STATISTICAL MODELS FOR FAILURE OF APPLE TISSUE UNDER CONSTANT-STRAIN-RATE LOADING1

The normal, two-parameter Weibull, and three-parameter Weibull probability models were proposed for the strength of apple tissue drawing on previous theoretical work on fiber-reinforced composite materials. To test the models, failure stress data were determined for 800 cylindrical specimens of apple tissue subjected to low strain rate compressive loading in an Instron Universal Testing Machine. The data were fitted to the probability models and the corresponding Kolmogorov-Smirnov D-statistics were calculated and compared to tabulated critical values. The statistical tests indicated that the failure stress data fitted the three-parameter Weibull distribution, but did not fit either the normal or the two-parameter Weibull distribution.     

Hydrodynamic aspects of particle clogging in porous media

Data from 6 filtration studies, representing 43 experiments, are analyzed with a simplified version of the single-parameter O'Melia and Ali clogging model. The model parameter displays a systematic dependence on fluid velocity, which was an independent variable in each study. A cake filtration model also explains the data from one filtration study by varying a single, velocity-dependent parameter, highlighting that clogging models, because they are empirical, are not unique. Limited experimental data indicate exponential depth dependence of particle accumulation, whose impact on clogging is quantified with an extended O'Melia and Ali model. The resulting two-parameter model successfully describes the increased clogging that is always observed in the top segment of a filter. However, even after accounting for particle penetration, the two-parameter model suggests that a velocity-dependent parameter representing deposit morphology must also be included to explain the data. Most of the experimental data are described by the single-parameter O'Melia and Ali model, and the model parameter is correlated to the collector Peclet number.     

COMPACTION CHARACTERISTICS OF AGGLOMERATED COFFEE DURING TAPPING

Three brands of instant coffee were used as model agglomerated powders. They were exposed to compaction in a tap density tester. Experiments were done confining samples of instant coffee in graduated cylinders with several diameters, i.e., 1.6, 2.0 and 2.4 cm; and different product heights, i.e., 3.2, 6.3, and 12.5 cm. Increased attrition was noticed with the number of tappings, which ranged from 0 to 10,000 taps. Changes in bulk density were fitted to two-parameter models used for compaction of food powders, using nonlinear regression. New three and four-parameter models were proposed, and their fit to experimental data was also examined. The fit of these new models was better than that of previous ones, indicating that the combined effect of attrition and compaction cannot be properly described by models containing less than three parameters. The container diameter, product height, and particle size were found to affect the parameters' estimates for the models examined.     

EFFECT OF PROCESSING, PRESERVATION AND STORAGE ON RHEOLOGY OF GUAVA PULP

Rheological behavior of white and pink guava pulps was investigated using Rheotest 2 coaxial cylinder viscometer over shear rates of 0.6 to 145.8 s⁻¹. The shear rate-shear stress data followed the power law, Casson, Herschel-Bulkley, Michaels and Bolger models. The power law flow behavior index values were in the range of 0.14 to 0.19. Presence of measurable yield stress indicated Bingham model of the pulps. Storage of pulps for 30 weeks had negligible influence on flow behavior index values. The consistency index and yield stress values decreased with extending storage from 0 to 30 weeks. The Michaels and Bolger model distinctly described the non-Newtonian nature of cold- and hot-break pulps as well as different behavior of the pink guava pulps. The structure shear resistance values for hot-break pulps at zero shear rate were considerably higher than those of the cold-break, indicating their high pseudoplasticity.     

FLOW PROPERTIES OF TOMATO CONCENTRATES

The flow properties of over seventy concentrates made from four cultivars of tomatoes were determined with a concentric cylinder viscometer. The apparent viscosity (100 s⁻¹, 25°C) of the concentrates of each variety was proportional to the 2.5 power of the concentration (% total solids). The apparent viscosity of the Nova cultivar obeyed the Arrhenius temperature relationship; the activation energy for the concentrates was 2.3 ± 0.3 kcal/mole. The simple power law and the Casson model described satisfactorily the flow data of the concentrates but the power law gave higher correlation coefficients. The Herschel-Bulkley model with the Casson yield stress was also satisfactory but the correlation coefficients were lower than for the simple power law. The consistency index of the power law model also showed a power dependence on the concentration. The natural logarithm of the yield stress and the concentration could be correlated by a quadratic equation.     

RHEOLOGICAL BEHAVIOR AND TIME-DEPENDENT CHARACTERIZATION OF ICE CREAM MIX WITH DIFFERENT SALEP CONTENT

The effect of salep concentration on the rheological characteristics of ice cream mixes (0.5–1.5% salep content), prepared from nonfat cow's milk and sugar, was studied using a controlled stress rheometer. The flow curves and time‐dependent flow properties of the ice cream mixes were assessed at different temperatures. The ice cream mixes’ samples showed slightly thixotropic behavior, which was reduced as the salep content decreased. The forward and backward measurements of the flow curves of ice cream mixes were modeled with the power law model. The ice cream mixes showed pseudoplastic flow behavior after destruction of the thixotropic structure. In mixes that were first presheared at a high shear rate flow properties could also be described by the power law model. The second‐order structural kinetic, first‐order stress decay and Weltman models were applied to model the time‐dependent flow properties of the ice cream mixes. Among these, the first‐order stress decay model was found to fit well the experimental data.     

APPLICABILITY OF RHEOLOGICAL MODELS TO THE INTERPRETATION OF FLOW AND PROCESSING BEHAVIOUR OF FLUID FOOD PRODUCTS

This review is concerned with the non-Newtonian behaviour of selected fluid food products and, in particular, with the applicability of the power law. Some alternative models are included which food scientists might find useful in correlating flow properties. The interpretation of rheological characteristics in terms of structure and consistency is mentioned and the need for more detailed studies, particularly with regard to thermodynamic aspects, is pointed out. Application of the power law model to food processing is illustrated with principles of heat transfer and mixing of non-Newtonian foodstuffs.     

Roller extrusion of biscuit doughs

Biscuit doughs are dense solid–liquid pastes which exhibit complex rheological behaviour. The rolling behaviour of sheets of commercial short and hard biscuit doughs was investigated using an instrumented counter-rotating roll mill, which allowed the roll torque, separating force and surface pressure to be monitored. The rheological characteristics of the two doughs were quantified by analysing data from ram extrusion experiments in terms of a quasi-plastic model (following the Benbow–Bridgwater approach) and a power law fluid model. The results indicated that the doughs were not ideally suited to the quasi-plastic analysis. The power law parameters varied noticeably between the doughs but both were strongly shear-thinning (power law shear indices of 0.25 and 0.5), with large extensional viscosities. These rheological model parameters were subsequently used to generate predictions of dough behaviour during rolling. A standard sheet metal plasticity model was modified to include strain rate dependency but neither dough’s behaviour could be adequately described by this model. The power law fluid approach based on the lubrication assumption reported by Levine tended to underpredict the work requirement owing to the significant contribution from extensional deformation. Interestingly, the system could be modelled in terms of an apparent power law rheology by fitting data to Levine’s model. Better agreement was obtained for some parameters but not consistently so, indicating that the power law approach is not adequate for these soft-solid materials.     

RHEOLOGICAL AND TEXTURE STUDIES OF BUTTER3

Four commercial butters (conventional batch and Westfalia, Contimab and Cherry-Burrell continuous churned) were stored at two temperatures and evaluated periodically for rheological and textural properties. Evaluation methods included four mechanical tests (quasistatic shear, quasistatic uniaxial compression, Penetrometer, and extrusion) and sensory ratings of spreadability, firmness, and other texture parameters. The first three mechanical methods produced quasistatic shear yield stress values that had close agreement. For quality control the three tests can be considered equivalent. Shear stress-strain rate data from extrusion testing developed using the Rabinowitch-Mooney equation could be represented well by the Casson model. Casson yield stress values were an order of magnitude lower than the quasistatic values. The power law equation with a yield stress also represented the butter flow well, and all four butters had similar power law exponents (approx. 0.56). The Cherry-Burrell butter had much higher quasistatic and Casson model constants than the other butters. It was also the most temperature sensitive and most stable with storage time. Temperature-shear rate equivalent effects on shear stress were demonstrated by developing shift factors. The quasistatic yield values for the butters best predicted sensory spread-ability and hardness. The changes in flow properties (Casson yield stress and Casson slope) correlated with aging.     

Steady Shear Rheology and Fluid Mechanics of Four Semi-Solid Foods

The steady shear rheology of four semi-solid food materials (ketchup, mustard, apple sauce and tomato paste) was studied by generating and comparing flow data using cone and plate, parallel plate and capillary measurements over the shear rate range of 0.05–1600 see^?1. Super-position of flow data was demonstrated and correlations obtained; using the power law, Bingham Plastic, Herschel-Bulkley and Casson models were compared. In the low shear rate range (y = 0.05 – 1.0 set^?1), the Bingham Plastic model and in the high shear rate range (y = 1.0 – 1600 sec^?1), the Herschel-Bulkley model were shown to be most successful. Comparison of average velocity data with mathematical predictions using the power law, Herschel-Bulkley and Cas-son models showed that the equation using the Herschel-Bulkley model was best and should be used in the design of flow processes for the foods studied.     

A distributed reactivity model for sorption by soils and sediments. 14. Characterization and modeling of phenanthrene desorption rates

Rates and extents of phenanthrene desorption were studied for more than 250 days as functions of sorbent type, initial loading level, and aging. Apparent first-order desorption rate constants for the slowly desorbing fraction were found to (i) range from 0.00086 to 0.148 days-1 for geosorbents that contain geologically mature kerogen and less rigid humic-type soil organic matter, respectively, (ii) decrease by as much as an order of magnitude with decreasing initial sorbed solid-phase phenanthrene concentration, (iii) decrease by a factor of 2 with increasing aging time for a humic topsoil but remain unaffected by aging time beyond 3 months for a shale, and (iv) be 1-2 orders of magnitude lower than rate constants for the rapidly desorbing phenanthrene fractions for any given contaminated sample. Six models were used to fit the desorption rate data. Biphasic diffusion and biphasic first-order models with three fitting parameters possess broad utility and are potentially useful in a variety of environmental applications. Disadvantages of a five-parameter triphasic first-order desorption model, a two-parameter gamma-function model, and a one- or two-parameter pore diffusion model are also discussed.     

RHEOLOGICAL CHARACTERIZATION OF SALAD DRESSINGS 2: EFFECT OF STORAGE

The consistency index and the flow behavior index of the power law model, and yield stress according to the Casson model that describe the viscoelastic nature of a model salad dressing were determined as a function of storage time and temperature. A four parameter model was employed to describe the creep-compliance data. Major changes in the magnitudes of the rheological parameters took place during the initial seven days of storage. The changes are attributed to coalescence of oil droplets and to hydration of the food gum. Creep-compliance data on six commercial salad dressings showed significant differences in the rheological behavior among the dressings.     

MODELLING THE GELLING BEHAVIOUR OF LINSEED POLYSACCHARIDE

The gelling behaviour of linseed polysaccharide was measured in the presence of sucrose as a function of both polysaccharide and sucrose concentrations. Yield stress, consistency index, and flow behaviour index were determined using the Herschel-Bulkley model. Transition concentrations of 0.7% for the polysaccharide and 55% for sucrose were found. Yield stress and consistency index increased with both polysaccharide and sucrose concentrations while flow behaviour index decreased. A polynomial model of the third degree on centred data after natural log transformation was found to give a satisfactory fit for the variations in rheological constants. The models for both yield stress and consistency index were a complex power law, and for flow behaviour index a complex semi-log relationship, on sucrose and polysaccharide concentrations.     

Kinetic model for osmotic dehydration and its relationship with Fick's second law

A two-parameter equation was developed from mass balance considerations and used to predict the kinetics of osmotic dehydration and the final equilibrium point. The model was tested using kinetic data from ten different experiments and was able to predict water loss and solids gained over long periods of drying. The final equilibrium point was estimated using data obtained during a relatively short period of time. Simple equations were obtained when the model was related to Fick's second law for non-steady one-dimensional diffusion through a thin slab, and apparent diffusion coefficients were readily estimated from these equations.     

聚氯乙烯涂层膜材料非线性蠕变性能预测

为深入研究建筑用膜材的蠕变行为,在室温条件下对聚氯乙烯（PVC）涂层膜材的单轴拉伸蠕变性能进行了测试和分析,采用Burgers模型及其修正模型和Findley幂函数模型对蠕变实测值进行了拟合,并比较了各模型的预测精度。研究结果表明,PVC涂层膜材的蠕变具有非线性特征,且非线性程度与蠕变时间和蠕变应力有关。拟合曲线和蠕变实测值对比显示,选用的蠕变模型均具有较好的拟合优度,均可用于描述PVC涂层膜材的蠕变特性。预测曲线与实测蠕变曲线对比显示,分数阶Burger模型预测精度最高,Findley幂函数模型次之,指数Burgers模型再次之,Burger模型最差。     

Kinetic Models for Ultrasound-Assisted Extraction of Water-Soluble Components and Polysaccharides from Medicinal Fungi

The aim of this study was to evaluate the suitable kinetic models for ultrasound-assisted extraction (UAE) of water-soluble constituents and polysaccharides from medicinal fungi. The fungal materials chosen for the study included several important edible/medicinal fungi in both mushroom fruit body and mycelial form. The UAE was performed of powdered fungal material in water at a fixed power and a temperature below 50 °C. The experimental data (extract yields versus time) were fitted to several kinetic models by linear regression. The total extract yields from the two mushrooms exhibited a close fit to the power law, Weibull’s exponential, and Elovich’s logarithmic model, and that from the fungal mycelia to the parabolic diffusion model. The polysaccharide yields isolated from the mycelial extracts also fitted closely to the parabolic model, but those from the mushroom extracts did not fit well to any of the kinetic models. The results suggested that the UAE kinetics was dependent on the biological form of fungal material and the aggregation/dispersion of solid particles in the extracting solvent. Ultrasound significantly enhanced the extraction of polysaccharides from the fungi without changing their molecular weight profiles.     

RHEOLOGY OF EGG YOLK

The rheological behaviour of egg yolk over the temperature range 5° to 60°C was studied and found to fit the power law. For egg yolk of different moisture content it was found that the data gave a better fit to the power law than to an exponential equation.     

BACK EXTRUSION OF POWER LAW FLUIDS1

A mathematical model, using dimensionless terms, was developed to describe the behavior of power law fluids in a back extrusion (annular pumping) device. A graph and a table were prepared to determine rheological properties from experimental data. Expressions to calculate shear stress and shear rate at the plunger wall were obtained. The model was experimentally validated by comparing values obtained with the back extrusion device to those obtained with a concentric cylinder viscometer.     

FLOW PROFILES OF POWER LAW FLUIDS IN SCRAPED SURFACE HEAT EXCHANGER GEOMETRY USING MRI

Scraped surface heat exchangers (SSHE) are prevalent in the food industry to heat/cool viscous fluids and to provide enhanced mixing. This work focused on developing and verifying a theoretical model to characterize the flow patterns in two-dimensional angular flow in an SSHE geometry under isothermal conditions. Experimentally, the model was verified by a noninvasive magnetic resonance imaging (MRI) technique. Good agreement was achieved between the theoretical model and experimental data for a polyalkylene glycol, which behaved as a Newtonian fluid (n = 1), and a 1% CMC solution, a power law fluid with n = 0.77. However, the experimental flow profile tomato puree was characterized by apparent wall slip. The best fit, with respect to the power law model, was a flow behavior index of 0.11. This study provides the framework to quantify the effects of heat transfer on flow profiles in this geometry and the effectiveness of mixing.