Capillary flow, shear viscosity

Flow processes iaside the spinneret are governed by shear viscosity and shear rate. PET is a non-Newtonian elastic fluid. Spinning filament tension and molecular orientation depend on polymer temperature and viscosity, spinneret capillary diameter and length, spin speed, rate of filament cooling, inertia, and air drag (69,70). These variables combine to attenuate the fiber and orient and sometimes crystallize the molecular chains (71). 

Capillary viscometers are useful for measuring precise viscosities of a large number of fluids, ranging from dilute polymer solutions to polymer melts. Shear rates vary widely and depend on the instmments and the Hquid being studied. The shear rate at the capillary wall for a Newtonian fluid may be calculated from equation 18, where Q is the volumetric flow rate and r the radius of the capillary the shear stress at the wall is = r Ap/2L. 

As demonstrated, Eq. (7) gives complete information on how the weight fraction influences the blend viscosity by taking into account the critical stress ratio A, the viscosity ratio 8, and a parameter K, which involves the influences of the phenomenological interface slip factor a or ao, the interlayer number m, and the d/Ro ratio. It was also assumed in introducing this function that (1) the TLCP phase is well dispersed, fibrillated, aligned, and just forms one interlayer (2) there is no elastic effect (3) there is no phase inversion of any kind (4) A < 1.0 and (5) a steady-state capillary flow under a constant pressure or a constant wall shear stress. 

There are commercially available in-line or on-line viscometer devices. In-line devices are installed directly in the process while on-line devices are used to analyze a side stream of the process. Most devices are based on measuring the pressure drop and flow rate through a capillary. The viscosity is either determined at a single shear rate or, at most, a few shear rates. Complex fluids, on the other hand, exhibit a viscosity that cannot be so easily characterized. In order to capture enough information that allows, for example, a molecular weight distribution to be inferred, it is necessary to determine the shear viscosity over reasonably wide ranges of shear rates. 

Note 4 Some experimental methods, such as capillary flow and flow between parallel plates, employ a range of shear rates. The value of tj evaluated at some nominal average value of Y is termed the apparent viscosity and given the symbol /app. It should be noted that this is an imprecisely defined quantity. 

The Vel data as a function of flow rate, Q, are shown for a 10 g/mol molecular weight polystyrene in Figure A. Both the Ubbelohde viscometric data and the membrane viscometer data are platted on the same graph for a 0.6 urn pore membrane at a low concentration of 100 ppm. The flow is Newtonian. The actual agreement of the capillary and membrane viscosities at low flow rates is always excellent when << Dj., and the concentration is extremely low. At small pore size, high concentrations, and high shear rates the flow can become non-Newtonian. The latter effects are only briefly discussed in this paper, but it is this effect that offers an oportunity to characterize the shape rather than the overall size. Even for a relatively large pore (0.6, Hi , membrane the shear rates vary from 100 s at E mi/Hr to 10 s at 200... 

This section describes two common experimental methods for evaluating i], Fj, and IG as functions of shear rate. The experiments involved are the steady capillary and the cone-and-plate viscometric flows. As noted in the previous section, in the former, only the steady shear viscosity function can be determined for shear rates greater than unity, while in the latter, all three viscometric functions can be determined, but only at very low shear rates. Capillary shear viscosity measurements are much better developed and understood, and certainly much more widely used for the analysis of polymer processing flows, than normal stress difference measurements. It must be emphasized that the results obtained by both viscometric experiments are independent of any constitutive equation. In fact, one reason to conduct viscometric experiments is to test the validity of any given constitutive equation, and clearly the same constitutive equation parameters have to fit the experimental results obtained with all viscometric flows. 

By assuming only that the polymer melt is viscous and time independent, and that the viscosity is a function of the shear rate, //( >), without the need to specify any specific viscosity function, we can state that for capillary flow at the wall,... 

The flow in a capillary is inhomogeneous in the sense that the shearing stress, T, and the rate of shear, G, vary with the position of the fluid inside the capillary. The velocity of the flow is maximum along the central axis but gradually drops to zero at the wall, whereas the reverse is true for the shearing stress and rate of shear. For a Newtonian flow the viscosity, j ( = r/6), remains constant at any point inside the capillary even though both T and G vary considerably from one point to another. On the other hand, for a non-Newtonian flow the viscosity varies along the radial distance of the axis. 

The melt viscosity of LCPs is sensitive to thermal and mechanical histories. Quite often, instrumental influences are important in the value of viscosity measured. For example, the viscosity of HBA/HNA copolyesters are dependent on the die diameter in capillary flow (59). LCP melts or solutions are very efficiently oriented in extensional flows, and as a result, the influence of the extensional stresses at the entrance to a capillary influence the shear flow in the capillary to a much greater extent than is usually found with non-LC polymers. 

The second Interesting observation based on ICR and RMS results Is related to the need for pressure correction In capillary flow. Already In Fig. 19 an agreement between the dynamic viscosity, n, and corrected for pressure effect capillary shear viscosity, n, was shown. In Fig. 22 five different measures of viscosity are shown for LLDPE-A (four for the other samples) steady state elongational viscosity, nE/3 conqplex and dynamic viscosity, n and n > as well as the steady state capillary viscosity corrected and uncorrected for the pressure effects, hcorr n(lCR), respectively. There Is a... 

Polymer viscosity is strongly shear dependent. If we use the bulk viscosity measured at different shear rates to describe the flow behavior in porous media, our first task is to calculate the shear rate which is equivalent to that in the bulk viscometer. To do that, we start with the capillary flow of a non-Newtonian fluid. 

Figure 1, shows a rapid increase in apparent viscosity for resin V as the shear rate reaches 17.3 sec1. The sharp increase in apparent viscosity is not any chemical change, such as crosslinking of polymeric chains. The apparent viscosity curve can be retraced by lowering the shear rate. This increase in apparent viscosity can be eliminated by increasing the measurement temperature, as shown in Figure 2. This same phenomenon has been reported for polystyrene by Penwell and Porter (12). The explanation of the apparent viscosity increase in capillary flow of polystyrene was quantitatively explained through the...

Typically, WPC based on polypropylene and polyethylene show deviation from the Cox-Merz rule. This is due to the different nature of flow. Capillary flow is a pressure-driven flow, including entrance and exit effects, wall slip, friction in the barrel, and orientation effects. Parallel-plate flow is pure drag shear flow, in which particle-particle and matrix-particle interactions result in higher viscosities for filled polymers. In other words, a straightforward question is a 100-fold increase in shear rate and 100-fold increase in frequency result in the same effects the answer would be yes for neat polymers, and no for wood-filled composites. 

Shear Viscosity. There are three main types of viscometers the rotational type, the flow-through-constriction type, and the flow-around-obstruction type. The concentric cylinder and the cone-and-plate are the two primary classes of rotational viscometers. The capillary tube is an example of the flow-through-constriction viscometers. Falling-ball or falling-needle viscometers are examples of the flow-around-obstruction type. 

In practical applications, flow of the material through an orifice is perhaps the most frequently encountered rheological phenomenon. It is then natural to be used for the viscosity measurement of suspensions (53-55). However, the flow through an orifice is not precise in terms of shear measurement because the shear rate is not well defined under such circumstances. To meet this objection, the orifice is in most cases extended to a tube. This leads to the capillary flow type of viscometers, the simplest, and for Newtonian fluids, the most accurate type, comprising the familiar Ostwald und Ubbelohde viscometers. The fully developed axial velocity in the laminar regime is given by... 

Senouci and Smith (1988) used a simplified analysis for converging flow in a piston-driving capillary rheometer at 120-130°C and obtained ratios of uniaxial extensional viscosities to shear viscosities of maize grits and potato powder in the range of 60-3900. 

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