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Peclet number polymers

The thermal conductivity of polymeric fluids is very low and hence the main heat transport mechanism in polymer processing flows is convection (i.e. corresponds to very high Peclet numbers the Peclet number is defined as pcUUk which represents the ratio of convective to conductive energy transport). As emphasized before, numerical simulation of convection-dominated transport phenomena by the standard Galerkin method in a fixed (i.e. Eulerian) framework gives unstable and oscillatory results and cannot be used. [Pg.90]

Peclet number, 352 trickle operation, 92-93 gas phase, 94 liquid phase, 103 Penetration theory, 340 Polymers, 38-40 n-Propane, 178 Propellants, solid combustion, 4-50 flameless, 45... [Pg.412]

Forced-Convection Flow. Heat transfer in pol3rmer processing is often dominated by the uVT flow advectlon terms the "Peclet Number" Pe - pcUL/k can be on the order of 10 -10 due to the polymer s low thermal conductivity. However, the inclusion of the first-order advective term tends to cause instabilities in numerical simulations, and the reader is directed to Reference (7) for a valuable treatment of this subject. Our flow code uses a method known as "streamline upwindlng" to avoid these Instabilities, and this example is intended to illustrate the performance of this feature. [Pg.274]

The application of finite strains and stresses leads to a very wide range of responses. We have seen in Chapters 4 and 5 well-developed linear viscoelastic models, which were particularly important in the area of colloids and polymers, where unifying features are readily achievable in a manner not available to atomic fluids or solids. In Chapter 1 we introduced the Peclet number ... [Pg.213]

The rod is visualised as being constrained to a tube in a similar fashion to entanglements constraining a polymer in reptation theory. So for a finite concentration our diffusion coefficient and rotary Peclet number changes ... [Pg.256]

Other dimensionless groups that compare the thickness of the adsorbed polymer layer to the radius of the particle or the radius of gyration of the polymer to the particle radius in polymer/colloid mixtures can also be easily defined. We are mostly concerned with the volume fraction and the Peclet number Pe in our discussions in this chapter. However, the other dimensionless groups may appear in the equations for intrinsic viscosity of dispersions when the dominant effects are electroviscous or sterically induced. [Pg.177]

The intrinsic viscosity [17] in the above expression includes the primary electroviscous effect. The experimental data of Stone-Masui and Watillon (1968) for polymer latices seem to be consistent with the above equation (Hunter 1981). Corrections for a for large values of kRs are possible, and the above equation can be extended to larger Peclet numbers. However, because of the sensitivity of the coefficients to kRs and the complications introduced by multiparticle and cooperative effects, the theoretical formulations are difficult and the experimental measurements are uncertain. For our purpose here, the above outline is sufficient to illustrate how secondary electroviscous effects affect the viscosity of charged dispersions. [Pg.179]

Parallel plates, 527 Parallel polarised light, 299 Paramagnetic, 355 Pardox of Kauzmann, 151 Partially immobilising sorption, 682 Partly oriented yams, 483 Peclet number, 56,59 P-electron conjugation, 140,161,183 Penetrant, 655 Performance properties, 52 Permachor, 676 Permeability, 656, 673, 676 coefficient, 656 magnetic, 287 of polymers, 675 Permeation coefficient, 673... [Pg.999]

However, for nonspherical particles, rotational Brownian motion effects already arise at 0(0). In the case of ellipsoidal particles, such calculations have a long history, dating back to early polymer-solution rheologists such as Simha and Kirkwood. Some of the history of early incorrect attempts to include such rotary Brownian effects is documented by Haber and Brenner (1984) in a paper addressed to calculating the 0(0) coefficient and normal stress coefficients for general triaxiai ellipsoidal particles in the case where the rotary Brownian motion is dominant over the shear (small rotary Peclet numbers)—a problem first resolved by Rallison (1978). [Pg.26]

The term Peclet number is common in the suspension literature, while the corresponding quantity is usually called the Deborah number or Weissenberg number in tbe polymer literature. From Eqs. (6-30) through (6-33) we find, in general, for a solvent of viscosity 1 cP, that Drd /b, where b — d or L) is the particle s longest dimension in units of pm, and is in sec. Since typical shear rates are in the range 10 > 10 sec , ... [Pg.281]

Although momentum convection is generally negligible for polymer melt flows (Reynolds numbers on the order of 10-5), thermal convection may be significant. The ratio of convective to conductive transport is given approximately by the Peclet number Pe ... [Pg.268]

Predicted Deformation Mechanisms. Recent work has developed maps of the deformation mechanisms expected in films with different properties. Two dimensionless groups were found to determine which of the deformation mechanism occurs. The first is the time for particle deformation compared to the time for evaporation, captured in 1 = ERt]o/yH, where E is the evaporation rate, t]o is the polymer viscosity, and y is the water-air surface tension. The second dimensionless group is the Peclet number, which determines the vertical homogeneity in the film, Pe = 6nt] R H E/kT. The deformation regimes are shown in Fig. 9. [Pg.1454]

Problem 9-24. Mass Transfer from a Sheet in Extension. Consider a polymer-solvent sheet in extension such that it is stretched as it is pulled horizontally. The dimensional tangential velocity of the sheet is given by u = uoEx/L, where uo is the initial velocity, E is a constant draw ratio, x is the distance downstream, and L is the extent of the draw zone. We wish to determine the mass transfer of solvent from the polymer. The concentration of solvent far from the sheet is zero, and on the surface of the sheet, it is Co. The Peclet number... [Pg.693]

The Peclet number is seen to increase as the cube of the Flory radius showing the relative increase in importance of viscous forces with increasing polymer length. [Pg.267]

It should be noted here that in polymer rheology, for viscoelastic fluids the commonly used dimensionless parameter to characterize the ratio of elastic force to viscous force is the Deborah number denoted by the symbol De. This parameter is essentially just the Peclet number. In terms of characteristic times, it is equal to the ratio of the largest time constant of the molecular motions or other appropriate relaxation time of the fluid compared to the characteristic flow time. [Pg.267]

This is exactly the Peclet number defined by Eq. (5.3.25), which measures the characteristic rotational Brownian diffusion time to the time scale defined by the reciprocal of the shear rate. It is the same measure found for dilute polymer solutions with the particle radius here replacing the Flory radius for the polymer. [Pg.270]

Probability of an open site or bond in Chapter 4 Hydrostatic pressure (mmHg) in Chapters 5 and 6 Persistence length on polymer chain (cm) in Chapter 4 Membrane permeability (cm/s) in Chapter 5 Probability density function Critical probability Peclet number... [Pg.366]

The conditions under which hydrodynamic retention can occur in flow of polymer solutions through porous media have been analyzed, leading to the conclusion that Peclet numbers corresponding to potential retention zones were too low to induce this type of retention. [Pg.67]

The Peclet number provides a measure of the importance of thermal convection relative to thermal conduction. The Peclet number in polymer processing is often quite large, typically of the order of 10= to 10 This indicates that convective heat transport is often quite important in polymer melt flow. [Pg.166]

From the effluent concentration profile in a polymer or tracer flood, the total core Peclet number is calculated by fitting the analytic form of the convection-dispersion equation as described above. The most direct experimental comparison between the dispersion appropriate for polymer and for an inert tracer should be done in experiments in which both species are present in the injected pulse of labelled polymer solution. This helps to reduce greatly errors that may arise when separate tracer and polymer experiments are carried out. For example, in the study by Sorbie et al (1987d), the dispersion properties of two different xanthans were examined in consolidated outcrop sandstone cores. In all floods, the inert tracer, Cl, was used, thus allowing the dispersion coefficient of the xanthan and tracer to be measured in the same flood. An example of this is shown for a low-concentration (low-... [Pg.216]

Figure 7.7. Calculated D/UL) group versus network Peclet number for both tracer and polymer species (Sorbie and Clifford, 1991). Figure 7.7. Calculated D/UL) group versus network Peclet number for both tracer and polymer species (Sorbie and Clifford, 1991).

See other pages where Peclet number polymers is mentioned: [Pg.54]    [Pg.98]    [Pg.99]    [Pg.14]    [Pg.234]    [Pg.190]    [Pg.153]    [Pg.567]    [Pg.579]    [Pg.786]    [Pg.274]    [Pg.268]    [Pg.269]    [Pg.272]    [Pg.1101]    [Pg.172]    [Pg.397]    [Pg.2817]    [Pg.56]    [Pg.65]    [Pg.248]    [Pg.1183]    [Pg.1705]    [Pg.9]    [Pg.134]    [Pg.220]    [Pg.443]    [Pg.357]   
See also in sourсe #XX -- [ Pg.286 , Pg.287 ]




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