jfsv64n6ms19990215 Vol 66, No 1, 2001—JOURNAL OF FOOD SCIENCE 137© 2001 Institute of Food Technologists Fo od En gin ee rin g a nd Ph ys ica l P ro pe rti es JFS Food Engineering and Physical Properti[.]
JFS: Food Engineering and Physical Properties Centrifugal Slump Test to Measure Yield Stress A.P OMURA AND J.F STEFFE ABSTRACT: The performance of a centrifugal viscometer (a new concept) was tested for its ability to accurately predict the yield stresses of semisolid foodstuffs This instrument is based on the traditional slump test concept, but utilizes centrifugal force rather than gravitational force to cause deformation Using dimensional analysis, there was a general agreement between the theoretical approximation of the yield stress, and experimental data generated using the vane method Key Words: rheology, yield stress, spreads, slump test, vane method T in food rheology because it has many important applications It is incorporated into the design of food processes, sensory assessment and engineering modeling (Rao 1997) It is also directly related to the spreadability of fluid foods (Daubert 1998), which is a fundamental quality parameter of the materials selected for this study Yield stress can be tested using numerous techniques such as the stress relaxation, vane method, uniaxial compression and flow through a capillary tube (Steffe 1992) The centrifugal viscometer uses a different approach to find the yield stress The concept is an extension of the slump test, which is traditionally applied to measure the “workability” of thick suspensions It is the most widely employed test for fresh concrete (Bartos 1992), and there is a standard method (ASTM 1990) to test for slump using a frustrum of a cone Slump, based on a circular cylindrical geometry, was investigated by Chandler (1986) The slump height was first related to the yield stress by Murata (1984) Later, that work was corrected by Christensen (1991) for an error in the mathematical analysis These concepts led to the study by Pashias and others (1996) that formed the basis for the current effort The vane method was selected as the basis for comparison because it has been established as a quick, simple, and reliable method of measuring the yield stress of food Accuracy of the vane method has been confirmed by studies involving direct comparisons to more traditional methods (Nguyen and Boger 1992; Yoshimura and others 1987) The utility of the vane method for food has been demonstrated for a wide range of © 2001 Institute of Food Technologists products: ice cream (Briggs and Steffe 1996), various food dispersions such as tomato products and baby food ( Yoo and others 1995), as well as peanut butter and margarine (Daubert and others 1995) The objective of this study was to determine if the centrifugal viscometer would generate yield stress values comparable to those found using the vane method cream cheese and peanut butter The centrifugal viscometer applies the needed force by using centrifugal acceleration generated from angular rotation The equations given here extended the work of Pashias and others (1996) by Food Engineering and Physical Properties Introduction HE YIELD STRESS CONCEPT IS USEFUL Theoretical Background Centrifugal Viscometer Testing used in this study is based on the principles set forth by Pashias and others (1996) for a gravitational slump test Their theoretical model is derived from a relationship between the pressure distribution and the stress distribution in a vertical cylinder composed of an incompressible material The model assumes that all the horizontal planes remain horizontal, that is, the interface layer between yielded and unyielded material remains flat In this development, the amount a cylindrical sample height is reduced from the original height is referred to as the slump height, z (Figure 1) Dimensionless slump height (z/H) is related to the yield stress by the following equation: (1) where: z = slump height (m) H = original height of the sample (m) so= yield stress (Pa) r = density of the sample (kg/m 3) g = gravitational acceleration (m/s2) Gravitational force alone will not cause deformation in solid materials that have high yield stresses, such as Figure 1—Sample before (a) and after (b) slump test Vol 66, No 1, 2001—JOURNAL OF FOOD SCIENCE 137 Centrufugal Slump Test replacing gravitational acceleration (g) with centrifugal acceleration (a) Using this concept, Eq (1) becomes (2) with acceleration defined as (3) where: a = centrifugal acceleration (m/s2) R = radial distance from axis of rota tion (m) N = rotational speed (rpm) For simplicity, a dimensionless yield stress may be defined as (4) Food Engineering and Physical Properties Using this definition, Eq (2) becomes (5) The ln(2s90 ) term may be expressed as an infinite series, for # s90 , 1, as, d = vane dia, (m) M0 = maximum torque (N m) L = length of vane (m) Materials and Methods Centrifugal Viscometer A bowl-shaped device was the main component of the testing apparatus (Figure 2) Four plastic base plates attached to the inner sides of the sample holder (Figure 3) were placed 90 degrees apart A mm wide pin was fastened perpendicular to the wall in the center of each of the plates Cylindrical samples were impaled on the pins The value of R, required in Eq (3), was defined as the distance from the axis of rotation to the base plate of the sample holder R was equal to 10 cm for all experiments An alternative definition of R would have been to make it the distance from the center of the bowl to the center of gravity of the sample This definition is impractical because the sample center of gravity continuously changes during the testing The bowl was attached to a mixer head by a rotating shaft located perpendicular to the bottom, in the center of the bowl A mixer head (Servodyne Model 50000-20, Cole-Parmer Instrument Co Vernon Hills, Ill., U.S.A.) and controller box (Servodyne Model 50000-00, Cole-Parmer Instrument Co.) provided rotational speed control Sample Preparation for Testing in the Centrifugal Viscometer The materials tested—Spartan Neufchatel Cheese, Philadelphia Regular Cream Cheese, Jif Creamy Peanut Butter, and Land O’ Lakes Margarine—were purchased at a local grocery store Cylindrical samples, approximately 1.8 cm tall with a dia of 1.8 cm, were obtained from a large product volume with a plastic bore and a spatula An attempt was made to maintain an aspect ratio (defined as the sample height divided by the dia) of 1.0 when cutting samples A larger aspect ratio resulted in the collapse of the samples during testing, and smaller ratios exhibited too little slump for good measurements A plunger was used to gently push the sample onto the pin (Figure 3) from the bore For sticky materials, such as the cream cheese and peanut butter, vegetable oil was applied to the end of the plunger to ease sample separation from the bore This procedure did not influence slump because it only left a thin coating of oil on the upper surface of the sample The density of each material was determined as an average of weights per unit volume measurements All testing Using just the first two terms of the above series, a simplified form of Eq (5) may be written as (6) Eqs (5) and (6) were used to examine the data generated in this study Vane Method Typically, this method employs a 4-bladed vane that is inserted into a sample and rotated at a low speed Torque is measured over time and the maximum torque (peak on the torque curve) is used to evaluate the yield stress If the vane is immersed in the sample so the upper edge is even with the material, the yield stress is calculated as (Steffe 1996) (7) where: h = height of the vane (m) Figure 2—Centrifugal viscometer showing rotational drive unit (a) and sample holder (b) 138 JOURNAL OF FOOD SCIENCE—Vol 66, No 1, 2001 Figure 3—Top and side view of sample holder showing sample loaded for testing was done at a temperature of 22 °C ± °C Measuring Yield Stress with a Vane Data were acquired using a Haake VT550 Viscometer (Haake, Paramus, N.J., U.S.A.) with a 4-blade vane (20.0 mm length × 10.1 mm dia) The vane was gently lowered into the sample until just the top of the vane was even with the surface of the material Sample volumes were not deformed in anyway prior to measurement The vane was rotated at a constant rate of 0.5 rpm for 30 sec Torque was measured over time, and the peak value was used to calculate yield stress with Eq (7) An average of at least vane measurements were taken to determine a representative yield stress for each sample tested in the centrifugal viscometer Testing in the Centrifugal Viscometer Samples were impaled on the pins of the sample holder as described above A caliper was used to measure all distances (± 0.02 mm) needed for calculations Two measurements of each dimension, length and diameter, were taken and averaged Each test was run for 30 sec and it took approximately sec to reach the maximum test speed At the completion of rotation, final heights were taken while the sample was still fixed on the pin H was found by subtracting the bowl thickness from the original height, and z was found by subtracting the initial height from the final height (Figure 1) Signs of sample slumping or tilting were noted Following the recommendation of Bartos (1992), completely collapsed samples were discarded Complete collapse occasionally occurred at high rotational speeds The Solver function in Microsoft® Excel was Results and Discussion gal acceleration is a unique function of the yield stress This result is consistent with the findings of Pashias and others (1996) for slump tests driven by gravitational acceleration alone When comparing the different food materials, some data sets were closer to the prediction equation (Figure 4) than others The Neufchatel and the margarine were the closest to the approximation line Cream cheese produced data above and parallel to the approximation line rather than converging at the ends Results for peanut butter showed the data that diverged from the model as the slump height increased Pashias and others (1996) suggested that various simplifying assumptions used in developing the theoretical model (Eq 5) might explain why the model failed to predict experimental behavior The proposed relationship between pressure and stress distribution may be invalid, and the assumption that horizontal planes remain horizontal during deformation is questionable Future work should include an examination of other spreadable food products Yield stresses measured with the vane ranged from approximately 1000 to 1600 Pa Overall, the general pattern of observed behavior followed the theoretical model for slump (Figure 4) The exact solution (Eq 5) underestimated the yield stress in all but cases; however, the approximation described by Eq (6) provided a good prediction of the dimensionless yield stress from slump height for cream cheese (Figure 4) Predictions were best over a dimensionless slump height ranging from 0.2 to 0.5 Results clearly show that slump height generated as a result of centrifu- The centrifugal viscometer can successfully predict yield stresses of fluid foods that are comparable to those measured using the vane method for the food spreads considered in this study: cream cheese, Neufchatel cheese, peanut butter, and margarine Slump in material induced from centrifugal acceleration is a unique function of the yield stress The centrifugal viscometer shows promise as a reliable, low-cost indicator of yield stress used to calculate the theoretical yield stresses using the above equations and the experimental data Fourteen tests of the cream cheese and peanut butter, and seventeen of the Neufchatel cheese and margarine were analyzed The number of tests depended on the amount of available material in each product package The Neufchatel was successfully tested at speeds from 400 to 650 rpm, the margarine and peanut butter were run at 450 to 700 rpm and the cream cheese trials ranged from 450 to 650 rpm Speeds ranging from 400 to 700 rpm generated centrifugal accelerations of 175.4 to 616.8 m/s or 17.9 to 54.8 G’s, respectively Dimensionless stresses (calculated using Eq (4)) were plotted against the dimensionless slump heights (z/H) for each material Those points were compared to the theoretical model and the model approximation, Eqs (2) and (6) respectively Conclusion References Figure 4—Theoretical and experiential results ASTM 1990 C143-90, Standard test method for slump of hydraulic cement concrete Philadelphia, PA American Society for Testing and Materials Bartos PJM 1992 Fresh Concrete: Properties and Tests Elsevier Amsterdam Briggs JL, Steffe JF 1996 Vane method to evaluate the yield stress of frozen ice cream J Dairy Sci 79: 527531 Chandler JL 1986 The stacking and solar drying process for disposal of bauxite tailings in Jamaica Proceedings of the International Conference on Bauxite Tailings, Kingston, Jamaica p 101-105 Christensen G 1991 Modeling the flow of fresh concrete: the slump test Ph D Thesis, Princeton, NJ: Princeton Univ Daubert CR, Tkachuk JA, Truong VD 1998 Quantitative measurement of food spreadability using the vane method J Texture Stud 29(4): 427-435 Murata J 1991 Flow and deformation of fresh concrete Mater Constr 17: 117-129 Nguyen QD, Boger DV 1985 Direct measurement with the vane method J Rheol 29(3): 335-347 Nguyen QD, Boger DV 1992 Measuring the flow properties of yield stress fluids Annual Review of Fluid Mechanics 24: 47-88 Pashias N, Boger DV, Summers J, Glenister DJ 1996 Vol 66, No 1, 2001—JOURNAL OF FOOD SCIENCE 139 Food Engineering and Physical Properties Centrufugal Slump Test Properties of Herring Protein Hydrolysate A fifty cent rheometer for yield stress measurement J Rheol 40(6): 1179-1189 Rao MA 1997 Rheological properties of fluid foods: recent developments In: Pedro Fito, Enrique Ortega-Rodrizguez, Gustavo V Barbosa-Canovas, editors Food Engineering 2000 New York, NY: Chapman and Hall p 55-63 Steffe JF 1992 Yield Stress: Phenomena and Measurement In: R Paul Singh, MA Wirakartakusumah, editors Advances in Food Engineering Boca Raton, FL: CRC Press p 363-376 Steffe JF 1996 Rheological Methods in Food Process Engineering, nd ed East Lansing, MI: Freeman Press Yoo B, Rao MA, Steffe JF 1995 Yield stresses of food dispersions with the vane method at controlled shear rate and shear stress J Texture Stud 26: 1-10 Yoshimura AS, Prud’homme RK, Princen HM, Kiss AD 1987 A comparison of techniques for measuring yield stresses J Rheol 31(8): 699-710 MS 20000342 Food Engineering and Physical Properties 140 JOURNAL OF FOOD SCIENCE—Vol 66, No 1, 2001 The authors thank Mr Richard Wolthuis for his assistance in constructing the centrifugal viscometer, and the Michigan Agricultural Experiment Station for financial support Authors Omura and Steffe are with the Dept of Agricultural Engineering, and author Steffe is with the Dept of Food Science and Human Nutrition, Michigan State Univ Direct inquiries to author Steffe, 209 Farrall Hall, Michigan State Univ., East Lansing, MI 48824-1323 (E-mail: steffe@ msu.edu)