Entrance pressure drop

Fig. 61. Degradation yield as a function of experimental entrance pressure drop (symbols are the same as used in Fig. 58) (The curves for r0 = 0.25 mm and r0 = 0.34 mm are experimentally indistin guisha ble)...

At right is shown data for the ratio of entrance pressure drop to shear stress at the capillary wall,... 

Person 1 Estimate the entrance region pressure drop, APgm, using the Bagley correction. What can you say about the percentage of the entrance pressure drop relative to the total pressure drop ... 

The ratio of entrance pressure drop to shear stress at the capillary wall versus Newtonian wall shear rate, r.i, PP n, PS o, LDPE +, HDPE , 2.5% PIBin mineral oil x, 10% PIB in decalin a, NBS-OB oil. Reprinted, by permission, from Z. Tadmorand C. G. Gogos, Principles of Polymer Processing, p. 537. Copyright 1979 by John Wiley Sons, Inc. 

Fig. 12.6 Bagley plots for a polystyrene (PS) melt at 200°C, from which N(T) can he evaluated AP at L/Dq —> 0 is the entrance pressure drop AP. [Reprinted by permission from J. L. White, Appl. Polym. Symp., No. 20, 155 (1973).]...

Polymer melts and solutions, on the other hand, are Theologically more complex fluids and, even under simple radiating flows in the entrance region, would need more stress components to sustain them thus there are larger entrance pressure drops. Additionally, the entrance flow patterns with polymer melts and solutions are typically more complex.6... 

The viscous contribution to the total entrance pressure loss is very small. [C. D. Han, Influence of the Die Entry Angle in the Entrance Pressure Drop, Recoverable Elastic Energy and Onset of Flow Instability in Polymer Melt Flow, AIChE. J., 17, 1480 (1970).]... 

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). 

Estimation of Entrance Pressure-Pressure Losses from the Entrance Flow Field17 Consider the entrance flow pattern observed with polymer melts and solutions in Fig. 12.16(a). The flow can be modeled, for small values of a, as follows for 0 < a/2 the fluid is flowing in simple extensional flow and for a/2 < 0 < rc/2 the flow is that between two coaxial cylinders of which the inner is moving with axial velocity V. The flow in the outer region is a combined drag-pressure flow and, since it is circulatory, the net flow rate is equal to 0. The velocity V can be calculated at any upstream location knowing a and the capillary flow rate. Use this model for the entrance flow field to get an estimate for the entrance pressure drop. 

A study was made of the ability of viscoelastic models to describe the measured material functions of unplasticised PVC during extrusion and to determine whether it was possible to reproduce the elastic properties of the large entrance pressure drop and small extrudate swell during the extrusion of PVC using a capillary rheometer. Models used were the Phan-Thien and Tanner model and the K-BKZ-Wagner model with a single exponential damping... 

In axisymmetric flow situations, the global pressure drop in a capillary rheometer is well described by the three constitutive equations. If one focuses on the entrance pressure drop, the numerical entrance pressure drop related to Bagley correction is foimd to be less important than the corresponding experimental data for the differential models for LDPE and LLDPE melts. For the Wagner integral constitutive equation, the computed entrance pressure drops are found to be lower for both fluids, but the computed values are closer to the experimental data for LLDPE than those related to the LDPE melt. This descrepancy, previously reported in the literature, needs further investigation. 

One technique for measurement of extensional flow that has been used to study various doughs is that of Cogswell (1972, 1978) for entrance flows. The analysis is based on several assumptions (Padmanabhan and Bhattacharya, 1993) (1) The flow is isothermal and creeping (negligible inertial effects), (2) the fluid is incompressible and has a pressure-independent viscosity, (3) the shear viscosity follows the power law model, t]a = Ky" (4) there is no slip at the edge of the converging profile, and (5) that the entrance pressure drop (Ape) in converging flow from a circular barrel in to a circular die can be considered to be made up of that due to shear (Ape,s) and extensional flow (Ape,E) ... 

The fundamental assumption of the classical rheological theories is that the liquid stmcture is either stable (Newtonian behavior) or its changes are well dehned (non-Newtonian behavior). This is rarely the case for flow of multiphase systems. For example, orientation of sheared layers may be responsible for either dilatant or pseudoplastic behavior, while strong interparticle interactions may lead to yield stress or transient behaviors. Liquids with yield stress show a plug flow. As a result, these liquids have drastically reduced extrudate swell, B = d/d (d is diameter of the extrudate, d that of the die) [Utracki et al, 1984]. Since there is no deformation within the plug volume, the molecular theories of elasticity and the relations they provide to correlate, for example either the entrance pressure drop or the extmdate swell, are not applicable. 

Convergent flow at the die entrance provides strong elongational flow. In 1989, Laun and Schuch, discussing the approximate methods of T g determination, derived the following relation between the entrance pressure drop in capillary flow and the shear stress at the capillary wall ... 

There are two main corrections that have to be applied to the information obtained from the capillary rheometer. First, there is an entrance pressure drop when the molten polymer enters the capillary, which is taken into account through the entrance or Bagley correction. This pressure drop is related to elastic deformations of the melt at the entry of the capillary [15]. Secondly, the non-Newtonian shear rate is expressed in terms of an apparent viscosity (defined in terms of a Newtonian flow). The relationship between the non-Newtonian and Newtonian shear rates, expressed as in the following equation, is known as the Rabinowitch correction [13, 16] ... 

Equation (17)allows an estimation of the entrance pressure drop, APent calculated, knowing the extrusion pressure and the... 

Using experimental results obtained with the three Santoprene grades studied, the entrance pressure drop and the apparent extensional viscosity were calculated according to equations (18) and and (19). Results are given in graphical terms in Figures 11 and 12 respectively. 

The entrance pressure drop (Pa, N/m ) can be found by the following relationship ... 

In order to investigate only the entrance pressure drop, Eq. 45 can be reduced as follows ... 

The first is the pressure rise which occurs due to the area change alone, without friction, and is identical to the corresponding term in the entrance pressure drop. The second term is the pressure loss associated with the irreversible free expansion following an abrupt expansion, and this term in the present case subtracts from the other. 

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