RHEOLOGICAL EVALUATION OF MOZZARELLA CHEESE BY …

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RHEOLOGICAL EVALUATION OF MOZZARELLA CHEESE BY UNIAXIAL HORIZONTAL EXTENSION M.M. AK', D. BOGENRIEF2, S. GUNASEKARAN' and N.F. OLSON3 'Department of Agricultural Engineering University of Wisconsin 460 Henry Mall, Madison WI 53706 2Center for Dairy Research University of Wisconsin 1605 Linden Drive, Madison, WI 53706 3Department of Food Science University of Wisconsin 1605 Linden Drive, Babcock Hall, Madison, WI 53706 (Manuscript received May 14, 1993; in final form August 11, 1993) ABSTRACT Rheological properties of low-moisture part-skim Mozarella cheese were evaluated as a function of storage time, test temperature, and deformation rate by uniaxial extension in a horizontalplane. Proteolysis of Momrella cheese caused marked decreases in the tensile strength and the deformability modulus, but not in the fracture strain. As the temperature increasedfrom 10 to 40C, the fracture strain increased more thanjve-fold, f i e strength and the deformability modulus decreased about 40 and 85 % , respectively, as the cheese temperature increased ,from 10 to 30C. The fracture strain of the cheese did not exhibit a clear trend with the deformation rate in the range of 50-500 mm/min. However, its strength and deformability modulus increased with the increasing deformation rate. INTRODUCTION More than 70% of all Mozzarella cheese produced in the U.S. is used as an ingredient in pizza and related foods (Kindstedt 1991). Consumer acceptance of these prepared foods will surely depend on the quality of the ingredient cheese. Journal of Texture Studies 24 (1993) 437-453. All Rights Reserved. 0 Copyright 1993 by Food & Nutrition Press, Inc.. Trumbull, Connecticut 437

Transcript of RHEOLOGICAL EVALUATION OF MOZZARELLA CHEESE BY …

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RHEOLOGICAL EVALUATION OF MOZZARELLA CHEESE BY UNIAXIAL HORIZONTAL EXTENSION

M.M. AK', D. BOGENRIEF2, S. GUNASEKARAN' and N.F. OLSON3

'Department of Agricultural Engineering University of Wisconsin

460 Henry Mall, Madison WI 53706

2Center for Dairy Research University of Wisconsin

1605 Linden Drive, Madison, WI 53706

3Department of Food Science University of Wisconsin

1605 Linden Drive, Babcock Hall, Madison, WI 53706

(Manuscript received May 14, 1993; in final form August 11, 1993)

ABSTRACT

Rheological properties of low-moisture part-skim Mozarella cheese were evaluated as a function of storage time, test temperature, and deformation rate by uniaxial extension in a horizontal plane. Proteolysis of Momrella cheese caused marked decreases in the tensile strength and the deformability modulus, but not in the fracture strain. As the temperature increasedfrom 10 to 40C, the fracture strain increased more than jve-fold, f i e strength and the deformability modulus decreased about 40 and 85 % , respectively, as the cheese temperature increased ,from 10 to 30C. The fracture strain of the cheese did not exhibit a clear trend with the deformation rate in the range of 50-500 mm/min. However, its strength and deformability modulus increased with the increasing deformation rate.

INTRODUCTION

More than 70% of all Mozzarella cheese produced in the U.S. is used as an ingredient in pizza and related foods (Kindstedt 1991). Consumer acceptance of these prepared foods will surely depend on the quality of the ingredient cheese.

Journal of Texture Studies 24 (1993) 437-453. All Rights Reserved. 0 Copyright 1993 by Food & Nutrition Press, Inc.. Trumbull, Connecticut 437

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438 M.M. AK, D. BOGENRIEF, S. GUNASEKARAN and N.F . OLSON

The use of Mozzarella for pizza or other applications is primarily determined by its rheological properties in both unmelted and melted states (Pilcher and Kind- stedt 1990; Kindstedt 1993).

Rheological and fracture properties of many types of cheese change significantly during ripening mostly because of protein hydrolysis (de Jong 1978; Creamer and Olson 1982; pertola et al. 1992). The extent of proteolysis in Mozzarella is lower than in Cheddar or Gouda cheeses (Creamer 1976), but a 20 to 40% decrease in asl-casein and 6-casein during 2 to 4 weeks of refrigerated storage has been shown to cause substantial changes in functional properties (Farkye et al. 1991; Kindstedt et al. 1988). Moreover, Tunick et al. (1991) reported that after 6 weeks of storage at 4C, the low-fat (9.5%), high-moisture (57.4%) cheese had textural properties similar to those of fresh high-fat (25.1 %), low-moisture (47.3 %) Mozzarella.

Temperature and deformation rate strongly affect the rheological and fracture properties of cheeses (Culioli and Sherman 1976; Dickinson and Goulding 1980; Luyten er al. 1991a,b; Ak and Gunasekaran 1992; Rohm and Lederer 1992). The temperature effect results from melting of fat globules and softening of pro- tein matrix. The rate effect is a result of the viscoelastic character of cheese. There is general agreement that the fracture stress of various cheeses increases with increasing deformation rate. However, the rate effect on the fracture strain seems to vary with the type of cheese.

Rheological measurements on Mozzarella have been performed in compres- sion and bending modes (Cervantes et al. 1983; Casiraghi et al. 1985; Masi and Addeo 1986). In studies where a tensile test was used with foods, the sample was held usually in a vertical position (Schoorl and Holt 1983; Luyten 1988; Lelievre er al. 1992) and rarely in a horizontal position (Halton and Scott Blair 1937; Gillett er al. 1978). The problem of deformation of the specimen under gravity, which might occur in both configurations, was generally overcome by surrounding the sample by a density matching medium which also served to main- tain temperature uniformity and to prevent food samples from drying out (Halton and Scott Blair 1937; Tschoegl et al. 1970; Vinogradov et al. 1972).

The main experimental difficulty in tensile tests is to ensure that the specimen does not break at the clamps. This problem has been overcome by adopting ap- proaches used in testing engineering materials, with some modifications, for testing cheese (Luyten 1988) and gellan gels (Lelievre et al. 1992). Recently, Luyten et al. (1992) discussed the merits of tensile experiments for studying the behavior of food materials at large deformations and compared the results with compres- sion and bending methods.

Our objective in this study was to determine tensile properties of Mozzarella cheese as a function of storage time, temperature, and deformation rate. Temperatures involved in food ingredient applications are normally higher than

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the range that could be covered with the experimental set-up used in this study. However, a new apparatus was fabricated which will allow us to study stretching characteristics of Mozzarella cheese under conditions comparable to baking.

EXPERIMENTAL

Description of the Uniaxial Extension Apparatus

A schematic of the uniaxial extension apparatus used is shown in Fig. 1. It consists of a testing machine (Instron Model 1 130, Instron Corp., Canton, MA) with a 2-kg compression load cell, a double-walled sample chamber, and a per- sonal computer. The interior height, width, and length of the chamber are 7.5, 10, and 90 cm, respectively. The sample chamber was filled with mineral oil to maintain temperature uniformity and to prevent moisture loss from samples during testing. Temperature of the oil bath was controlled by circulating water through the hollow wall of the chamber. The stationary clamp was attached to the chamber and the moving clamp was connected to the Instron crosshead via a pulley system. Cheese specimens were stretched as the crosshead moved downwards at a constant speed. The testing machine was interfaced with the com- puter through a data system adaptor. Instron Series IX software was used for data acquisition, machine control, and analysis.

li, load cell

walerin fixedclamp

FIG. 1. COMPONENTS OF UNIAXIAL HORIZONTAL EXTENSION APPARATUS

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Materials

Fresh rectangular blocks of brine-salted low-moisture, part-skim (LMPS) Moz- zarella cheese ( - 2.7 kg each) were obtained from a commercial cheese plant. Cheese blocks were stored in their original packaging in a refrigerator (6-8C) until sample preparation (i.e., one day before testing). Average composition of the cheese was 46.5 f 0.6% moisture, 23.5 f 0.6% fat, 1.6 f 0.4% salt, with a pH of 5.23 f 0.09.

A cheese block was cut into thin slices ( -6 mm) parallel to the long axis of the block using a hand-operated slicer. The surface slice from each side of the block was discarded. Then, dumbbell-shaped samples were cut from the slices with a sharp-edged stainless steel template. Finally, another template (“trimmer”) was used to make the central part of the specimen thinner. Specimens were in- dividually wrapped in Saran film and stored overnight in the refrigerator. A typical specimen ready for stretching is shown in Fig. 2 (see below for details in pic- ture). An incubator (VWR Model 2005, VWR Scientific, Chicago, IL) was used to precondition the specimens to the desired test temperatures. Care was exercised to avoid pretest stressing and deformation of specimens. A plexiglass carrier was used to transfer the gripped specimen to the clamps in the chamber. When a

FIG. 2. A TYPICAL CHEESE SPECIMEN IN THE SAMPLE CHAMBER Specimen dimensions (mm): Length = 60, Width = 8. and Thickness = 6.

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specimen failed at the grips, the data were discarded. Tests were carried out at temperatures 10,20,30, and 4OC, and crosshead speeds 50,200, and 500 d m i n on days 7, 14, 21, and 28 after the production date.

Electrophoretic Analysis

Urea-polyacrylamide gel electrophoresis was performed on the cheese with an SE 600 Vertical Slab Gel Unit (Hocfcr Scientific, San Francisco, CA) using the modified method of Andrews (1983) as described by Shalabi and Fox (1987). The staining solution was prepared by the method of Blakesley and Boezi (1977). Cheese sample (10 mg) was dissolved in 1 ml sample buffer (1.5 g Tris + 96 g urea + 0.8 ml concentrated HCl + 1.4 ml beta-mercaptoethanol + 1 ml bromophenol made up to 200 ml with distilled water) and 10 pl of this solution were applied in the wells. The quantitative analysis of the casein bands in the gel was accomplished using the FotolAndyst computer imaging system (Fotodyne, Inc., New Berlin, WI). The Foto/Analyst uses a video camera to acquire an im- age, a Macintosh I1 computer to process the information, and Collage software (Fotodyne, Inc.) to analyze the image. The intensities of individual casein bands were expressed as a percentage of their values at day 2.

Data Analysis

The force-deformation data from simple extension tests were transformed into Hencky strain, 4 t ) , and true stress, a(t), values using the following equations (Peleg 1984):

where L, To, and W, are the initial specimen length, thickness, and width, respec- tively. AL(t), F(t), and A(t) are the momentary deformation, force, and cross- sectional area, respectively. It was assumed that the cheese was incompressible. Stress at fracture (tensile strength) was calculated as the maximum force divided by the actual cross-sectional area. Strain at fracture was the value of Hencky strain corresponding to the stress at fracture. A correction to account for the slack in the cord at the start of stretching was applied to the strain values. The defor- mability modulus was calculated from the slope of the initial part of stress-strain curves.

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The deformation of a specimen was computed from the crosshead speed and the time elapsed, and the resulting value was used in Eq. 1 and 2. For some samples, deformation was also measured from the photographs taken of the specimen during stretching. In this second method, lines with 10 mm distance were drawn on the specimen by a marker pen. A piece of chart paper with 2 mm divisions, a stop-watch, and a label were placed on the test chamber (Fig. 2). The specimen was photographed at various times during the test. Then the amount of elongation was measured from enlarged photocopies of the photographs. The deformation values of the first method differed, on average, about 8% from those obtained from the second method. It was also evident from these photographs that the deformation outside the thin section of the specimen was negligible (i.e., less than 5 % of total deformation).

The force required to overcome friction in the apparatus and the drag force exerted by the oil on the moving clamp were experimentally found to be negligible.

Statistical Analysis

Three to four specimens were used at each testing condition. A multifactor analysis of variance was performed for each of the material properties against the independent variables (age of cheese, test temperature, and deformation rate) by using the Statgraphics software (STSC, Inc., Rockville, MD). Diagnostic checks on residual plots indicated that the standard deviation increased as the mean value increased. A logarithmic transformation of data was used to properly apply the statistical procedure (Box et al. 1978).

RESULTS AND DISCUSSION

Figure 3 illustrates an example of the stress-strain behavior of Mozzarella cheese in uniaxial horizontal extension. The graph contains data points from three replicate runs. It shows that the results were fairly reproducible. The average coefficients of variation were 22, 24, and 30% for fracture strain, deformability modulus, and fracture stress, respectively. Variations of similar magnitudes were also found for Mozzarella (Masi and Addeo 1986), Provolone (Pompei er al. 1987), Brie (Molander et al. 1990), Cheddar (Ak and Gunasekaran 1992), and Emmentaler (Rohm and Lederer 1992) cheeses tested by uniaxial compression.

The mean values of the tensile properties of Mozzarella are plotted against the age of cheese in Fig. 4. The fracture strain tended first to increase and then to decrease with the age of cheese, but the latter trend was not statistically signifi- cant (p > 0 .05). The fracture stress of the cheese initially remained unchanged and then decreased nearly 40% during the last two weeks of storage (p < 0.05). Deformability modulus decreased significantly with the age of cheese.

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I ""

90

80

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60

50

40

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0

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0 0.1 0.2 0.3 0.4 0.5

Hencky strain

5

FIG. 3. AN EXAMPLE OF THE STRESS-STRAIN RELATIONSHIP OF MOZZARELLA CHEESE IN UNIAXIAL TENSION (IOC, 50 mm/min)

Brine-salting of Mozzarella or other cheese varieties causes a variation of salt- in-moisture (S/M) level within a cheese block (Guinee and Fox 1983; Kindstedt 1990). Such variations have been shown to affect rheological properties of Camembert (Mpagana and Hardy 1986) and Gouda (Luyten 1988) cheeses measured by uniaxial compression. Part of the changes in the properties of Moz- zarella during the first two weeks of aging may also be attributed to variations in S/M since the proteolysis was minimal during this period (Fig. 5). Luyten (1988) observed an increase in strain at fracture as the S/M of Gouda cheese was in- creased from 0.5 to 5%. A dramatic decrease in strain at fracture occurred at S/M of 5 to 6%. She ascribed the increase at lower S/M to unfolding and swell- ing of the cheese protein mass and the drastic decrease to the salting-out of the proteins. At 7 days, the NaCl concentration (S/M) in the outer portion of the cheese in this study would approximate 5 to 6%. Diffusion of the salt during the next 7 days would lower the concentration near the edge of the cheese and would increase the level closer to 4% S/M in the cheese interior. Both effects would tend to increase the average strain at fracture. The pH of Mozzarella cheese tends to increase 0.1 to 0.2 units after manufacturing which would also increase strain at fracture (Luyten 1988).

Fusion of the curd strands, formed during mixing and molding of Mozzarella cheese during manufacturing, over the first 14 days could enhance the cohesiveness and consequently the strain at fracture. Luyten (1988) reported fusion of curd grains in Gouda cheese during the first week of aging. This coincided with in- creased deformability and viscous-like behavior of the cheese.

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FIG. 4 . MEANS AND 95% CONFIDENCE INTERVALS OF FRACTURE STRAIN, FRACTURE STRESS, AND DEFORMABLITY MODULUS OF MOZZARELLA CHEESE AT DIFFERENT AGING

Changes in the properties of Mozzarella cheese during the last two weeks of refrigerated storage was primarily because of proteolysis. The extent of hydrolysis of caseins in the cheese is shown in Fig. 5 . The total decreases in the intensity of the aSl- and @-casein bands were about 70 and 50%, respectively. The

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FIG. 5 . PROTEOLYSIS IN MOZZARELLA CHEESE DURING ONE MONTH OF REFRIGERATED STORAGE AS MEASURED BY INTENSITY OF

CASEIN BANDS AFTER ELECTROPHORESIS

hydrolysis of these caseins weakens the protein network and likely results in decreases in the values of fracture stress and deformability modulus. However, the fracture strain of Mozzarella was not affected significantly by the hydrolysis of caseins (Fig. 4).

Both aSl- and /3-caseins presumably take part in the formation of protein net- work (Creamer and Olson 1982), and consequently affect the cheese properties when degraded. The effects of casein hydrolysis may be explained by the limited number of peptide bonds cleaved during initial proteolysis. This minimal change in structure could affect the force necessary to deform the cheese structure but not the ability of the protein structure to deform before fracture. Luyten (1988) concluded that the initial proteolysis of crsl-casein was not sufficient to reduce the fracture strain but might be a reason for the increased viscous-like behavior of Gouda cheese during the first few days of aging. Further research looking into the relative effects of individual caseins on the rheological properties can contribute greatly to our understanding of structure-property relation. Moreover, the rate of hydrolysis of specific proteins in Mozzarella cheese during short-term aging has been shown to depend on the type of coagulant (Kindstedt ef al. 1991). Since Mozzarella is used as an ingredient in processed foods, it is essential to ensure the desired rheological behavior. A better understanding of the coagulant effect on the objectively measurable parameters can point out some ways of ob- taining the target rheological properties.

The effect of temperature on the selected tensile parameters of Mozzarella cheese

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5 10 15 20 25 30 35

Temperature ("C)

FIG. 6. MEANS AND 95% CONFIDENCE INTERVALS OF FRACTURE STRAIN, FRACTURE STRESS, AND DEFORMABILITY MODULUS

OF MOZZARELLA CHEESE AT DIFFERENT TEMPERATURES

is shown in Fig. 6. Specimens tested at 40C and at 50 and 200 mm/min deforma- tion rates did not break throughout the length of the sample chamber (90 cm). This corresponded to nearly 650% extension of the original specimen. At the

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120

100

80

60

Deformation rate (mm/min)

FIG. 7 . MEANS AND 95% CONFIDENCE INTERVALS OF FRACTURE STRAIN, FRACTURE STRESS, A N D DEFORMABILITY MODULUS

OF MOZZARELLA CHEESE AT DIFFERENT DEFORMATION RATES

highest deformation rate (500 mm/min) and 40C, most of the samples failed at about 200% extension.

In the first region from 1OC to 30C, as shown in Fig. 6, there was about 100% increase in the fracture strain. However, in the second region from 30C to 40C

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the increase was more pronounced, nearly 200%. The greatest decreases in values of tensile strength (60%) and deformability modulus (85%) occurred in the first region (Fig. 6). Because of extensive shape distortion and some sagging, accurate strength and modulus calculations were not possible for results at 40C, and therefore not reported. Nevertheless, specimens were stretched just to observe if they would ever break within the length of the apparatus.

It has been noticed that, despite their textural differences, other cheese varieties also exhibited essentially the same kind of temperature dependency (Dickinson and Goulding 1980; Luyten 1988). The temperature effect, in the region 14 to 26C, on the strength and modulus of cheese was generally associated with the change in rigidity of fat particles (Visser 1991). This could also be true for the properties of Mozzarella cheese in the first region. However, in the second region where all the fat would be liquid, the changes in the properties of the cheese should result presumably from the effect of temperature on the protein network. Understanding this strong temperature effect, particularly on the fracture strain, can be important in relation to the stretching properties of Mozzarella.

Tests were performed at three deformation rates to establish its influence on the properties of Mozzarella. The trend observed for fracture strain was not clear within the range considered in this study (Fig. 7). Data from literature indicated that the dependency of fracture strain on the deformation rate was markedly dif- ferent for several cheese varieties (Table 1).

Since the energy storing and dissipating mechanisms of a viscoelastic material depend on its relaxation times, the time scale of deformation affects the material properties (Ferry 1980). Deformation of cheese at a slower rate allows more time for dissipating mechanisms to occur and, therefore, requires lower stresses to attain a given strain (van Vliet and Peleg 1991). The behavior of Mozzarella cheese was consistent with this explanation (Fig. 7). Deformability modulus followed a trend similar to that of fracture stress and, consequently, the cheese appeared stiffer when stretched at higher rates.

CONCLUSIONS

Tensile strength and deformability modolus of Mozzarella cheese decreased during one month of refrigerated storage. Hydrolysis of both aa1- and 0-caseins were probably responsible for the changes in these properties of the cheese. Frac- ture strain of the cheese first increased and then remained constant after 14 days of storage.

The fracture strain of Mozzarella was a strong function of temperature, par- ticularly in the region from 30 to 40C where samples often did not break even at 650% extension. Changes in the protein structure was probably the reason for

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such high extensions. Both deformability modulus and strength of the cheese decreased as the temperature increased.

The influence of deformation rate on the fracture strain was not consistent with previously observed trends which varied with the type of cheese. However, both strength and deformability modulus increased at higher stretching rates as ex- pected from the viscoelastic nature of the cheese.

ACKNOWLEDGMENT

The authors wish to thank Bill Tricomi for his help with the electrophoresis experiments and Dr. Robert Bremel of the Department of Dairy Science for making available the image analysis system for our use. We gratefully acknowledge finan- cial support from the National Dairy Promotion and Research Board, and the Center for Dairy Research of the University of Wisconsin.

REFERENCES

AK, M.M. and GUNASEKARAN, S. 1992. Stress-strain curve analysis of Ched- dar cheese under uniaxial compression. J. Food Sci. 57, 1078-1081.

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BERTOLA, N.C., BEVILACQUA, A.E. and ZARITZKY, N.E. 1992. Pro- teolytic and rheological evaluation of maturation of Tybo Argentino cheese. J. Dairy Sci. 75, 3273-3281.

BLAKESLEY, R.W. and BOEZI, J.A. 1977. A new staining technique for pro- teins in polyacrylamide gels using Coomassie brilliant blue G250. Anal. Biochem. 82, 580-582.

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CASIRAGHI, E.M., BAGLEY, E.B. and CHRISTIANSON, D.D. 1985. Behavior of Mozzarella, Cheddar and processed cheese spread in lubricated and bonded uniaxial compression. J. Texture Studies 16, 281-301.

CERVANTES, M.A., LUND, D.B. and OLSON, N.F. 1983. Effects of salt con- centration and freezing on Mozzarella cheese texture. J. Dairy Sci. 66,

CREAMER, L.K. 1976. Casein proteolysis in Mozzarella-type cheese. N. Z. 204-213.

J. Dairy Sci. Technol. 11, 130-131.

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CREAMER, L.K. and OLSON, N.F. 1982. Rheological evaluation of maturing Cheddar cheese. J . Food Sci. 47, 631-636, 646.

CULIOLI, J . and SHERMAN, P. 1976. Evaluation of Gouda cheese firmness by compression tests. J. Texture Studies 7, 353-372.

de JONG, L. 1978. The influence of the moisture content on the consistency and protein breakdown of cheese. Neth. Milk Dairy J. 32, 1-14.

DICKINSON, E. and GOULDING, I.C. 1980. Yield behaviour of crumbly English cheeses in compression. J. Texture Studies 11, 51-63.

FARKYE, N.Y., KIELY, L.J., ALLSHOUSE, R.D. and KINDSTEDT, P.S. 199 1. Proteolysis in Mozzarella cheese during refrigerated storage. J. Dairy Sci. 74, 1433-1438.

FERRY, J.D. 1980. Viscoelastic Properties of Polymers, 3rd Ed., John Wiley & Sons, New York.

GILLET, T.A., BROWN, C.L., LEUTZINGER, R.L., CASSIDY, R.D. and SIMON, S. 1978. Tensile strength of processed meats determined by an ob- jective Instron technique. J . Food Sci. 43, 1121-1 124, 1129.

GUINEE. T.P. and FOX, P.F. 1983. Sodium chloride and moisture changes in Romano-type cheese during salting. J . Dairy Res. 50. 51 1-518. perties of flour doughs in relation to their bread-making qualities. Cereal Chem.

KINDSTEDT, P.S. 1990. Physic0 chemical aspects of Mozzarella cheese. Proc. 2nd Cheese Symposium. National Dairy Products Research Centre, Moorepark, Fermoy, 95-106.

KINDSTEDT, P.S. 1991. Functional properties of Mozzarella cheese on pizza: A review. Cult. Dairy Prod. J. 26, 27-31.

KINDSTEDT, P.S. 1993. Effect of manufacturing factors, composition, and pro- teolysis on the functional characteristics of Mozzarella cheese. Crit. Rev. Food Sci. Nutr. 33, 167-187.

KINDSTEDT, P.S., DUTHIE, C.M. and RIPPE, J.K. 1988. Rheological and proteolytic changes in Mozzarella cheese during refrigerated storage. J. Dairy Sci. 71 (Suppl. I ) , 70.

KINDSTEDT, P.S., KIELY, L.J., YUN, J.J. and BARBANO, D.M. 1991. Rela- tionship between Mozzarella manufacturing parameters, cheese composition, and functional properties: Impact of coagulant. Proc. 28th Annu. Marschall Invit. Ital. Cheese Sem., Madison, WI, 89-109.

LELIEVRE, J., MIRZA, I.A. and TUNG, M.A. 1992. Failure testing of gellan gels. J . Food Eng. 16, 25-37.

LUYTEN, H. 1988. The rheological and fracture properties of Gouda cheese. Ph. D. Dissertation, Agricultural University, Wageningen, The Netherlands.

LUYTEN, H. , van VLIET, T. and WALSTRA, P. 1991a. Characterization of

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