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. 

In a Newtonian material the rate of shear deformation is proportional to the shear stress except at very low stresses this is not true of elastomers which are accordingly termed non-Newtonian. 

For this simple geometry the shear rate, 7, is equal to the difference between the velocity at the top of the element, U, and the velocity at the bottom of the element, zero, divided by the height of element H. The shear stress is again r = F/A, the element surface area divided by the force. The viscosity, q, is the ratio of shear stress, r, divided by shear rate, 7, at any shear rate, q = rjq. For Newtonian materials such as water, molasses, or gasoline at the nominal shear rates found in everyday life, the slope of the shear stress with shear rate curve is a constant and equal to the Newtonian viscosity. 

Polymer rheology can respond nonllnearly to shear rates, as shown in Fig. 3.4. As discussed above, a Newtonian material has a linear relationship between shear stress and shear rate, and the slope of the response Is the shear viscosity. Many polymers at very low shear rates approach a Newtonian response. As the shear rate is increased most commercial polymers have a decrease in the rate of stress increase. That is, the extension of the shear stress function tends to have a lower local slope as the shear rate is increased. This Is an example of a pseudoplastic material, also known as a shear-thinning material. Pseudoplastic materials show a decrease in shear viscosity as the shear rate increases. Dilatant materials Increase in shear viscosity as the shear rate increases. Finally, a Bingham plastic requires an initial shear stress, to, before it will flow, and then it reacts to shear rate in the same manner as a Newtonian polymer. It thus appears as an elastic material until it begins to flow and then responds like a viscous fluid. All of these viscous responses may be observed when dealing with commercial and experimental polymers. 

When a polymer is extruded through an orifice such as a capillary die, a phenomenon called die swell is often observed. In this case, as the polymer exits the cylindrical die, the diameter of the extrudate increases to a diameter larger than the diameter of the capillary die, as shown in Fig. 3.9. That is, it increases in diameter as a function of the time after the polymer exits the die. Newtonian materials or pure power law materials would not exhibit this strong of a time-dependent response. Instead they may exhibit an instantaneous small increase in diameter, but no substantial time-dependent effect will be observed. The time-dependent die swell is an example of the polymer s viscoelastic response. From a simplified viewpoint the undisturbed polymer molecules are forced to change shape as they move from the large area of the upstream piston cylinder into the capillary. For short times in the capillary, the molecules remember their previous molecular shape and structure and try to return to that structure after they exit the die. If the time is substantially longer than the relaxation time of the polymer, then the molecules assume a new configuration in the capillary and there will be less die swell. 

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)... 

The extrusion pressure could be further modulated by choice of dies or screens with appropriate L/D ratios. The pressure differential between points of die entry and exit due to viscosity for a Newtonian material moving within a cylinder is represented by Equation (4), derived from the Hagen-Poisuille expression for pressure drop in a pipe of constant diameter as (41)... 

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... 

An extrusion symposium (El) contains papers which deal extensively with the mathematics of viscous flow in screw extruders but which are limited to Newtonian materials. An extension of this work to materials which may be assumed to be Bingham plastic in behavior has been reported in Japan (M18, M19). The first of these papers deals with a screw extruder with a uniform channel the second with an extruder for which the depth of the channel decreases linearly with channel length. The mathematical results are shown graphically in terms of four dimensionless groups ... 

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. 

Unsteady state phenomena have been stated to be of greater importance for non-Newtonian than for Newtonian materials and therefore warrant experimental investigation. The prediction of pressure drop for two-phase flow of a gas and a non-Newtonian fluid seems to be in a well-perfected state but requires extension to situations in which the liquid flow is laminar. Apparently no information is yet available on the problems of mixing, entrainment, and other similar relationships which are of importance if such contactors are to be designed for chemical rather than mechanical purposes. 

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... 

Materials that exhibit a direct proportionality between shearing stress and rate of shear are called Newtonian materials. These include water and aqueous solutions, simple organic liquids, and dilute suspensions and emulsions. Most foods are non-Newtonian in character, and their shearing stress-rate-of-shear curves are either not straight or do not go through the origin, or both. This introduces a considerable difficulty, because their flow behavior cannot be expressed by a single value, as is the case for Newtonian liquids. 

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