Shear stress capillary

Densification during liquid-phase sintering occurs in tliree stages. Initially, liquid fonns at particle intersections and redistributes tliroughout the particulate mass under the influence of the capillary action. Shear stresses due to the... 

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. 

Gla.ss Ca.pilla.ry Viscometers. The glass capillary viscometer is widely used to measure the viscosity of Newtonian fluids. The driving force is usually the hydrostatic head of the test Hquid. Kinematic viscosity is measured directly, and most of the viscometers are limited to low viscosity fluids, ca 0.4—16,000 mm /s. However, external pressure can be appHed to many glass viscometers to increase the range of measurement and enable the study of non-Newtonian behavior. Glass capillary viscometers are low shear stress instmments 1—15 Pa or 10—150 dyn/cm if operated by gravity only. The rate of shear can be as high as 20,000 based on a 200—800 s efflux time. 

Polymer melts are frequendy non-Newtonian. In this case the earlier expression given for the shear rate at the capillary wall does not hold. A correction factor (3n + 1)/4n, called the Rabinowitsch correction, must be appHed in such a way that equation 21 appHes, where 7 is the tme shear rate at the wall and nis 2l power law factor (eq. 22) determined from the slope of a log—log plot of the tme shear stress at the wad, T, vs 7. For a Newtonian hquid, n = 1. A tme apparent viscosity, Tj, can be calculated from equation 23. 

More recent developments in the rolling ball area include an automated micro viscometer, the Paar AMV 200, from Paar Physica. The specimen to be measured is introduced into a glass capillary down which a gold-covered steel ball roUs. The rolling time is measured automatically. The shear stress may be varied by changing the inclination angle of the capillary tube. The shear rate range is 10 1000, which makes the instmment useflil for... 

The melt-spinning process used to convert mesophase pitch into fiber form is similar to that employed for many thermoplastic polymers. Normally, an extruder melts the pitch and pumps it into the spin pack. Typically, the molten pitch is filtered before being extruded through a multi-holed spinnerette. The pitch is subjected to high extensional and shear stresses as it approaches and flows through the spinnerette capillaries. The associated torques tend to orient the liquid crystalline pitch in a regular transverse pattern. Upon emerging from the... 

Swelling Ratios Due to Shear Stresses (a) Long Capillary... 

Fig. 5.10 shows an annular element of fluid of radius r and thickness dr subjected to a shear stress in the capillary. When the element of fluid emerges from the die it will recover to the form shown by ABCD. 

A slit die is designed on the assumption that the material is Newtonian, using apparent viscous properties derived from capillary rheometer measurements, at a particular wall shear stress, to calculate the volumetric flow rate through the slit for the same wall shear stress. Using the correction factors already derived, obtain an expression for the error involved in this procedure due to the melt being non-Newtonian. Also obtain an expression for the error in pressure drop calculated on the same basis. What is the magnitude of the error in each case for a typical power law index n = 0.377... 

Under the steady-state flow conditions, there is an increasing tendency of this fiberlike structure moving toward the capillary wall as shear stress, flow flux, and radial position increase. In fact, we often obtained extru-dates with a very thin TLCP-rich skin layer from the capillary test [8]. 

The shear-stress distribution is uneven in a capillary. Since an interfacial slippage takes place only at a point where the shear stress exceeds a critical value, a critical radius r,- can be defined as ... 

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. 

Hollow fiber reactors [7] and dialysis reactors [8] avoid shear stress by separating cells and flowing media. In both reactors nutrient supply takes place by diffusion through the capillary wall or the dialysis membrane. 

Fig. 2. Variation of specific death rate with average shear stress, under laminar and turbulent conditions, in the capillary flow loop apparatus [54,121]...

In capillary shear studies involving M. citrifolia, the extent of cell damage was found to increase with the prevailing level of shear stress (Fig. 2). Trials involving capillary tubes of different lengths yielded similar levels of viability loss at equivalent exposure times, indicating that the death rate is determined by the shear stress alone. 

Consistency Indices for the reciprocating capillary viscometers are calculated In a similar manner except that 1C 1s determined directly from log shear rate vs log shear stress data. 

There are a number of techniques that are used to measure polymer viscosity. For extrusion processes, capillary rheometers and cone and plate rheometers are the most commonly used devices. Both devices allow the rheologist to simultaneously measure the shear rate and the shear stress so that the viscosity may he calculated. These instruments and the analysis of the data are presented in the next sections. Only the minimum necessary mathematical development will he presented. The mathematical derivations are provided in Appendix A3. A more complete development of all pertinent rheological measurement functions for these rheometers are found elsewhere [9]. 

Before the viscosity can be calculated from capillary data, as mentioned above, the apparent shear rate, 7 , must be corrected for the effect of the pseudoplastic nature of the polymer on the velocity profile. The calculation can be made only after a model has been adopted that relates shear stress and shear rate for this concept of a pseudoplastic shear-thinning material. The model choice is a philosophical question [11] after rheologlsts tried numerous models, there are in general two simple models that have withstood substantial testing when the predictions are compared with experimental data [1]. The first Is ... 

The calculation of the shear rate at the capillary wall, 7 , is computed from the function slope of Fig 3.18 and the apparent shear rate using Eq. 3.36. The derivative of the function appears relatively constant over the shear stress range for Fig. 3.18. Many resin systems will have derivatives that vary from point to point. The corrected viscosity can then be obtained by dividing the shear stress at the wall by the shear rate i ,. Equation 3.36 is known as the Weissenberg-Rabinowitsch equation [9]. 

Capillary Length, mm Pressure Change, MPa Regressed Pressure Change, MPa Corrected Pressure Change, Mpa Wall Shear Stress, Pa Capillary Length Divided by Radius, L/R... 

The shear stresses at the wall of the capillaries are calculated using the corrected pressure change and Eq. 3.34. 

The melt Index test measures the flow property at a fixed wall shear stress In the capillary. The shear stress depends on the load specified for the condition and it is provided in Table 3.8. The apparent shear rate at the capillary wall that the resin experiences depends on the Ml value measured, and it can be calculated using a modification of Eq. 3.33 as follows ... 

Table 3.8 Test Conditions and Shear Stress at the Capillary Wall for Melt Index Testing as Prescribed by ASTM D1238-04c [15]...

Condition Temperature, °C Total Load with Piston, kg Shear Stress at the Capillary Wall, kPa... 

It should be noted that the shear stress caused by the flow of blood through arteries and capillaries can be very high. 

Many authors have worked on drop deformation and breakup, beginning with Taylor. In 1934, he published an experimental work [138] in which a unique drop was submitted to a quasi-static deformation. Taylor provided the first experimental evidence that a drop submitted to a quasi-static flow deforms and bursts under well-defined conditions. The drop bursts if the capillary number Ca, defined as the ratio of the shear stress a over the half Laplace pressure (excess of pressure in a drop of radius R. Pl = where yint is the interfacial tension) ... 

Two main types of viscometers are suitable for the determination of the viscosity of a polymer melt The rotation viscometer (Couette viscometer, cone-plate viscometer) and the capillary viscometer or capillary extrusiometer. The latter are especially suitable for laboratory use since they are relatively easy to handle and are also applicable in the case of high shear rates. With the capillary extrusiometer the measure of fluidity is not expressed in terms of the melt viscosity q but as the amount of material extruded in a given time (10 min). The amount of ex-trudate per unit of time is called the melt index or melt flow index i (MFI). It is also necessary to specify the temperature and the shearing stress or load. Thus MFI/2 (190 °C)=9.2 g/10 min means that at 190 °C and 2 kg load, 9.2 g of poly-... 

On the one hand in a flow field shear stresses t are exerted on a droplet which cause a deformation into an ellipsoid on the other hand the surface area of the droplet is increased by this deformation, so that the interfacial energy first effect becomes smaller in comparison to the second one, which results in an eqnilibrium at which no droplets are broken-np (expressed in the capillary number Ca = tI(cj/R), (see MT 9.1.5). 

The membrane viscometer must use a membrane with a sufficiently well-defined pore so that the flow of isolated polymer molecules in solution can be analyzed as Poiseuille flow in a long capillary, whose length/diameter is j 10. As such the viscosity, T, of a Newtonian fluid can be determined by measuring the pressure drop across a single pore of the membrane, knowing in advance the thickness, L, and cross section. A, of the membrane, the radius of the pore, Rj., the flow rate per pore, Q,, and the number of pores per unit area. N. The viscosity, the maximum shear stress, cr. and the velocity gradient, y, can be calculated from laboratory measurements of the above instrumental parameters where Qj =... 

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