Flow behaviors time-dependent

The Weltman (1943) model has been used to characterize thixotropic (Paredes et al., 1988) behavior and of antithixotropic behavior (da Silva et al., 1997) of foods  

A model to study thixotropic behavior of foods exhibiting yield stress was devised by Tiu and Boger (1974) who studied the time-dependent rheological behavior of mayonnaise by means of a modified Herschel-Bulkley model  

It can be shown (Tiu and Boger, 1974), that a plot of 1 /( ja— e) versus time will yield a straight line of slope a and repeating the procedure at other shear rates will establish the relationship between a and y, and hence k and y from Equation 2.20. For a commercial mayonnaise sample, values of the different parameters were Ae = 0.63, (TOH = 7.0 Pa, ATh = 28.5 Pa s , h = 0.32, and k was a weak function of shear rate specifically, k = 0.012 (Tiu and Boger, 1974). 

Once in a while, polymer systems will falsely appear to be thixotropic or rheopectic. Careful checking (including before and after molecular weight determinations) invariably shows that the phenomenon is not reversible and is due to degradation or crosslinking of the polymer when in the viscometer for long periods of time, particularly at elevated temperatures. Other transient time-dependent effects in polymers are due to elasticity, and will be considered later, but for chemically stable polymer melts or solutions, the steady-state viscous properties are time independent. We treat only such systems from here on. 

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Flow models have been used also to derive expressions for velocity profiles and volumetric flow rates in tube and channel flows, and in the analysis of heat transfer phenomenon. Numerous flow models can be encountered in the rheology literature and some from the food rheology literature are listed in Table 2-1. Also, here those models that have found extensive use in the analysis of the flow behavior of fluid foods are discussed. Models that account for yield stress are known as viscoplastic models (Bird et al., 1982). For convenience, the flow models can be divided in to those for time-independent and for time-dependent flow behavior. 

Similarly, the majority of the investigations reported conclude that for both rectangular and cylindrical columns the high frequency instabilities are 3D and have to be resolved by the use of 3D models. Nevertheless, in a few recent papers [5, 6, 21] it has been shown that 2D mixture model formulations can be used to reproduce the time-dependent flow behavior of 2D bubble... 

One further variable that greatly influences flow behavior is time. It is often found that, at constant shear rate, a fluid s viscosity varies as a fimction of time. The two types of time dependent flow behavior are shown in Figure 13.9. Thixotropy is encountered when the viscosity decreases with time, returning to its original value... 

The Newtonian and non-Newtonian fluids discussed in section 8.2 are time independent that is, the viscosity remains constant as long as the shear rate does not change. However, some fluids exhibit time-dependent flow behavior and their viscosities change with the time of shearing. Two most important time-dependent fluids are thixotropic and rheopectic. At a fixed shear rate, the viscosity of a thixotropic fluid decreases with time, while the viscosity of a rheopectic fluid increases with time (Figure 8.7). 

Time dependence Viscoelastic deformation is a transition type behavior that is characterized by the occurrence of both elastic strain and time-dependent flow. It is the time dependence of the mechanical properties of plastics that makes the behavior of these materials difficult to analyze by mathematical theory. 

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. 

This section draws heavily from two good books Colloidal Dispersions by Russel, Seville, and Schowalter [31] and Colloidal Hydrodynamics by Van de Ven [32] and a review paper by Jeffiey and Acrivos [33]. Concentrated suspensions exhibit rheological behavior which are time dependent. Time dependent rheological behavior is called thixotropy. This is because a particular shear rate creates a dynamic structure that is different than the structure of a suspension at rest. If a particular shear rate is imposed for a long period of time, a steady state stress can be measured, as shown in Figure 12.10 [34]. The time constant for structure reorganization is several times the shear rate, y, in flow reversal experiments [34] and depends on the volume fraction of solids. The viscosities discussed in Sections 12.42.2 to 12.42.9 are always the steady shear viscosity and not the transient ones. 

For time-dependent flows, in addition to the factors discussed above, the values of time step and number of iterations per time step, govern the overall convergence behavior. In general, the selected time step should be at least an order of magnitude smaller than the smallest relevant time scale of the modeled flow process. If the... 

Time-dependent flow. None of the curves in Fig. 3.2 depends on the history of the fluid, and a given sample of material shows the same behavior no matter how... 

Another drawback to capillary viscometers is that time-dependent rheological behavior cannot be investigated because the flowing fluid has different shearing time history. 

Amorphous solid dispersions are prepared primarily with amorphous and/or semicrystalline materials, and therefore, the mechanical behavior of the extrudate is generally viscoelastic in nature. The materials viscoelasticity implies a strain-rate dependence of the mechanical response and time-dependent mechanical behavior such as creep and stress relaxation. For example, in cases of high strain rates, these materials tend to be more brittle than under slower strain rates where viscous flow and other molecular relaxations can dissipate the energy without fracture. Thus, high strain rates are beneficial for particle size reduction operations. 

Substituting the appropriate values shows that the capillary pressure drop will increase from 78% to 100% of the applied pressure as the melt flow indexer goes from completely filled to empty. Thus, a 50% increase in the output rate is possible, as has been shown for polyethylene (PE) by Skinner [13]. With PF, the position is shown to be worse by Charley [IS], who performed extensive experiments for using the MFI test for molten PP. Despite this time-dependent deformation behavior, there is no conection recommended for entrance and exit abnormalities. This would also be difficult to specify, because the conections would be expected to vary from polymer to polymer. 

Thixotropy and Other Time Effects. In addition to the nonideal behavior described, many fluids exhibit time-dependent effects. Some fluids increase in viscosity (rheopexy) or decrease in viscosity (thixotropy) with time when sheared at a constant shear rate. These effects can occur in fluids with or without yield values. Rheopexy is a rare phenomenon, but thixotropic fluids are common. Examples of thixotropic materials are starch pastes, gelatin, mayoimaise, drilling muds, and latex paints. The thixotropic effect is shown in Figure 5, where the curves are for a specimen exposed first to increasing and then to decreasing shear rates. Because of the decrease in viscosity with time as weU as shear rate, the up-and-down flow curves do not superimpose. Instead, they form a hysteresis loop, often called a thixotropic loop. Because flow curves for thixotropic or rheopectic Hquids depend on the shear history of the sample, different curves for the same material can be obtained, depending on the experimental procedure. 

Results from measurements of time-dependent effects depend on the sample history and experimental conditions and should be considered approximate. For example, the state of an unsheared or undisturbed sample is a function of its previous shear history and the length of time since it underwent shear. The area of a thixotropic loop depends on the shear range covered, the rate of shear acceleration, and the length of time at the highest shear rate. However, measurements of time-dependent behavior can be usehil in evaluating and comparing a number of industrial products and in solving flow problems. 

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