Time-independent flow

Based on a mechanical model in a time-independent flow, de Gennes derivation tries to extrapolate it to a time-dependent chain behavior. His implicit assumptions have been criticised by Bird et al. [55]. More recent calculations extending the de Gennes dumbbell to the bead-spring situation [56] tend, nevertheless, to confirm the existence of a well-characterized CS transition results with up to 100-bead chains show a critical value of the strain rate at scs = 0.5035/iz which is just 7% higher than the value predicted by de Gennes. 

To stress this difference between the local and the classical Teorell s model let us work out the overall stationary resistance of the filter R(v, A, D) for a given time-independent flow rate v. We have analogously to (6.3.30)... 

TIME-INDEPENDENT FLOW BEHAVIOR Newtonian Model... 

For the most part, PFDs exhibit shear-thinning (pseudoplastic) rheological behavior that is either time-independent or time-dependent (thixotropic). In addition, many PFDs also exhibit yield stresses. The time-independent flow curves are illustrated in Figure 1. The shear-thinning behavior appears to be the result of breakdown of relatively weak structures and it may have important relationship to mouthfeel of the dispersions. Because the viscosity of non-Newtonian foods is not constant but depends on the shear rate, one must deal with apparent viscosity defined as ... 

Figure 1. Time-independent flow behavior of fluid...

Thus, the time-dependence of the flow generates chaotic trajectories that will enhance the mixing of fluid within these regions. However, the KAM tori formed by the remaining quasiperiodic orbits separate the domain into a set of disconnected regions with no advec-tive transport between them. Therefore, when the time-dependence is weak the fluid is only mixed within narrow layers around the resonant streamlines of the original time-independent flow. The areas... 

In the simplest case when chaotic advection is generated by a time-independent flow (e.g. in a three dimensional system) the asymp-... 

We considered time-independent flow rates into the system, but what if we had to handle a situation in which the flow rates were time dependent How would we handle the analysis of that situation ... 

Figure 1.4 Types of time-independent flow behaviour...

Here our interest is the time-independent flow. Taking the time average of the above equation over one period of oscillation gives... 

Fig. 5 shows the relation of shear stress and shear rate of silver paste with different wt % of thinner. The trend of non-Newtonian behavior is consistent with the results found by Chhabra Richardson, (1999) for the types of time-independent flow behavior. The time-independent non-Newtonian fluid behavior observed is pseudoplasticity or shear-thinning characterized by an apparent viscosity which decreases with increasing shear rate. Evidently, these suspensions exhibit both shear-thinning and shear thickening behavior over different range of shear rate and different wt% of thinner. The viscosity and shear stress relationship with increasing percentage of thinner is plotted in Fig 6. It is clearly observed that both viscosity and shear stress decreases resp>ectively. 

Summary of Transducer Comparison. In summary, the point measurement techniques of CTA and LDA can offer good spatial and temporal response. This makes them ideal for measurements of both time-independent flow statistics, such as moments of velocity (mean, RMS, etc.) and time-dependent flow statistics such as flow spectra and correlation functions at a point. Although rakes of these sensors can be built, multipoint measurements are limited due primarily to cost. 

---