Shear flow characteristics

Parameters of the shear flow, characteristic angles of orientation and experimental root mean... 

A general study of shear flow characteristics was performed on a material containing about 60% of starch and natural additives and 40% of ethylene-vinyl alcohol copolymer 40/60 mol/mol [120]. A strong pseudoplastic... 

X. Li and S.-Q. Wang. Studying steady shear flow characteristics of entangled polymer solutions with parallel mechanical superposition. Macromolecules, 43 (2010), 5904-5908. 

To constitute the We number, characteristic values such as the drop diameter, d, and particularly the interfacial tension, w, must be experimentally determined. However, the We number can also be obtained by deduction from mathematical analysis of droplet deforma-tional properties assuming a realistic model of the system. For a shear flow that is still dominant in the case of injection molding, Cox [25] derived an expression that for Newtonian fluids at not too high deformation has been proven to be valid ... 

At least, in absolute majority of cases, where the concentration dependence of viscosity is discussed, the case at hand is a shear flow. At the same time, it is by no means obvious (to be more exact the reverse is valid) that the values of the viscosity of dispersions determined during shear, will correlate with the values of the viscosity measured at other types of stressed state, for example at extension. Then a concept on the viscosity of suspensions (except ultimately diluted) loses its unambiguousness, and correspondingly the coefficients cn cease to be characteristics of the system, because they become dependent on the type of flow. 

Newtonian flow It is a flow characteristic where a material (liquid, etc.) flows immediately on application of force and for which the rate of flow is directly proportional to the force applied. It is a flow characteristic evidenced by viscosity that is independent of shear rate. Water and thin mineral oils are examples of fluids that posses Newtonian flow. 

Dilatant Basically a material with the ability to increase the volume when its shape is changed. A rheological flow characteristic evidenced by an increase in viscosity with increasing rate of shear. The dilatant fluid, or inverted pseudoplastic, is one whose apparent viscosity increases simultaneously with increasing rate of shear for example, the act of stirring creates instantly an increase in resistance to stirring. 

The branch of science which is concerned with the flow of both simple (Newtonian) and complex (non-Newtonian) fluids is known as rheology. The flow characteristics are represented by a rheogram, which is a plot of shear stress against rate of shear, and normally consists of a collection of experimentally determined points through which a curve may be drawn. If an equation can be fitted to the curve, it facilitates calculation of the behaviour of the fluid. It must be borne in mind, however, that such equations are approximations to the actual behaviour of the fluid and should not be used outside the range of conditions (particularly shear rates) for which they were determined. 

Because it is very difficult to measure the flow characteristics of a material at very low shear rates, behaviour at zero shear rate can often only be assessed by extrapolation of experimental data obtained over a limited range of shear rates. This extrapolation can be difficult, if not impossible. From Example 3.10 in Section 3.4.7, it can be seen that it is sometimes possible to approximate the behaviour of a fluid over the range of shear rates for which experimental results are available, either by a power-law or by a Bingham-plastic equation. 

A highly concentrated suspension of flocculated kaolin in water behaves as a pseudo-homogeneous fluid with shear-thinning characteristics which can be represented approximately by the Ostwald-de Waele power law, with an index of 0.15. It is found that, if air is injected into the suspension when in laminar flow, the pressure gradient may be reduced even though the flowrate of suspension is kept constant, Explain how this is possible in slug flow and estimate the possible reduction in pressure gradient for equal volumetric flowrates of suspension and air. 

Viscoelasticity illustrates materials that exhibit both viscous and elastic characteristics. Viscous materials tike honey resist shear flow and strain linearly with time when a stress is applied. Elastic materials strain instantaneously when stretched and just as quickly return to their original state once the stress is removed. Viscoelastic materials have elements of both of these properties and, as such, exhibit time-dependent strain. Viscoelasticity is the result of the diffusion of atoms or molecules inside an amorphous material. Rubber is highly elastic, but yet a viscous material. This property can be defined by the term viscoelasticity. Viscoelasticity is a combination of two separate mechanisms occurring at the same time in mbber. A spring represents the elastic portion, and a dashpot represents the viscous component (Figure 28.7). 

Viscoelastic properties have been discussed in relation to molar mass, concentration, solvent quality and shear rate. Considering the molecular models presented here, it is possible to describe the flow characteristics of dilute and semi-dilute solutions, as well as in simple shear flow, independent of the molar mass, concentration and thermodynamic quality of the solvent. The derivations can be extended to finite shear, i.e. it is possible to evaluate T) as a function of the shear rate. Furthermore it is now possible to approximate the critical conditions (critical shear rate, critical rate of elongation) at which the onset of mechanical degradation occurs. With these findings it is therefore possible to tune the flow features of a polymeric solution so that it exhibits the desired behaviour under the respective deposit conditions. 

Shah and Nelson [33] introduced a convective mass transport device in which fluid is introduced through one portal and creates shear over the dissolving surface as it travels in laminar flow to the exit portal. They demonstrated that this device produces expected fluid flow characteristics and yields mass transfer data for pharmaceutical solids which conform to convective diffusion equations. 

Shear cell measurements offer several pieces of information that permit a better understanding of the material flow characteristics. Two parameters, the shear index, n, and the tensile strength, S, determined by fitting simplified shear cell data to Eq. (6), are reported in Table 2. Because of the experimental method, only a poor estimate of the tensile strength is obtained in many cases. The shear index estimate, however, is quite reliable based on the standard error of the estimate shown in parenthesis in Table 2. The shear index is a simple measure of the flowability of a material and is used here for comparison purposes because it is reasonably reliable [50] and easy to determine. The effective angle of internal... 

The influence of consolidation load on the flowability of sucrose is shown in Fig. 8. For this material, the effective angle of internal friction is nearly constant yet the shear index is seen to change with state of consolidation. Apparently, for sucrose, increased consolidation results in a somewhat more free flowing although still cohesive material. As such, sucrose can be considered a complex powder [49] with perhaps somewhat better flow characteristics when consolidated (as might occur in a hopper). 

The second subscript N is a reminder that this is the wall shear rate for a Newtonian fluid. The quantity (8u/d,), or the equivalent form in equation 3.13, is known as the flow characteristic. It is a quantity that can be calculated for the flow of any fluid in a pipe or tube but it is only in the case of a Newtonian fluid in laminar flow that it is equal to the magnitude of the shear rate at the wall. 

Owing to the different relationship between t and y for a non-Newtonian fluid, the shear rate at the wall is not given by equation 3.13 but can be expressed as the flow characteristic multiplied by a correction factor as shown in Section 3.2. 

The flow rate-pressure drop measurements shown in Table 3.1 were made in a horizontal tube having an internal diameter d, = 6 mm, the pressure drop being measured between two tappings 2.00 m apart. The density of the fluid, p, was 870 kg/m3. Determine the wall shear stress-flow characteristic curve and the shear stress-true shear rate curve for this material. 

Using these expressions for tw and 8u/d, enables the values in the first two columns of Table 3.2 to be calculated. This provides the shear stress-flow characteristic curve. 

Wall shear stress-flow characteristic curves and scale-up for laminar flow... 

Equation 3.17 shows that the flow characteristic is a unique function of the wall shear stress for a particular fluid ... 

Recall that the wall shear rate for a Newtonian fluid in laminar flow in a tube is equal to —8w/d,. In the case of a non-Newtonian fluid in laminar flow, the flow characteristic is no longer equal to the magnitude of the wall shear rate. However, the flow characteristic is still related uniquely to tw because the value of the integral, and hence the right hand side of equation 3.17, is determined by the value of tw. 

If the fluid flows in two pipes having internal diameters dti and dt2 with the same value of the wall shear stress in both pipes, then from equation 3.17 the values of the flow characteristic are equal in both pipes ... 

Shear stress at the pipe wall against flow characteristic for a non-Newtonian fluid flowing in a pipe... 

Logarithmic plot of wall shear stress against flow characteristic the gradient at a point defines n ... 

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