Non-Newtonian materials

The other models can be appHed to non-Newtonian materials where time-dependent effects are absent. This situation encompasses many technically important materials from polymer solutions to latices, pigment slurries, and polymer melts. At high shear rates most of these materials tend to a Newtonian viscosity limit. At low shear rates they tend either to a yield point or to a low shear Newtonian limiting viscosity. At intermediate shear rates, the power law or the Casson model is a useful approximation. 

Mewtonian andMon-Mewtonian Materials. A Newtonian material s viscosity is shear-independent, whereas non-Newtonian materials are shear-dependent (Eig. 7). Eor most potting materials, a Newtonian material is preferred because the material is required to flow under all electronic components, but not be susceptible to shear. However, when flowable material is used for conformal coating appHcations, a non-Newtonian material with thixotropy agent added is desired since the material should flow on the electronic substrate but stop at the edge without creeping or mnover at the circuitry. 

Viscosity, apparent Defined as the ratio between shear stress and shear rate over a narrow range for a plastic melt. It is a constant for Newtonian materials but a variable for plastics that are non-Newtonian materials. 

Rheologically, the flow of many non-Newtonian materials can be characterized by a time-independent power law function (sometimes referred to as the Ostwald-deWaele equation)... 

A discussion of the flow of non-Newtonian materials under certain complex industrial conditions such as in calendering and coating machines was not felt to be warranted at this time in view of the general dearth... 

In view of the usually viscous nature of highly non-Newtonian materials it is not likely that Reynolds numbers appreciably greater than 70,000 will be very common, at least for some time to come. This fact places great importance on the region below NRe = 70,000, and its detailed study would appear to be of primary importance. In well-developed turbulent flow, which apparently may be delayed to... 

Meskat (M8) has presented a mathematical analysis of the effect of fluctuations in pressure and other variables on the comparative fluctuations in extrusion rates of Newtonian and non-Newtonian fluids. This work indicates the possibility of amplification of such fluctuations under certain circumstances with non-Newtonians rather than the uniform damping predicted for Newtonian behavior. If the validity of this analysis can be proved, it would warrant major attention being given to the problem of unsteady flow of non-Newtonian materials. 

Since the data from both rotational viscometers and capillary tubes may be used to obtain the desired shear stress-rate of shear relationships, it may be concluded that properly designed viscometers of both types are theoretically of equal utility. The reader who may be concerned by the many invalid literature statements to the contrary should refer to some of the many references (A3, Kl, 06, P4, R2, V2) where this has also been proved experimentally on a great variety of non-Newtonian materials. 

If one considers fluid flowing in a pipe, the situation is highly illustrative of the distinction between shear rate and flow rate. The flow rate is the volume of liquid discharged from the pipe over a period of time. The velocity of a Newtonian fluid in a pipe is a parabolic function of position. At the centerline the velocity is a maximum, while at the wall it is a minimum. The shear rate is effectively the slope of the parabolic function line, so it is a minimum at the centerline and a maximum at the wall. Because the shear rate in a pipe or capillary is a function of position, viscometers based around capillary flow are less useful for non-Newtonian materials. For this reason, rotational devices are often used in preference to capillary or tube viscometers. 

It is clear then, that the measurement of non-Newtonian materials presents special challenges for a viscometer. Many industrial viscometers designed to give a single point determination have a deceptively simple operating principle. Examples include the speed at which a liquid flows out of a container through a known orifice, a bubble rises in a column of fluid, or a ball falls in a column of fluid. These simple devices are actually very complex in terms of the shear field that is generated. The shear field is the variation of shear stress or shear rate as a function of position within the... 

The viscosity of non-Newtonian materials can vary by many orders of magnitude, and it is important to know as much of this range as possible. Differences in food stability can be seen at ultra-low shear rates (<0.01 sec-1), while differences in consumption are seen at moderate shear rates ( 50 sec-1), and differences in application of the product (e.g., spreading peanut butter) are seen at high shear rates (>100 sec-1). 

This section describes common steps designed to measure the viscosity of non-Newtonian materials using rotational rheometers. The rheometer fixture that holds the sample is referred to as a geometry. The geometries of shear are the cone and plate, parallel plate, or concentric cylinders (Figure HI. 1.1). The viscosity may be measured as a function of shear stress or shear rate depending upon the type of rheometer used. 

A specially designed thin-film machine can be used to process very viscous, non-Newtonian materials. The apparatus can also be used to remove solvents from polymers and polycondensation processes having viscosities exceeding 10,000 poises. The Luwa thin-film machine has a small clearance between the heated wall and rotor blade. This clearance results in high shear gradients and considerably reduces apparent viscosity. The increased turbulence and improved surface renewal that ensue improve reaction velocities and aid the required forced product flow on the walls of the apparatus. 

According to the change of strain rate versus stress the response of the material can be categorized as linear, non-linear, or plastic. When linear response take place the material is categorized as a Newtonian. When the material is considered as Newtonian, the stress is linearly proportional to the strain rate. Then the material exhibits a non-linear response to the strain rate, it is categorized as Non Newtonian material. There is also an interesting case where the viscosity decreases as the shear/strain rate remains constant. This kind of materials are known as thixotropic deformation is observed when the stress is independent of the strain rate [2,3], In some cases viscoelastic materials behave as rubbers. In fact, in the case of many polymers specially those with crosslinking, rubber elasticity is observed. In these systems hysteresis, stress relaxation and creep take place. 

Some materials, including solutions of certain kinds of polymers, however behave strangely. When subjected to some force, their viscosities can change, and in weird ways. Such materials are said to be non-Newtonian materials. Consider two funnels, one containing honey and the other mayonnaise (Figure 6-2). Although both are viscous fluids, only the honey flows from the... 

The ratio of shearing stress and rate of shear in such materials is not a constant value, so the value is designated apparent viscosity. To be useful, a reported value for apparent viscosity of a non-Newtonian material should be given together with the value of rate of shear or shearing stress used in the determination. The relationship of shearing stress and rate of shear of non-Newtonian materials such as the dilatant and pseudoplastic bodies of Figure 8-5 can be represented by a power law as follows ... 

For non-Newtonian materials that have a yield stress, the Casson or Hershel-Bulkley models can be used. The Casson model is represented by the equation,... 

The viscosity of Newtonian liquids can be measured simply, by one-point determinations with viscometers, such as rotational, capillary, or falling ball viscometers. For non-Newtonian materials, measurement of... 

This illustrates that the viscous layer is an order of magnitude smaller for the non-Newtonian material when compared to a corresponding Newtonian material. 

The viscosity of Newtonian and non-Newtonian materials increases exponentially with an increase in pressure. However, these changes are extremely small, and under atmospheric conditions of lbar, they are hardly detectable. Hence, the pressure is normally not controlled during rheological measurements. In some circumstances, the pressure exerted on, for example, oils and lubricants, can take up values in excess of 1 GPa (oil rigs, lubricants in gears), and the increase in viscosity is substantial. In such applications, it is thus required to consider the pressure as a factor when studying their rheological properties. 

A cone and plate geometry is illustrated in Fig. 17. The plate remains stationary, while the cone rotates, or vice versa. The angle between the cone and plate surfaces is usually less than 5°. For larger angles, the analysis of the results obtained from non-Newtonian materials would be complex or even impossible. For the small angles, sample ejection is less pronounced and temperature control can be easily achieved. ° ... 

Grease is a non-Newtonian material insofar as flow is not initiated until stress is applied. 

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