Flow curve reversal

The second category, time-dependent behaviour, is common but difficult to deal with. The best known type is the thixotropic fluid, the characteristic of which is that when sheared at a constant rate (or at a constant shear stress) the apparent viscosity decreases with the duration of shearing. Figure 1.21 shows the type of flow curve that is found. The apparent viscosity continues to fall during shearing so that if measurements are made for a series of increasing shear rates and then the series is reversed, a hysteresis loop is observed. On repeating the measurements, similar behaviour is seen but at lower values of shear stress because the apparent viscosity continues to fall. 

Cp X heating rate) is termed the reversing heat flow component. The non-reversing part is obtained by subtracting this value from the total heat flow curve. It is important to note that all... 

Pipe Flow. The rheological properties of cement slurries have also been characterized using pipe viscometers (13,15-18). The experimental results show different flow patterns. In some circumstances, relatively large pipe diameters and high shear rates, the flow curves, and shear-stress at the wall versus Newtonian shear rate at the wall are independent of pipe diameter (16, 17). The reverse situation is observed when pipe diameters are relatively small, of the order of 5 mm (13, 15). The diameter dependency of the flow curves can be explained, as discussed... 

Thixotropic Pseudoplastic flow that is time-dependent. At constant applied shear rate, viscosity gradually decreases, and in a flow curve hysteresis occurs. That is, after a given shear rate is applied and then reduced, it takes some time for the original dispersed species alignments to be restored. Thixotropy in gels is sometimes termed reversible sol-gel transformation. 

Figure 7. TMDSC reversing and nonreversing heat flow curves for the heating cycle of as-received Nitinol SE [37]. Reproduced with permission from Elsevier Science.

The TMDSC plots in Figures 11 and 12 for Nitinol are complex with shallow peaks [36]. Because of the high-sensitivity setting on the vertical axis, the reversing heat flow curve is not a straight line. 

Figure 5. Reversing heat flow curves of PS/P(S-pSF46) (50-50wt%) aged for indicated times at 92 °C.

Fan surge also can occur if a fan s pressure versus flow curve has a hump as the flow demand moves back and forth across that hump, momentarily creating higher pressure downstream than upstream at the fan outlet, causing reverse flow and cycling. 

Thixotropy is a reversible process and in an immobile state of fluid the continuous, progressive ordering of structure occurs. The one flow curve without hysteresis can be obtained, but the share must continue until the equihbrium is attained. The structure of ordinary tixotropic fluids is totally destroyed at high shear stress. After the shear stress elimination they behave like normal fluids until the stracture is rebuilt. There are also the tixotropic plastic fluids (Fig. 5.5) which do not lose totally the features of plastic fluids which is evident from the stable, however, even low yield stress value. Some suspensions show outstanding features the stracture is formed under the shear stress exclusively and without shear it collapses these fluids show a rheopexy. These properties are appear at moderate shear rate only. 

When the arterial obstruction is complete, color Doppler imaging can show flow inversion in the cavernosal artery, easily detected in the longitudinal and transversal scans because of the different color of flow (Fig. 6.16). At spectral analysis the flow is reversed in the proximal portion of the artery and normally directed in the distal part. The curve obtained is of low amplitude with increased time to peak. The... 

The flow curve (upward) was measured with a shear-rate ramp over 1 min from 0 to 50 1/s, then the ramp was reversed to measure the downward flow curve. The area between the upward and downward curves was calculated as a measure for the thixotropy using the data analysis option of RheoWin software. 

The COAST computer program is used to calculate the reactor coolant flow coast down transient for any combination of active and inactive pumps and forward or reverse flow in the hot or cold legs. The equations of conservation of momentum are written for each of the flow paths of the COAST model assuming unsteady one-dimensional flow of an incompressible fluid. The equation of conservation of mass is written for the appropriate nodal points. Pressure losses due to friction, and geometric losses are assumed proportional to the flow velocity squared. Pump dynamics are modelled using a head-flow curve for a pump at fiill speed and using four-quadrant curves, which are parametric diagrams of pump head and torque on coordinates of speed versus flow, for a pump at other than full speed. 

The formulas just developed allow the relation of pressure gradient, velocity profile, and volumetric flow rate os long as the shear stress-shear rate relation (flow curve) for the fluid is known. The problem in viscometry is just the reverse How is the flow curve obtained from pressure drop-volumetric flow rate measurements in a cylindrical tube If the mathematical form of the flow curve, that is, a particular constitutive equation, is assumed a priori, the integrated equations as developed above may be used to establish the parameters in the constitutive relation. For example, if it is assumed that the power law represents the flow curve of a fluid under investigation, two readings of dP/dx versus Q in a tube of known R will allow calculation of K and n from (16.13). However, in the general case, the form of the constitutive equation is not known a priori, and must be established by viscometry. This may be done, first by integrating (16.12) by parts... 

For those gels in which shear thinning occurs (ALSP 1-3%), the process can be reversed by either the removal or the reduction of the shem-strain rate. That is, the breakdown process is reversible. Each point on the non-linear zone of the flow curve corresponds to a state of dynamic equilibrium between processes of deformation and recovery of structure of the matrix. The situation can be represented by the following equation ... 

Figure 9.40 Total, reversing and non-reversing heat flow curves obtained during the heating of a non-annealed 65% w/w sucrose solution. Endothermic changes are in the negativedirection. 7, glass transition ER, enthalpic relaxation D, devitrification ID, ice dissolution. (Taken from [140, Copyright (2001), with kind permission of Springer Science and Business Media.)...

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