Non-Newtonian fluids time-independent

It may be concluded that kinetic-energy terms can be evaluated for all time-independent non-Newtonian fluids with an accuracy probably sufficient for all engineering work. 

Figure H1.1.4 A complete flow curve for a time-independent non-Newtonian fluid. r 0 and i , are the viscosities associated with the first and second Newtonian plateaus, respectively. Regions (1) and (2) correspond to viscosities relative to low shear rates induced by sedimentation and leveling, respectively. Regions (3) and (4) correspond to viscosities relative to the medium shear rates induced by pouring and pumping, respectively. Regions (5) and (6) correspond to viscosities relative to high shear rates by rubbing and spraying, respectively.

Two protocols are presented for non-Newtonian fluids. Basic Protocol 1 is for time-independent non-Newtonian fluids and is a ramped type of test that is suitable for time-independent materials. The test is a nonequilibrium linear procedure, referred to as a ramped or stepped flow test. A nonquantitative value for apparent yield stress is generated with this type of protocol, and any model fitting should be done with linear models (e.g., Newtonian, Herschel-Bulkley unithit). 

The generalized approach of Metzner and Reed AIChE /., 1, 434 [1955]) for time-independent non-Newtonian fluids defines a modified Reynolds number as... 

Time-Independent Non-Newtonian Fluids. Time-independent non-Newtonian fluids are characterized by having the fluid viscosity as a function of the shear rate (or shear stress). However, the fluid viscosity is independent of the shear history of the fluid. Such fluids are also referred to as non-Newtonian viscous fluids". Figure 1 shows a typical shear diagram for the various time-independent non-Newtonian fluids. 

Calculate the frictional pressure gradient APf L for a time independent non-Newtonian fluid in steady state flow in a cylindrical tube if... 

Based on viscosity of the samples, the flow of samples is broadly classified into three categories, namely, Newtonian, time independent non-Newtonian and time dependent non-Newtonian. Newtonian fluids show shear stress independent constant viscosity profile where as non-Newtonian fluids show a viscosity profile, which is dependent on the shear force and time. In time independent non-Newtonian fluids, the shear stress does not vary proportionally to the shear rate. The time independent non-Newtonian fluids show mainly three types of flow. A decreasing viscosity with an increase of shear rate is called shear thinning or pseudoplastic flow (Figure 46.12a). An increasing viscosity with an increase of shear rate is called shear thickening or dilatant flow. Some fluids need application of certain amount of force before any flow is induced that are known as Bingham plastics. 

The most common type of time-independent non-Newtonian fluid behavioiu observed is pseudoplasticity or shear-thinning, characterised by an apparent viscosity which decreases with increasing shear rate. Both at very low and at very high shear rates, most shear-thinning polymer solutions and melts exhibit Newtonian behaviour, i.e. shear stress-shear rate plots become straight lines. 

Thus, the index m is the slope of the log-log plots of the wall shear stress Xw versus (8V/D) in the laminar region (the limiting condition for laminar flow is discussed in Section 3.3). Plots of x versus (8V/D) thus describe the flow behaviour of time-independent non-Newtonian fluids and may be used directly for scale-up or process design calculations. 

It should be realised that by defining the Reynolds number in this way, the same fiiction factor chart can be used for Newtonian and time-independent non-Newtonian fluids in the laminar region. In effect, we are writing. 

In the same way as there are many equations for predicting friction factor for turbulent Newtonian flow, there are munerous equations for time-independent non-Newtonian fluids most of these are based on dimensional considerations combined with experimental observations [Govier and Aziz, 1982 Heywood and Cheng, 1984]. There is a preponderance of correlations based on the power-law fluid behaviour and additionally some expressions are available for Bingham plastic fluids [Tomita, 1959 Wilson and Thomas, 1985], Here only a selection of widely used and proven methods is presented. 

The prediction of power consmnption for agitation of a given time-independent non-Newtonian fluid in a particular mixer, at a desired impeller speed, may be evaluated by the following procedme ... 

Figure 3.5-1. Shear diagram for Newtonian and time-independent non-Newtonian fluids.

E Laminar Flow of Time-Independent Non-Newtonian Fluids... 

Flow properties of a fluid. In determining the flow properties of a time-independent non-Newtonian fluid, a capillary-tube viscometer is often used. The pressure drop AP N/m for a given flow rate q m s is measured in a straight tube of length L m and diameter D m. This is repeated for different flow rates or average velocities V m/s. If the fluid is time-independent, these flow data can be used to predict the flow in any other pipe size. 

Pseudoplastic fluids are time-independent non-Newtonian fluids that are characterized by the following ... 

The Metzner and Reed approach has become a classical method of dealing with time-independent non-Newtonian fluids. It has been extended to Bingham slurries but the opinion of the author is that this approach is fairly difficult to use for Bingham slur-... 

Govier and Aziz (1972) indicated that once the initial period of stabilization is reached, the general form of pressure loss equations are the same as for time-independent non-Newtonian fluids. At the entry to a pipe, the flow may be laminar, but at a certain distance, once the entrance effects are overcome, the flow can transit to turbulence. 

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. 

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