Capillary entrance

Finally, because the results obtained in capillary viscometry, especially for capillaries of small UR, are influenced by both extensional and shear flow phenomena associated with the fluid spatial accelerations at the capillary entrance, it is necessary to correct the values of tw given in Eq. E3.1-3. Chapter 13 covers the nature, magnitude, and significance of these, commonly known as Bagley corrections. 

About 50 % of the temperature rise occurs near the capillary entrance, z < 0.2L. Thus, shortening the capillary length does not decrease the temperature rise due to viscous heating, proportionally. 

So far in this chapter we have looked into the viscous phenomena associated with the flow of polymer melts in capillaries. We now turn to the phenomena that are related to melt elasticity, namely (a) swelling of polymer melt extrudates (b) large pressure drops at the capillary entrance, compared to those encountered in the flow of Newtonian fluids and (c) capillary flow instabilities accompanied by extmdate defects, commonly referred to as melt fracture. ... 

It follows then that the capillary entrance angle affects the value of APent- Han (37) has shown that, for HDPE, APmt decreases with increasing entrance angle, up to 60°, then remains constant from 60° to 180°. 

Recently, Muliawan et al. (52), who have been studying melt fracture, and in particular sharkskin extrudate instabilities over the last decade, have presented interesting experimental results relating the extensional stress-Hencky strain behavior of polymer melts to their sharkskin (exit) and gross (capillary entrance) melt fracture behavior. For the purposes of this discussion, results obtained with two Nova Chemicals... 

We now turn to the gross melt fracture behavior. Estimates of the prevailing extensional rates at the capillary entrance indicate that their value corresponding to the critical gross melt fracture conditions is larger that the 20 s 1 used in this work. Nevertheless, since... 

H. L. LaNieve IE, and D. C. Bogue, Correlation of Capillary Entrance Pressure Drops with Normal Stress Data, J. Appl. Polym. Sci., 12, 353 (1968). 

All flows can be decomposed into shear and exten-sional components. The effectiveness of the flow field is dependent on the deformation rate, the relative values of shear and extension, and the micro structure of the fluid. Extensional flows are more effective in microstructure development, such as droplet breakup and mechanochemical reactions. However, such flows are difficult to generate and to maintain and therefore, in practical applications, capillary entrance/exit flows provide a suitable means of achieving extensional flows where the shear component of the flow field changes with the capillary entry-exit angle. Indeed, OFRs also generate extensional flows, which result in efficient droplet breakup in emulsification. Mixers in which the deformation rate and the relative values of shear/extension rates can be controlled are known as controlled deformation mixers. 

To illustrate the use of equation (1-120), we use the parameters of Table 1.3, with an oxygen consumption of 0.4 cm3 02/cm3-min, and estimate that the lowest oxygen partial pressure in the tissue surrounding the capillary entrance is 55.7 torr at r = Rr Therefore, all the tissue at this position is exposed to a healthy oxygen concen-... 

Since the tensile yield stress for solid PA-6 at 150°C was determined as = 15 kPa, independent of the rate of straining, the extensional stress in the capillary entrance was more than sufficient to deform the amorphous part of PA-6. Owing to crystallization, the elongated structures, once created, could neither disintegrate nor elastically retract to spherical shapes. 

One of the remarkable predictions of the theory that Taylor sought to check by his experiments was that an initially concentrated mass would be dispersed symmetrically about the point x = Ut. To this end the introduction of the small volume of permanganate solution at the capillary entrance could be modeled as a delta function input at time zero, namely... 

That such increases have been observed in apparently dilute solutions, particularly in capillary entrance and pore-flow experiments (23-26) (Figure... 

Nevertheless, as we shall show, we do see much larger dilatant effects are associated with the pore flow and capillary entrance results (23-26, 33) as we increase polymer concentration (though still below conventional C, the concentration at which contact between spheres is established). 

HPAA in Pore Flow. The preceding findings lead us to reinterpret results from porous media and capillary entrance flow. Strong non-Newtonian effects have previously been attributed to the increase in extensional viscosity associated with the coil-stretch transition, occurring when the strain rate exceeds the reciprocal of the lowest order conformational relaxation time (47-49),... 

Second, the strain required to stretch out a high molecular weight polymer into its nonlinear region is typically 200 (6). In capillary entrance experiments, however, the fluid strain is often quite small 25) (24). This small fluid strain does not apparently prevent the observation of the phenomenon of flow-resistance enhancement. The primary effect observed corresponds to the transient network flare behavior, and the evidence for this conclusion is as follows. 

In platelet perfusion experiments, platelet accumulation on reactive adhesive surfaces such as collagen coated glass shows a steady decrease with distance from the capillary inlet, as previously observed in similar flow systems (20,21). This axial dependence does not, in our system, appear to follow a simple mathematical law as a function of distance from the capillary entrance (22). Platelet deposition is thus calculated as the mean deposition over the entire length ( < 10 cm) of a single capillary and in comparative studies capillaries cf equal length and internal diameter are considered. 

FIGURE 3.15 Effect of capillary entrance angle on die swell for polypropylenes. (From Huang, D. White J.L. Polym. Eng. ScL, 1980, 20, 182. With permission.)... 

Evaluating the transient flux equation (12.2-7) at the capillary entrance (that is x = 0), and then integrating the result with respect to time from 0 to t we obtain the following quantity diffusing into the capillary ... 

A plot of Qo(t) versus t is shown in Figure 12.2-7. There is a rapid decrease of the pressure of the supply reservoir due to the very sharp pressure gradient at the capillary entrance at very short times. At sufficiently long time, the supply reservoir pressure approaches a linear asymptote given by ... 

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