Viscosity Newtonian liquids

Newtonian liquid viscosity, U is the bubble velocity, and aQ is the equilibrium surface tension), where surface tension and viscous forces dominate the bubble shape (15). Using a lubrication analysis, Bretherton established that the bubble slides over a stationary, constant-thickness film whose thickness divided by the radius of the tube, h R., varies as the... 

Agitated-film evaporator, newtonian liquid, viscosity ... 

A convenient physical interpretation may be illustrated by simulating mechanical or electronic models. In the mechanical simulation, a spring represents an elastic or Hookean solid (modulus), while a piston moving in an infinite cylinder filled with a viscous liquid (a dash-pot) represents the Newtonian liquid (viscosity). Thus, the deformation of the solid (spring) is completely recoverable, while that of the liquid (dash-pot) is irrecoverable and is converted to heat. See Figures 4-7, 4-8, 4-9. In conclusion, the elastic energy is conserved and recovered while the viscous energy is dissipated. 

For a Newtonian liquid, viscosity is expressed by a dashpot model as shown in Fig. IB and by the relationship given by Newtonian laws as... 

Polymers owe much of their attractiveness to their ease of processing. In many important teclmiques, such as injection moulding, fibre spinning and film fonnation, polymers are processed in the melt, so that their flow behaviour is of paramount importance. Because of the viscoelastic properties of polymers, their flow behaviour is much more complex than that of Newtonian liquids for which the viscosity is the only essential parameter. In polymer melts, the recoverable shear compliance, which relates to the elastic forces, is used in addition to the viscosity in the description of flow [48]. 

Flow behaviour of polymer melts is still difficult to predict in detail. Here, we only mention two aspects. The viscosity of a polymer melt decreases with increasing shear rate. This phenomenon is called shear thinning [48]. Another particularity of the flow of non-Newtonian liquids is the appearance of stress nonnal to the shear direction [48]. This type of stress is responsible for the expansion of a polymer melt at the exit of a tube that it was forced tlirough. Shear thinning and nonnal stress are both due to the change of the chain confonnation under large shear. On the one hand, the compressed coil cross section leads to a smaller viscosity. On the other hand, when the stress is released, as for example at the exit of a tube, the coils fold back to their isotropic confonnation and, thus, give rise to the lateral expansion of the melt. 

A simple starting point for such a discussion is Poiseuille s law [42] for the flow of a Newtonian liquid of viscosity in a tube of radius r under the influence of a pressure P ... 

All three methods discussed above appear to provide equally high quality ionic liquid viscosity data. However, the rotational viscometer could potentially provide additional information concerning the Newtonian behavior of the ionic liquids. The capillary method has been by far the most commonly used to generate the ionic liquid viscosity data found in the literature. This is probably due to its low cost and relative ease of use. 

In Eq. (13), medium resistance to bubble compression-decompression depends on viscosity r, and is described by the second member in the right-hand part of the equation. It should be mentioned at this point that bubble growth in a Newtonian liquid was originally examined by the Soviet physicist Y. I. Frenkel [29], in a rarely cited work published in 1946. 

The modulus sign is used because shear stresses within a fluid act in both the positive and negative senses. Gases and simple low molecular weight liquids are all Newtonian, and viscosity may be treated as constant in any flow problem unless there are significant variations of temperature or pressure. 

A Newtonian liquid of viscosity 0.1 N s/m2 is flowing through a pipe of 25 mm diameter and 20 m in lenglh, and the pressure drop is 105 N/m2. As a result of a process change a small quantity of polymer is added to the liquid and this causes the liquid to exhibit non-Newtonian characteristics its rheology is described adequately by the power-law model and the flow index is 0.33. The apparent viscosity of the modified fluid is equal to ihc viscosity of the original liquid at a shear rate of 1000 s L... 

In many instances, two or more miscible liquids must be mixed to give a product of a desired specification, such as, for example, in the blending of petroleum products of different viscosities. This is the simplest type of mixing as it involves neither heat nor mass transfer, nor indeed a chemical reaction. Even such simple operations can however pose problems when the two liquids have vastly different viscosities. Another example is the use of mechanical agitation to enhance the rates of heat and mass transfer between the wall of a vessel, or a coil, and the liquid. Additional complications arise in the case of highly viscous Newtonian and non-Newtonian liquids. 

Considering a stirred vessel in which a Newtonian liquid of viscosity p, and density p is agitated by an impeller of diameter D rotating at a speed N the tank diameter is DT, and the other dimensions are as shown in Figure 7.5, then, the functional dependence of the power input to the liquid P on the independent variables (fx, p, N, D, DT, g, other geometric dimensions) may be expressed as ... 

Figures 8.5 and 8.6. The liquid is carried round in the spaces between consecutive gear teeth and the outer casing of the pump, and the seal between the high and low pressure sides of the pump is formed as the gears come into mesh and the elements of fluid are squeezed out. Gear pumps are extensively used for both high-viscosity Newtonian liquids and non-Newtonian fluids. The lobe-pump (Figures 8.7 and 8.8) is similar, but the gear...

In order to model viscoelasticity mathematically, a material can be considered as though it were made up of springs, which obey Hooke s law, and dashpots filled with a perfectly Newtonian liquid. Newtonian liquids are those which deform at a rate proportional to the applied stress and inversely proportional to the viscosity, rj, of the liquid. There are then a number of ways of arranging these springs and dashpots and hence of altering the... 

Most pectin solutions behave like Newtonian liquids below a pectin concentration of about 1 % (w/w). Onogi (1966) derived the critical concentration of polymer solutions from plotting the double logarithmic curves of viscosity (ii) against concentration at constant shear rates. Each curve consists of two straight lines intersecting at the critical concentration. At higher... 

Consistency, working time, setting time and hardening of an AB cement can be assessed only imperfectly in the laboratory. These properties are important to the clinician but are very difficult to define in terms of laboratory tests. The consistency or workability of a cement paste relates to internal forces of cohesion, represented by the yield stress, rather than to viscosity, since cements behave as plastic bodies and not as Newtonian liquids. The optimum stiffness or consistency required of a cement paste depends upon its application. 

In equation 5.3, and when calculating the Reynolds number for use with Figure 5.7, the fluid viscosity and density are taken to be constant. This will be true for Newtonian liquids but not for non-Newtonian liquids, where the apparent viscosity will be a function of the shear stress. 

For non-Newtonian liquids and suspensions, an apparent viscosity is determined using correlations which include power input and the Reynolds number. Scale-up comparisons based on heat generation data only were determined by comparison of results from RC1 experiments and from a 675-liter reactor [208]. In the experiments, a Bingham plastic fluid was used to determine the film heat transfer coefficient. This presents a worst case because of the low thermal conductivity of the Bingham plastic. Calculated inside film heat transfer coefficients determined in the RC1 tests were about 60% lower than the values determined in the pilot plant reactor, even though substantial effort was made to obtain both geometric and kinematic similarity in the pilot reactor. 

A general time-independent non-Newtonian liquid of density 961 kg/m3 flows steadily with an average velocity of 2.0 m/s through a tube 3.048 m long with an inside diameter of 0.0762 m. For these conditions, the pipe flow consistency coefficient K has a value of 1.48 Pa s0,3 and n a value of 0.3. Calculate the values of the apparent viscosity for pipe flow p.ap, the generalized Reynolds number Re and the pressure drop across the tube, neglecting end effects. 

Uhl and Voznick showed that the mixing effectiveness of a particular anchor agitator in a Newtonian liquid of dynamic viscosity 40 Pa s was the same as for a particular turbine agitator in a Newtonian liquid of dynamic viscosity 15 Pa s. 

It is possible to calculate the apparent viscosities of non-Newtonian liquids in agitated tanks from the appropriate power curves for Newtonian... 

The Cannon-Fenske viscometer is used for measuring the kinematic viscosity of transparent Newtonian liquids, especially petroleum products and lubricants. The Ubbelohde viscometer is also used for the measurement of kinematic viscosity of transparent Newtonian liquids, but by the suspended level principle. 

Note 3 For non-Newtonian liquids, when CT12 is not directly proportional toy, q varies withy. The value of q evaluated at a given value of y is termed the non-Newtonian viscosity. 

Note 5 Extrapolation of rj or /app for non-Newtonian liquids to zero y gives the zero-shear viscosity, which is given the symbol rja. 

---