Liquid Newtonian

Ideal liquids are incompressible and their flow is by definition frictionless. Real liquids are characterized by cohesion forces operating between the molecules, which bring about frictional forces, whose action is known as internal friction. 

If a liquid between two plates with parallel faces is considered (see Fig. 1.27) with the lower plate stationary (r = 0), while the upper plate moves with a constant velocity v to the right, the uppermost liquid layer moves with a velocity v, while the lowermost liquid layer is stationary. A velocity gradient is thereby produced in the liquid. This does not have to be linear, a differential velocity gradient perpendicular to the flow direction (x) is hence defined by dvx/dy. If the individual liquid layers slide over each other with different velocities without mixing, this flow is termed laminar (lat. lamen = the layer). 

The frictional force Ff, necessary to displace the upper plate with surface area A with constant velocity u parallelly, is proportional to the surface area A and the velocity gradient dux/dy  

With the shear stress r = Ff/A [Pa], Newton s Law of friction (1723) can be derived  

For the velocity gradient d x/dy the term shear rate y is used. The proportion- 

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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. 

AIChE, Cenhifugal Pumps (Newtonian Liquids), 2d ed.. Publication... 

In fact with a Newtonian liquid y = 4Q/ nR. This latter expression, viz. 4Q/ uR, is obviously much easier to calculate than the true wall shear rate and, since they are uniquely related and the simple expression is just as useful, in design practice it is very common when plotting flow curves to plot against... 

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 ... 

Consider a stirred tank vessel having a Newtonian liquid of density p and viseosity p, is agitated by an impeller of diameter D, rotating at a rotational speed N. Let the tank diameter be D, the impeller width W, and the liquid depth H. The power P required for agitation of a single-phase liquid ean be expressed as ... 

Equation (2) is valid only for very dilute suspensions of nondeformable, smooth, uniform spheres. It assumes a Newtonian liquid phase and neglects interaction between particles, a plausible condition when the volume of the solid phase is small compared with the liquid phase. 

The charts are to be used on Newtonian liquids, but not for gels, slurries, paperstock, or any other non-uni-form liquids [17]. 

Agitated-film evaporators, Newtonian liquid B = (-3.08 + 3.075X + 0.32567X2... 

Fig. 11. Typical flow curves of dispersions of fibre-forming particles in a Newtonian liquid. The arrow indicates the direction in which the filler concentration increases...

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. 

Here is a brief account of the main experimental and theoretical results obtained in the analysis of the rheological properties of low-molecular (Newtonian) liquids with gas bubbles ... 

When water (a Newtonian liquid) is in an open-ended pipe, pressure can be applied to move it. Doubling the water pressure doubles the flow rate of the water. Water does not have a shear-thinning action. However, in a similar situation but using a plastic melt (a non-Newtonian liquid), if the pressure is doubled the melt flow may increase from 2 to 15 times, depending on the plastic used. As an example, linear low-density polyethylene (LLDPE), with a low shear-thinning action, experiences a low rate increase, which explains why it can cause more processing problems than other PEs. The higher-flow melts include polyvinyl chloride (PVC) and polystyrene (PS). 

Astarita and Apuzzo (A3,. A4) have recently reviewed the available theoretical knowledge of the motion of gas bubbles in Newtonian liquids and the... 

Fig. 37. Strain rate distribution along the centerline in a 2-dimensional hyperbolic flow (the flow geometry is shown as an insert). The solid curve, redrawn according to ref. 131, corresponds to a viscoelastic fluid (the spike at x = 2 is a calculation artefact) the dotted curve is calculated with POLYFLOW for a Newtonian liquid...

Chapter 3 Flow of Newtonian and non-Newtonian Liquids Chapter 4 Flow of Compressible Fluids (Gases)... 

Pressure drop for flow of Newtonian liquids through a pipe... 

A further important property which may be shown by a non-Newtonian fluid is elasticity-which causes the fluid to try to regain its former condition as soon as the stress is removed. Again, the material is showing some of the characteristics of both a solid and a liquid. An ideal (Newtonian) liquid is one in which the stress is proportional to the rate of shear (or rate of strain). On the other hand, for an ideal solid (obeying Hooke s Law) the stress is proportional to the strain. A fluid showing elastic behaviour is termed viscoelastic or elastoviseous. 

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... 

For streamline flow of non-Newtonian liquids, the situation is completely different and the behaviour of two-phase mixtures in which the liquid is a shear-thinning fluid is now... 

Chhabra, R. P. and Richardson, J. F. In Encyclopedia of Fluid Mechanics, Volume 3, Gas-Liquid Flow Cheremisinoff, N, P. eds (Gulf Publishing Co. 1986). Co-current horizontal and vertical upwards flow of gas and non-Newtonian liquid. 

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. 

At the other extreme, in the formation of composite materials, especially filled polymers, fine particles must be dispersed into a highly viscous Newtonian or non-Newtonian liquid. The incorporation of carbon black powder into rubber is one such operation. Because of the large surface areas involved, surface phenomena play an important role in such applications. 

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