Newtonian viscosity of the

The measurement of viscosity is important for many food products as the flow properties of the material relate directly to how the product will perform or be perceived by the consumer. Measurements of fluid viscosity were based on a correlation between relaxation times and fluid viscosity. The dependence of relaxation times on fluid viscosity was predicted and demonstrated in the late 1940 s [29]. This type of correlation has been found to hold for a large number of simple fluid foods including molten hard candies, concentrated coffee and concentrated milk. Shown in Figure 4.7.6 are the relaxation times measured at 10 MHz for solutions of rehydrated instant coffee compared with measured Newtonian viscosities of the solution. The correlations and the measurement provide an accurate estimate of viscosity at a specific shear rate. 

Bueche-Ferry theory describes a very special second order fluid, the above statement means that a validity of this theory can only be expected at shear rates much lower than those, at which the measurements shown in Fig. 4.6 were possible. In fact, the course of the given experimental curves at low shear rates and frequencies is not known precisely enough. It is imaginable that the initial slope of these curves is, at extremely low shear rates or frequencies, still a factor two higher than the one estimated from the present measurements. This would be sufficient to explain the shift factor of Fig. 4.5, where has been calculated with the aid of the measured non-Newtonian viscosity of the melt. A similar argumentation may perhaps be valid with respect to the "too low /efi-values of the high molecular weight polystyrenes (Fig. 4.4). 

In equations 5-8, the variables and symbols are defined as follows p0 is reference mass density, v is dimensional velocity field vector, p is dimensional pressure field vector, x is Newtonian viscosity of the melt, g is acceleration due to gravity, T is dimensional temperature, tT is the reference temperature, c is dimensional concentration, c0 is far-field level of concentration, e, is a unit vector in the direction of the z axis, Fb is a dimensional applied body force field, V is the gradient operator, v(x, t) is the velocity vector field, p(x, t) is the pressure field, jl is the fluid viscosity, am is the thermal diffiisivity of the melt, and D is the solute diffiisivity in the melt. The vector Fb is a body force imposed on the melt in addition to gravity. The body force caused by an imposed magnetic field B(x, t) is the Lorentz force, Fb = ac(v X v X B). The effect of this field on convection and segregation is discussed in a later section. 

In a wide-gap Couette rheometer, migration of spheres was followed by nuclear magnetic resonance imaging [Abbott et al, 1991]. Migration to the low shear rate region was found to be determined by the total strain, proportional to the shear rate and square of the particle diameter, but independent of the (Newtonian) viscosity of the matrix liquid. More recently, similar studies were undertaken for suspensions of rods with... 

Under the Stokes flow and particle separation assumptions, the viscous force between two approaching particles should scale as fiaU, with n the Newtonian viscosity of the medium and U the approach velocity. With U ay, where y is the applied shear rate, the energy dissipation within the gap between the particles scales as fJi-a y. We have here assumed that the interaction frequency between the particles is of the order of y. This will be true so long as the particle concentration is not so high that we are close to the maximum packing fraction for which flow can occur, a point which is discussed in greater detail in the following section. 

Newton s law of motion for liquids describes a linear relationship between the deformation of a fluid and the corresponding stress, as indicated in Equation 22.16, where the constant of proportionality is the Newtonian viscosity of the fluid. The generalized Newtonian fluid (GNF) refers to a family of equations having the structure of Equation 22.16 but written in tensorial form, in which the term corresponding to viscosity can be written as a function of scalar invariants of the stress tensor (x) or the strain rate tensor (y). For the GNF, no elastic effects are taken into account [12, 33] ... 

Parameter P governs the eontribution of the Maxwell element to effective viscosity, T, (Newtonian viscosity of the solution). Equation [7.2.26] is similar to the Oldroyd-type equation [7.2.15] with the only difference that in the former the upper convective derivative is used to account for nonlinear effects instead of partial derivative, d/dt. 

Figure 7.2.14. The relation between the relative heat transfer coefficient for boiling PIB solutions in cyclohexane and the Newtonian viscosity of the solutions measured at T=298 K. AT = 16.67 K - PIB Vistanex L-100 in cyclohexane, o - PIB Vistanex L-80 in cyclohexane, X - pure cyclohexane. [Reprinted from H.J. Gannett, and M.C. Williams, Int. J. Heat Mass Transfer, 14, 1001, Copyright 1971, the reference 57, with permission from Elsevier Science]...

Viscoelasticity, Table 1 Evolution of the mid-filament diameter in a fluid filament undergoing capillary-driven breakup. Note Ac is the characteristic relaxation time of the sample, to is the filament breakup time, and ps is the Newtonian viscosity of the solvent... 

The temperature dependence of the Newtonian viscosity of the polymer melts is given by the WLF equation ... 

Once the length and radius of the capillary have been determined, the basic characteristics of the fluid must be determined. In addition to the use of experiments or correlations to determine the density and thermal properties, a conventional capillary viscometer such as a Cannon-Fenske viscometer is used to determine the viscosity of the fluid as a function of temperature in the Newtonian, low-shear, region. These viscosity measurements not only provide Information concerning the influence of temperature on the Newtonian viscosity of the polymer solution at low-shear rates, but the semi-em p i r ica1 correlation of So and Klaus (24) is utilized to estimate the influence of pressure on the viscosity from these data. 

The stress from the main flow is determined by the Newtonian viscosity of the suspending fluid and the average rate of deformation tensor (recall assumption 9)... 

PAO and three different additive packages were studied. Six viscosity modifiers (VM) and three different viscosity grades have been evaluated. Within each viscosity grade it is possible to vary the Newtonian viscosity of the oil (that is the part which is independent of shear rate), and still achieve the same finished oil viscometrics (HTHS and kVlOO). This is achieved by using different amounts of viscosity modifier to boost the viscosity at low and medium shear rates. This is illustrated schematically in Figure 1. 

Let us first consider a dilute system of rigid spherical particles dispersed at a volume fraction m Newtonian liquid of shear viscosity rjo. According to Einstein,the Newtonian viscosity of the whole system, rj, is increased by the presence of the particles according to the equation... 

Pa-s (pure viscous liquid with Newtonian viscosity of the solution), for curve 2, a=l, for curve 3, a = 0, that is, the latter two graphs correspond to viscoelastic solution with and without account for the rheological non-linearity, respectively. 

In polymer systems, however, the high non-Newtonian viscosity of the fluid would make dispersion based on these forces a slow process. Dispersive mixing is achieved by the application of shear stress to the mixture and the efficiency of dispersion therefore depends on machine design ... 

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