Rheological measurements flow models

Knowledge of the rheological properties of food pastes, slurries and sauces, such as ketchup, mayonnaise and salad creams, is important both for quality assurance and for optimizing industrial flow and mixing processes. Unfortunately, many food slurries and pastes are opaque and do not lend themselves to flow studies with conventional techniques such as laser Doppler anemometry. Moreover, conventional rheological measurements are model-dependent in that it is necessary to fit the data by assuming a function relationship between the stress and strain (or strain rate) and to assume a set of boundary conditions (such as slip or stick) at the fluid-container... 

Many materials are conveyed within a process facility by means of pumping and flow in a circular pipe. From a conceptual standpoint, such a flow offers an excellent opportunity for rheological measurement. In pipe flow, the velocity profile for a fluid that shows shear thinning behavior deviates dramatically from that found for a Newtonian fluid, which is characterized by a single shear viscosity. This is easily illustrated for a power-law fluid, which is a simple model for shear thinning [1]. The relationship between the shear stress, a, and the shear rate, y, of such a fluid is characterized by two parameters, a power-law exponent, n, and a constant, m, through... 

The theoretical basis for spatially resolved rheological measurements rests with the traditional theory of viscometric flows [2, 5, 6]. Such flows are kinematically equivalent to unidirectional steady simple shearing flow between two parallel plates. For a general complex liquid, three functions are necessary to describe the properties of the material fully two normal stress functions, Nj and N2 and one shear stress function, a. All three of these depend upon the shear rate. In general, the functional form of this dependency is not known a priori. However, there are many accepted models that can be used to approximate the behavior, one of which is the power-law model described above. 

Navarrete R.C. 1991. Rheology and Structure of Hocculated Suspensions. [CWM, LES] Chen K.S.A. 1992. Studies of Multilayer Slide Coating and Related Processes. [LES] Cai J.J. 1993. Coating Rheology Measurements, Modeling and Applications. [CWM, LES] Benjamin D.F. 1994. Roll Coating Flows and Multiple Roll Systems. [LES]... 

Barthes-Biesel, D. (1988) Mathematical modeling of two-phase flows in Rheological Measurements (eds A.A. Collyerand D.W. Clegg), Elsevier Applied Science, London, 595-634. 

RhGOlogy. Flow properties of latices are important during processing and in many latex applications such as dipped goods, paint, and fabric coatings. Rheology is used to characterize the stability of latices (45). For dilute, nonionic latices, the relative latex viscosity is a power-law expansion of the particle volume fraction. The terms in the expansion account for flow aroimd the particles and particle-particle interactions. For ionic latices, electrostatic contributions to the flow around the diffuse double layer and enhanced particle-particle interactions must be considered (46). A relative viscosity relationship for concentrated latices was first presented in 1972 (47). A review of empirical relative viscosity models is available (46). In practice, latex viscosity measurements are carried out with rotational viscometers (see Rheological Measurements). 

During the experiments, the solid concentration was increased to 20% by volume. Except for suspensions with plastic particles, the suspensions showed a Newtonian behavior up to volume contents of 15 %. Suspensions with glass beads and s = 0.2 as well as all examined suspensions with plastic particles showed a shear thinning behavior. Considering the non-Newtonian behavior of these suspensions in the calculation of the time steady flow based on Eqs. (5.9-5.21), the viscosity of the suspension had to be described by a model depending on the deformation speed y. A Carreau-Yasuda model according to Eq. (5.52) fitted well to measurements carried out with a Couette system. The parameters Hq, a, n, and X were determined by the rheological measurements. 

Correlations based primarily on theoretical models of polymer flow in porous media assume that the power-law index for polymer flow in porous media, <,> is identical to the power-law index determined from rheological measurements. This is not a good assumption, and tic for fio i porous media must be determined from analysis of experimental data. Several polymer/rock systems have been studied in which 26.27,38 en sufficient experimental data are taken, correlations may be developed relating polymer mobility to polymer and rock properties. Willhite and Uhl26 correlated and tic with k p for three xanthan concentrations with Eqs. 5.23a through 5.23g. Units for are... 

The correlations represented by Eqs. 5.26a through 5.26e can be extended to interpolate for polymer concentrations between 1,000 and 2,000 ppm by use of a correlation based on the modified Blake-Kozeny model for the flow of non-Newtonian fluids. 62 Eq. 5.27 is an expression for A bk derived from the Blake-Kozeny model. Note that all parameters are either properties of the porous medium or rheological measurements. Eq. 5.27 underestimates A/ by about 50%. However, Hejri et al. 6 were able to correlate pBK and A for the unconsolidated sandpack data with Eq. 5.28. Eqs. 5.27 and 5.28, along with Eq. 5.24, predict polymer mobility for polymer concentrations ranging from l.,000 to 2,000 ppm within about 7%. 

In a series of experiments on the flow of flocculated kaolin suspensions in laboratory and industrial scale pipelines(26-27-2Sl, measurements of pressure drop were made as a function of flowrate. Results were obtained using a laboratory capillary-tube viscometer, and pipelines of 42 mm and 205 mm diameter arranged in a recirculating loop. The rheology of all of the suspensions was described by the power-law model with a power law index less than unity, that is they were all shear-thinning. The behaviour in the laminar region can be described by the equation ... 

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