Time-independent fluids

CLASSIFICATION OF INELASTIC TIME-INDEPENDENT FLUIDS 5 L2.2 Generalized Newtonian Unids... 

CLASSIFICATION OF INEL,ASTIC TIME-INDEPENDENT FLUIDS 7... 

Purely viscous fluids are further classified into time-independent and time-dependent fluids. For time-independent fluids, the shear stress depends only on the instantaneous shear rate. The shear stress for time-dependent fluids depends on the past history of the rate of deformation, as a result of structure or orientation buildup or breakdown during deformation. 

All fluids for which the viscosity varies with shear rate are non-Newtonian fluids. For uou-Newtouiau fluids the viscosity, defined as the ratio of shear stress to shear rate, is often called the apparent viscosity to emphasize the distiuc tiou from Newtonian behavior. Purely viscous, time-independent fluids, for which the apparent viscosity may be expressed as a function of shear rate, are called generalized Newtonian fluids. 

Fluids whose behaviour can be approximated by the power-law or Bingham-plastic equation are essentially special cases, and frequently the rheology may be very much more complex so that it may not be possible to fit simple algebraic equations to the flow curves. It is therefore desirable to adopt a more general approach for time-independent fluids in fully-developed flow which is now introduced. For a more detailed treatment and for examples of its application, reference should be made to more specialist sources/14-17) If the shear stress is a function of the shear rate, it is possible to invert the relation to give the shear rate, y = —dux/ds, as a function of the shear stress, where the negative sign is included here because velocity decreases from the pipe centre outwards. 

Until much more progress is made on these very fundamental approaches, greater accuracy is believed possible in engineering work that is based on the better developed discussion reviewed here. To this end a method has recently been proposed whereby the properties of all four time-independent fluids (Newtonian, pseudoplastic, dilatant, and Bingham plastic) may be quantitatively compared. 

Chapter HI relates to measurement of flow properties of foods that are primarily fluid in nature, unithi.i surveys the nature of viscosity and its relationship to foods. An overview of the various flow behaviors found in different fluid foods is presented. The concept of non-Newtonian foods is developed, along with methods for measurement of the complete flow curve. The quantitative or fundamental measurement of apparent shear viscosity of fluid foods with rotational viscometers or rheometers is described, unithi.2 describes two protocols for the measurement of non-Newtonian fluids. The first is for time-independent fluids, and the second is for time-dependent fluids. Both protocols use rotational rheometers, unit hi.3 describes a protocol for simple Newtonian fluids, which include aqueous solutions or oils. As rotational rheometers are new and expensive, many evaluations of fluid foods have been made with empirical methods. Such methods yield data that are not fundamental but are useful in comparing variations in consistency or texture of a food product, unit hi.4 describes a popular empirical method, the Bostwick Consistometer, which has been used to measure the consistency of tomato paste. It is a well-known method in the food industry and has also been used to evaluate other fruit pastes and juices as well. 

Figure H1.1.2 Rheograms or flow curves for five time-independent fluids. The Newtonian fluid yields a straight line that emanates from the origin. The other four examples are non-Newtonian fluids. o0 represents a yield stress point, which is common for plastic fluids.

Following Gaskell s work, a great deal of effort was invested by numerous researchers in the field to improve on his model. Most of this effort, however, basically concentrated on solving the Gaskell model with more realistic, constitutive equations and attempts to account for nonisothermal effects. In the original Gaskell model, a purely viscous (nonelastic and time-independent) fluid model is assumed, with specific... 

Time-independent fluids Fluids in which the viscous properties do not vary with time. 

Figure 3.79 shows the viscosity profiles for time-dependent fluids. From Figure 3.79 one may define the following systems. Time-independent fluids obviously undergo no change in viscosity with respect to time. Rheopectic fluids show an increase in viscosity with respect to time. Thixotropic fluids show a decrease in viscosity with respect to time. 

The cone-and-plate viscometer is another type of rotational viscometer and is schematically shown in Fig. 10.4. For any time-independent fluid, the following equations apply if the... 

Time-independent fluids in which the shear stress is a nonlinear and single-valued function of the strain rate. 

Capillary viscometers are the most commonly used instruments for the measurement of viscosity due, in part, to their relative simplicity, low cost and (in the case of long capillaries) accuracy. However, when pressure drives a fluid through a pipe, the velocity is a maximum at the centre the velocity gradient or shear rate y are a maximum at the wall and zero in the centre of the flow. The flow is therefore non-homogeneous and capillary viscometers are restricted to measuring steady shear functions, i.e. steady shear stress-shear rate behaviour for time independent fluids [Macosko 1994]. Due to their inherent similarity to... 

Generalised approach for laminar flow of time-independent fluids... 

It is useful to define an appropriate Reynolds number whieh will result in a unicpie frietion factor-Reynolds number curve for all time-independent fluids in laminar flow in circular pipes. Metzner and Reed [1955] outlined a generalised approach obviating this difficulty. The starting point is equation 3.21 ... 

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