Viscous flow temperature dependence

Rheology. Both PB and PMP melts exhibit strong non-Newtonian behavior thek apparent melt viscosity decreases with an increase in shear stress (27,28). Melt viscosities of both resins depend on temperature (24,27). The activation energy for PB viscous flow is 46 kj /mol (11 kcal/mol) (39), and for PMP, 77 kJ/mol (18.4 kcal/mol) (28). Equipment used for PP processing is usually suitable for PB and PMP processing as well however, adjustments in the processing conditions must be made to account for the differences in melt temperatures and rheology. 

In connection with the earlier consideration of diffusion in liquids using tire Stokes-Einstein equation, it can be concluded that the temperature dependence of the diffusion coefficient on the temperature should be T(exp(—Qvis/RT)) according to this equation, if the activation energy for viscous flow is included. 

Strength and Stiffness. Thermoplastic materials are viscoelastic which means that their mechanical properties reflect the characteristics of both viscous liquids and elastic solids. Thus when a thermoplastic is stressed it responds by exhibiting viscous flow (which dissipates energy) and by elastic displacement (which stores energy). The properties of viscoelastic materials are time, temperature and strain rate dependent. Nevertheless the conventional stress-strain test is frequently used to describe the (short-term) mechanical properties of plastics. It must be remembered, however, that as described in detail in Chapter 2 the information obtained from such tests may only be used for an initial sorting of materials. It is not suitable, or intended, to provide design data which must usually be obtained from long term tests. 

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. 

A similar thing takes place when we consider flow curves obtained at different temperatures. As seen from Fig. 7, if we take a region of low shear rates, then due to the absence of the temperature dependence Y, the apparent activation energy vanishes. At sufficiently high shear rates, when a polymer dispersion medium flows, the activation energy becomes equal to the activation energy of the viscous flow of a polymer melt and the presence of the filler in this ratio is of little importance. 

While electrical conductivity, diffusion coefficients, and shear viscosity are determined by weak perturbations of the fundamental diffu-sional motions, thermal conductivity is dominated by the vibrational motions of ions. Heat can be transmitted through material substances without any bulk flow or long-range diffusion occurring, simply by the exchange of momentum via collisions of particles. It is for this reason that in liquids in which the rate constants for viscous flow and electrical conductivity are highly temperature dependent, the thermal conductivity remains essentially the same at lower as at much higher temperatures and more fluid conditions. 

That particular combination of properties possessed by high polymers, characterising the rubber-like state. Depending on the temperature and the time of stressing, a high polymer may show viscous flow or high elasticity. See Elasticity, Glass Transition, Thixotropy and Viscosity. 

Hence the heat transport, in this case, depends on the dimension and shape of the liquid container. As we can see in Fig. 2.13, the thermal conductivity (and the specific heat) of liquid 4He decreases when pressure increases and scales with the tube diameter. At temperatures below 0.4 K, the data of thermal conductivity (eq. 2.7) follow the temperature dependence of the Debye specific heat. At higher temperatures, the thermal conductivity increases more steeply because of the viscous flow of the phonons and because of the contribution of the rotons. 

The solvent composition affects not only the hysteresis or history dependence of the viscosity, but also its magnitude and temperature dependence. The viscosity was 10% higher using pure MeOH as the solvent than when a 1 1 MIBK/MeOH mixture was used. However, the 9 1 solvent mixture produces the highest solution viscosity by more than a factor of four. (A solution using a 19 1 MIBK/MeOH solvent mixture was so viscous it would barely flow in the flask in which it was prepared.) The apparent activation energy for flow... 

The total deformation in the four-element model consists of an instantaneous elastic deformation, delayed or retarded elastic deformation, and viscous flow. The first two deformations are recoverable upon removal of the load, and the third results in a permanent deformation in the material. Instantaneous elastic deformation is little affected by temperature as compared to retarded elastic deformation and viscous deformation, which are highly temperature-dependent. In Figure 5.62b, the total viscoelastic deformation is given by the curve OABDC. Upon unloading (dashed curve DFFG),... 

Although electrical measurements have confirmed the ionic nature of borate melts, viscous flow and volumetric studies clearly indicated their difference from liquid silicates. Shartsia and co-workers (4 ) have suggested that an equilibrium exists in the melt between BOj triangles and B04 Letrahedra, this being both temperature and composition dependent. The only ionic model for the borates is that of Bockris and Mellors (8) which... 

Since the activation energy for ionic recombination is mainly due to viscosity we use the activation energy for viscous flow (10kJ.mol l). AH ] and 3 were determined from conductance as 44.2kJ.mol and 11,4kJ.mol From the data presented in Table III it is clear that the temperature dependence of the slope is very satisfactorily described by A% +l/2(AHd-AH3). Another, and rather critical, test for the applicability of eq. 14b is the effect of pressure since the slope of eq. 14b is largely pressure independent so that we ask here for a compensation of rather large effects. From Table III we Indeed see an excellent accordance between the experimental value and the pressure-dependence calculated from the activation volume of viscous flow (+20.3 ctPmol ), AVd (-57.3 cnAnol" ) and (-13.9 cnAnol ) the difference between the small experimental and calculated values is entirely with the uncertainties of compressibility - corrections and experimental errors. 

Further the pressure and temperature dependences of all the transport coefficients involved have to be specified. The solution of the equations of change consistent with this additional information then gives the pressure, velocity, and temperature distributions in the system. A number of solutions of idealized problems of interest to chemical engineers may be found in the work of Schlichting (SI) there viscous-flow problems, nonisothermal-flow problems, and boundary-layer problems are discussed. 

Equations 1 and 3 are coupled through the mass flow, pgq, which depends in a complicated manner on the charge temperature and the vapor pressure of the source material. The flow through the exit orifice can range from free molecular flow to viscous flow. If the Knudsen number (ratio of the mean free path, m, to the orifice diameter, D) is greater than 1 (i.e., JD > 1), then the flow is free molecular. If m/D < 0.01, the flow is viscous. A transition region exists between these limits. 

Telegina et al. 72> showed that the activation energy for the viscous flow of a polyester oligomer filled with glass microspheres is 46.9 kJ/mol, while that of an epoxy oligomer is 78.3 kJ/mol. They also established the important fact that the addition of microspheres to an oligomer composition does not change the temperature viscosity coefficient. This means that the viscosity of a mixture with microspheres can be controlled, if the temperature dependence of the viscosity of the binder is known. 

The results of the calculations shown in Fig. 2.32 represent a complete quantitative solution of the problem, because they show the decrease in the induction period in non-isothermal curing when there is a temperature increase due to heat dissipation in the flow of the reactive mass. The case where = 0 is of particular interest. It is related to the experimental observation that shear stress is almost constant in the range t < t. In this situation the temperature dependence of the viscosity of the reactive mass can be neglected because of low values of the apparent activation energy of viscous flow E, and Eq. (2.73) leads to a linear time dependence of temperature ... 

The intense heat dissipated by viscous flow near the walls of a tubular reactor leads to an increase in local temperature and acceleration of the chemical reaction, which also promotes an increase in temperature the local situation then propagates to the axis of the tubular reactor. This effect, which was discovered theoretically, may occur in practice in the flow of a highly viscous liquid with relatively weak dependence of viscosity on degree of conversion. However, it is questionable whether this approach could be applied to the flow of ethylene in a tubular reactor as was proposed in the original publication.199 In turbulent flow of a monomer, the near-wall zone is not physically distinct in a hydrodynamic sense, while for a laminar flow the growth of viscosity leads to a directly opposite tendency - a slowing-down of the flow near the walls. In addition, the nature of the viscosity-versus-conversion dependence rj(P) also influences the results of theoretical calculations. For example, although this factor was included in the calculations in Ref.,200 it did not affect the flow patterns because of the rather weak q(P) dependence for the system that was analyzed. 

---