processing Industry. Academic Press, Inc., 1985.
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McKinney, H.F., F.C. Wear, H.L. Sandy, V.E. Petrucci, and C.D. Clary. Process of making hollow dried grape. U.S. Patent 4,418,083. November 23, 1983.
McKinney H.F. and F.C. Wear. Zoned microwave drying apparatus and process - U.S. Patent 4,640,020. February 4, 1987.
Onress, Ernest C. Microwave Power Engineering, Vol II, Academic Press, 1968. Page 35.
Pettruci, V.E. and C.D. Clary. Microwave Vacuum Drying of Food Products. EPRI Report CU-6247. Electric Power Research Institute Inc., 4312 Hillview Ave., Palo Alto, CA 94304: EPRI. 1989.
Thuery, J. Microwaves: Industrial, Scientific, and Medical Applications. Artech House Inc. 1992
Toledo, R.T. Fundamentals of Food Process Engineering, 2nd Edition, Van Nostrand Reinhold. 1991 .
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CALIFORNIA AGRICULTURAL TECHNOLOGY INSTITUTE - CATI
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California State University, Fresno
