Rheology constant

Extensional Viscosity. In addition to the shear viscosity Tj, two other rheological constants can be defined for fluids the bulk viscosity, iC, and the extensional or elongational viscosity, Tj (34,49,100—107). The bulk viscosity relates the hydrostatic pressure to the rate of deformation of volume, whereas the extensional viscosity relates the tensile stress to the rate of extensional deformation of the fluid. Extensional viscosity is important in a number of industrial processes and problems (34,100,108—110). Shear properties alone are insufficient for the characterization of many fluids, particularly polymer melts (101,107,111,112). 

Maximum Flow-Rater Production of Flat Sheets Calculate the maximum flow rate per unit width, qmax, for producing a smooth fracture-free sheet with a die of 0.05-cm opening for HDPE - Alathon 7040, LDPE - Alathon 1540 at 473 K PS -Dylene 8, ABS and HIPS at 483 K. Use the Power Law model and the rheological constants below. qmax has to be such that xw < xcrit 105N/m2. 

Of all the physico-chemical properties, it is the rheology which shows the strongest temperature dependence. For instance, the decrease in apparent viscosity at a fixed shear rate is well represented by the Arrhenius-type exponential expression the pre-exponential factor and the activation energy are then both fimctions of shear rate. It is thus customary to denote the temperature dependence using rheological constants such as the power-law consistency coefficient and flow behaviour index. It is now reasonably well established that the flow behaviour index, n, of suspensions, polymer melts and solutions is nearly independent of temperature, at least over a range of 40-50°C, whereas the consistency coefficient exhibits an exponential dependence on temperature, i.e. 

Typical flow-property constants (rheological constants) for some fluids are given in Table 3.5-1. Some data give y values instead of K values, but Eq. (3.5-8) can be used to convert these values if necessary. In some cases in the literature, K or K values are given... 

The flow-property or rheological constants of non-Newtonian fluids can be measured using pipe flow as discussed in Section 3.5E. Another, more important method for measuring flow properties is by use of a rotating concentric-cylinder viscometer. This was first described by Couette in 1890. In this device a concentric rotating cylinder (spindle) spins at a constant rotational speed inside another cylinder. Generally, there is a very small gap between the walls. This annulus is filled with the fluid. The torque needed to maintain this constant rotation rate of the inner spindle is measured by a torsion wire from which the spindle is suspended. A typical commercial instrument of this type is the Brookfield viscometer. Some types rotate the outer cylinder. 

Most of the studies on heat transfer, with fluids have been done with Newtonian fluids. However, a wide variety of non-Newtonian fluids are encountered in the industrial chemical, biological, and food processing industries. To design equipment to handle these fluids, the flow property constants (rheological constants) must be available or must be measured experimentally. Section 3.5 gave a detailed discussion of rheological constants for non-Newtonian fluids. Since many non-Newtonian fluids have high effective viscosities, they are often in laminar flow. Since the majority of non-Newtonian fluids are pseudoplastic fluids, which can usually be represented by the power law, Eq. (3.5-2), the discussion will be concerned with such fluids. For other fluids, the reader is referred to Skelland (S3). 

Laminar flow in tubes. A large portion of the experimental investigations have been concerned with heat transfer of non-Newtonian fluids in laminar flow through cylindrical tubes. The physical properties that are needed for heat transfer coefficients are density, heat capacity, thermal conductivity, and the rheological constants K and n or K and n. 

Various equations have been derived to solve the power law factor of pseudoplastics. These equations are presented to help the reader appreciate the rheological constants that must be determined by testing, as will be described in Section 3-6. 

The EUis equation is more flexible but is an empirical equation and uses three rheological constants. SkeUand (1967) demonstrates how the equation is based on the work of Ellis and Round and is explicit with respect to the velocity gradient rather than the shear rate ... 

The orientation of particles of a liquid is characterized by one unit vector 71 The rheological constants p, t, tij, 112, and X are usually experimentally determined. The differential equation characterizes the change in the orientation of the particles of the liquid caused by flow. The viscosity tensor of a simple Ericksen liquid is... 

For non-circular shapes, the equations of motion may result in nonlinear partial differential equations, which are difficult to solve analytically. Therefore, approximate methods such as the variational method (Kantorovich and Krylov, 1958) are generally used for solving non-Newtonian flow problems. Schechter (1961) used the application of the variational method to solve the non-linear partial differential equations of pressure drop and flow rate of the polymer for non-circular shapes such as a rectangle or square. Moreover, Mitsuishi and Aoyagi (1969 1973) used similar methods for other non-circular shapes such as an isosceles triangle. The results were based on the Sutterby model (1966), which incorporates a viscosity function based on the rheological constants. Flow curves with pressure drop and flow rate for both circular and non-circular shapes were generated and the results were compared with the power law model. 

Tanigawa Y., Mori H., Tsutsui K., Kurokawa Y., Estimation of rheological constants of fresh concrete by slump test and flow test. Trans. of the Japan Concrete Inst. vol.6, Tokyo 1906, pp.65-72. 

The data given in Table 4-10 were obtained with Th02 slurries having a pH less than 6 and whose rheological constants were relatively insensi-... 

Many works (see [69, 71, 188, 260, 261]) toueh upon the issue of the system prehistory influence on its rheological constants. The interpretation of these effects is related to different models of the struetured liquid [69,71,177,144,244] in one way or another. 

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