Newtonian fluid, ideal

In a fluid under stress, the ratio of the shear stress, r. to the rate of strain, y, is called the shear viscosity, rj, and is analogous to the modulus of a solid. In an ideal (Newtonian) fluid the viscosity is a material constant. However, for plastics the viscosity varies depending on the stress, strain rate, temperature etc. A typical relationship between shear stress and shear rate for a plastic is shown in Fig. 5.1. 

A special case of a Newtonian fluid is that of an ideal fluid, in which the viscosity /x = 0. Ideal fluids do not exist however, in many noncritical applications, the friction can be ignored to simplify calculations. 

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. 

Such an ideal material is called an inviscid (Pascalian) fluid. However, if the molecules do exhibit a significant mutual attraction such that the force (e.g., the shear stress) is proportional to the relative rate of movement (i.e., the velocity gradient), the material is known as a Newtonian fluid. The equation that describes this behavior is... 

Plug flow is an idealization. Deviations arise with viscous or non-Newtonian fluids. A mathematically simple deviation from the plug flow pattern is that of power law fluids whose velocity in a tube depends on the radial position, /3 = r/R, according to the equation,... 

It is convenient to use a simple weightless Hookean, or ideal, elastic spring with a modulus G and a simple Newtonian (fluid) dashpot or shock absorber having a liquid with a viscosity of 17 as models to demonstrate the deformation of an elastic solid and an ideal liquid, respectively. The stress-strain curves for these models are shown in Figure 14.1. 

Maxwell element or model Model in which an ideal spring and dashpot are connected in series used to study the stress relaxation of polymers, modulus Stress per unit strain measure of the stiffness of a polymer, newtonian fluid Fluid whose viscosity is proportional to the applied viscosity gradient. 

Capillary viscometers are ideal for measuring the viscosity of Newtonian fluids. However, they are unsuitable for non-Newtonian fluids since variations in hydrostatic pressure during sample efflux results in variations in shear rate and thus viscosity. This unit contains protocols for measuring the viscosity of pure liquids and solutions (see Basic Protocol) and serums from fruit juices and pastes (see Alternate Protocol). 

Equation (6.4) is applicable to a description of the flow behaviour of ideal fluids, or Newtonian fluids. Examples include water, mineral oils, bitumen, and molasses. However, many fluids, especially colloidal dispersions, do not obey Eq. (6.4), usually due to the mutual orienting and even structure formation of the dispersed species in the flow. 

The ideal viscous element can be represented by a dashpot filled with a Newtonian fluid, whose deformation is linear with time while the stress is applied, and is completely irrecoverable (Newton element). In a dynamic mechanical experiment the stress is exactly 90° out of phase with the strain [Pg.412]

In solutions, the most important physical factors that influence the solubility of ingredients are type of fluid, mixing equipment, and mixing operations. Generalized Newtonian fluids are ideal fluids for which the ratio of the shear rate to the shear stress is constant at a particular time. Unfortunately, in practice, usually liquid dosage forms and their ingredients are non-Newtonian fluids in which the ratio of the shear rate to the shear stress varies. As a result, non-Newtonian fluids may not have a well-defined viscosity [32],... 

Fig. 8.1 Idealized plots of shear rate (y) against shear stress (x) for fluids of various types. (A) Newtonian fluid. (B) Bingham fluid. (C) Shear thinning, (D) Shear thickening. (E) Positive hysteresis 1, 2, 3A thixotropy 1,2, 3B. rhcodestruction, (F) Negative hysteresis with antithixotropy.

An ideal, Newtonian fluid was described on page 4.33. Such a material has no elastic character it cannot support a strain and the instantaneous response to a... 

In a dilute polymer solution, there are no entanglements of the individual molecules and the molecules can be considered to be essentially isolated from each other, so that treatment of an individual molecule is sufficient. Much work was done to understand the rheological behavior of dilute polymer solutions using the concept that a polymer molecule can be idealized as dumbbells, that is, two beads connected by a spring. The hydrodynamic. Brownian, and intramolecular forces acting on the beads are considered when the dumbbells are suspended in a Newtonian fluid. Because experimental data cannot be taken at concentrations considered to be sufficiently low for the absence of intermolecular interactions, data obtained at low polymer concentrations (e.g., c < 10" gmL ) must be extrapolated to infinite dilution (Ferry, 1980). 

A fluid in which the shear stress is proportional to the shear velocity, corresponding to this law, is called an ideal viscous or Newtonian fluid. Many gases and liquids follow this law so exactly that they can be called Newtonian fluids. They correspond to ideal Hookeian bodies in elastomechanics, in which the shear strain is proportional to the shear. A series of materials cannot be described accurately by either Newtonian or Hookeian behaviour. The relationship between shear stress and strain can no longer be described by the simple linear rule given above. The study of these types of material is a subject of rheology. 

Under very rapid mechanical actions or in observations with characteristic time t < to, the substance behaves as an ideal elastic medium. For t to the developing flow becomes stronger than the elastic deformation, and the substance can be treated as a simple Newtonian fluid. It is only if t is of the same order of magnitude as to that the elastic and viscous effects act simultaneously, and the complex nature of the deformation displays itself. 

Newtonian Fluid - A term to describe an ideal fluid in which shear stress and shear rate is proportional (e g., water). The proportionality coefficient is called viscosity, which is independent of shear rate, contrary to non-ideal fluids where viscosity is a function of shear rate. Paints and polymer melts are examples of non-Newtonian liquids. 

Fluids treated in the classical theory of fluid mechanics and heat transfer are the ideal fluid and the newtonian fluid. The former is completely frictionless, so that shear stress is absent, while the latter has a linear relationship between shear stress and shear rate. Unfortunately, the behavior of many real fluids used in the mechanical and chemical industries is not adequately described by these models. Most real fluids exhibit nonnewtonian behavior, which means that the shear stress is no longer linearly proportional to the velocity gradient. Metzner [3] classified fluids into three broad groups ... 

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