Rheological models modified

II. The modified Bingham body - a useful rheological model. J. Text. Stud. 3, 194-205. Enjalbert, F., M. C., Nicot, C., Bayourthe, M., Vernay, Moncoulon, R. 1997. Effects of dietary calcium soaps of unsaturated fatty acids on digestion, milk composition, and physical properties of butter. J. Dairy Res. 64, 181-195. 

Doraiswamy et al. (1991) developed a non-linear rheological model combining elastic, viscous and yielding phenomena for filled polymers. The model predicts a modified Cox Merz relationship for filled melts ... 

In principle there are two possibilities to get the informations over the material parameters. First we have a theoretic model modified from the model over high filled polymere melts. This model allows to meassure and evaluate the rheological parameters. On the other hand we have a rheological computer model called ESM (extruder simulation model), developed by the author, which brings us in the position to simulate the material parameters. 

Note that many bioreactor CFD simulations assume that the biological content has a neghgible effect on the bioreactor hydrodynamics or, if there is an effect, only the fluid rheology is modified. Hence, many of the available bioreactor CFD studies focus on gas-liquid modeling (Roy et al., 2006). A few gas-liquid-solid CFD studies have been completed (Hamidipour et al., 2012 Jia et al., 2007 Ram-pure et al., 2003), and the interested reader is referred to these studies for further information. 

Nanoparticle-modified thermosets are known to differ greatly from neat thermosetting resins. With the effects of fillers on the chemorheology of thermosetting resins having been studied for decades [7], rheological models are today basically... 

The rheological models for unified conq>lex viscosity versus frequency curves can be ea y written based on the modified Cox-Mertz rule discussed in Quarter 5. Thus, using Eq. (5.5), the modified Carreau model for complex viscosity can be written from Eq. (6.1) as... 

Columns I to K are prepared by inputting known data on the polymers for TG, E, and L2, whereas Columns N to Q are used to store model parametric values for the General Rheological model given by Eq. (6.4) (see Rg. 7.1b). Thus, columns N and O contain n and K values for the modified power-law model, whereas columns P and Q contain P and t) X MFI. Because the values of K and iv, x MFI are typically lai], it is better to use scientific notation through... 

In modem industrial practice, compositions often contain pigments, reinforcements, rheological modifiers, surfactants, and other materials in addition to fillers. These materials can function synergisticaHy in the system. Hence, more complex models are needed to predict the optimal filler loading. ExceUent discussions of filler loading and selection in plastics are given (9,10). 

A Newtonian liquid of viscosity 0.1 N s/m2 is flowing through a pipe of 25 mm diameter and 20 m in lenglh, and the pressure drop is 105 N/m2. As a result of a process change a small quantity of polymer is added to the liquid and this causes the liquid to exhibit non-Newtonian characteristics its rheology is described adequately by the power-law model and the flow index is 0.33. The apparent viscosity of the modified fluid is equal to ihc viscosity of the original liquid at a shear rate of 1000 s L... 

A modified version of the free-volume theory is used to calculate the viscoelastic scaling factor or the Newtonian viscosity reduction where the fractional free volumes of pure polymer and polymer-SCF mixtures are determined from thermodynamic data and equation-of-state models. The significance of the combined EOS and free-volume theory is that the viscoelastic scaling factor can be predicted accurately without requiring any mixture rheological data. 

Both the Carreau and the Cross models can be modified to include a term due to yield stress. For example, the Carreau model with a yield term given in Equation (2.16) was employed in the study of the rheological behavior of glass-filled polymers (Poslinski et al., 1988) ... 

A model to study thixotropic behavior of foods exhibiting yield stress was devised by Tiu and Boger (1974) who studied the time-dependent rheological behavior of mayonnaise by means of a modified Herschel-Bulkley model ... 

In conclusion, exact relationships between the Young s modulus and the microstructure of particulate aggregate networks have been obtained. The elastic properties of such materials are a function of the total amount of solid material present, the properties of the particles which make up the solid, and the spatial distribution of solid particles within the network. This model can be utilized to better understand and modify the macroscopic rheological properties of soft materials and fat crystal networks in particular. 

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