Temperature Dependence of Flow Properties

Also of engineering interest is the variation of flow properties with temperature. The temperature dependence of the zero-shear viscosity can often be represented by the relation 

The /o s from Fig. 15.8 are plotted according to (15.11) in Fig. 15.9. The fit is quite good. The slope is /2.303jR, from which E 11.4kcal/moL Thus, the combination of (15.11) and (15.9) does a pretty good job of describing both the shear rate and temperature dependence of viscosity, at least for these data. 

Example 2. What must the temperature be to reduce the 100 C zero-shear viscosity of L-80 PIB by an order of magnitude  

Solution. The temperature- dependence of zero-shear viscosity is given by (15.11). Therefore, between temperatures Ti and T, 

The temperature is, therefore, an effective means of controlling melt viscosity in processing operations, but two drawbacks must be kept in mind (1) it takes time and costs money to put in and take out thermal energy, and (2) excessive temperatures can lead to degradation of the polymer. 

The famous Williams-Landell-Ferry (WLF) equation [13] is useful for describing the temperature dependence of several linear mechanical properties of polymers (see Chapter 16). For the zero-shear viscosity, it may be written as 

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If you consider the number of processes that use molten polymers (e.g., injection-molded CDs), it is obvious that the temperature dependence of flow properties must be understood. The temperature dependence of the zero-shear viscosity can often be represented by the relation ... 

TEMPERATURE DEPENDENCE OF FLOW PROPERTIES 261 By analogy to Equation 14.10, these functions are approximated by... 

Softening as a result of micro-Brownian motion occurs in amorphous and crystalline polymers, even if they are crosslinked. However, there are characteristic differences in the temperature-dependence of mechanical properties like hardness, elastic modulus, or mechanic strength when different classes of polymers change into the molten state. In amorphous, non-crosslinked polymers, raise of temperature to values above results in a decrease of viscosity until the material starts to flow. Parallel to this softening the elastic modulus and the strength decrease (see Fig. 1.9). 

For highly viscous, non-Newtonian flows, even without considering reaction, the temperature dependence of the properties such as density and viscosity has an important influence in determining the flow patterns. A consequence of this is that heat transfer dominates the design because of heat generation due to chemical reaction. In the case of a polymer reaction, temperature has an important effect on the molecular weight distribution so it is essential to try to ensure a uniform temperature in the reactor. 

By comparing experimentally determined stress versus temperature hysteresis loops with simple constitutive models of plastic deformation, approximate estimates of plastic properties such as the film yield strength in tension or compression, extent of strain hardening, and the temperature-dependence of flow stress can be inferred for some thin film materials (see, for example. Figures 7.16 and 7.19). 

The flow behavior of the polymer blends is quite complex, influenced by the equilibrium thermodynamic, dynamics of phase separation, morphology, and flow geometry [2]. The flow properties of a two phase blend of incompatible polymers are determined by the properties of the component, that is the continuous phase while adding a low-viscosity component to a high-viscosity component melt. As long as the latter forms a continuous phase, the viscosity of the blend remains high. As soon as the phase inversion [2] occurs, the viscosity of the blend falls sharply, even with a relatively low content of low-viscosity component. Therefore, the S-shaped concentration dependence of the viscosity of blend of incompatible polymers is an indication of phase inversion. The temperature dependence of the viscosity of blends is determined by the viscous flow of the dispersion medium, which is affected by the presence of a second component. 

One-step chemistry is often employed as an idealized model for combustion chemistry. The primary difference with the results presented above is the strong temperature dependence of the reaction rate constant k T). For constant-property flows, the temperature can be related to the mixture fraction and reaction-progress variable by a linear expression of the form... 

Because of the strong temperature dependence of exhaustion and the poor migration properties, dye absorption must be as level as possible from the start. Correspondingly, attention should be paid to uniform packaging, package density, liquor flow or movement of textile material, and controlled machine conditions. 

Sizing the reactor implies calculating, besides reactor volume, the heat-transfer area of the cooling coils and of the FEHE. We assume constant volumetric flows and coolant temperature, and neglect the temperature dependence of the reaction heat and physical properties. With these assumptions, the mathematical model of the reactor which includes the energy balance is given by ... 

Several differing simple models of molten salts do indeed give reasonably close calculations of equilibrium properties, e.g., compressibility and surface tension. What these models do not do, however, is to quantitatively rationalize the data on the temperature dependence of conductance, viscous flow, and self-diffusion. The discovery by Nanis and Richards of the fact that simple liquids have heats of activation for all three properties given approximately by 3. lART presents a clear and challenging target for testing models of liquids. 

This suggestion is in agreement with the well-known fact that the equilibrium rigidity of cellulose ether and ester molecules changes greatly with solvent composition and is also confirmed by the stroi n ative temperature dependence of the statistical size of their chains. The latter property is manifested in a decrease of the intrinsic viscosity, translational friction - and the flow birefringence ) with increasing temperature (Fig. 32) ... 

Abstract Grease lubrication is a complex mixture of science and engineering, requires an interdisciplinary approach, and is applied to the majority of bearings worldwide. Grease can be more than a lubricant it is often expected to perform as a seal, corrosion inhibitor, shock absorber and a noise suppressant. It is a viscoelastic plastic solid, therefore, a liquid or solid, dependent upon the applied physical conditions of stress and/or temperature, with a yield value, ao- It has a coarse structure of filaments within a matrix. The suitability of flow properties of a grease for an application is best determined using a controlled stress rheometer for the frequency response of parameters such as yield, a, complex shear modulus, G phase angle, 5, and the complex viscosity, rj. ... 

A thorough analysis of forming processes relies on mathematical descriptions of the physical steps. These are independent of the material and are formulated with the equations of continuity, momentum and energy. These equations applied to the particular geometry must be combined with the rheological equation of state of the material. Furthermore, the relations expressing the temperature and pressure dependencies of such properties such as density, thermal conductivity, etc., are required. The combination of these relations constitutes the mathematical formulation of the flow process. These formulations are beyond the scope of the Chapter. 

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