Fluid inelastic

In an inelastic, time-independent (Stokesian) fluid the extra stre.ss is considered to be a function of the in.stantaneous rate of defomiation (rate of strain). Therefore in this case the fluid does not retain any memory of the history of the deformation which it has experienced at previous stages of the flow. 

CLASSIFICATION OF INELASTIC TIME-INDEPENDENT FLUIDS 5 L2.2 Generalized Newtonian Unids... 

Water Hammer When hquid flowing in a pipe is suddenly decelerated to zero velocity by a fast-closing valve, a pressure wave propagates upstream to the pipe inlet, where it is reflected a pounding of the hne commonly known as water hammer is often produced. For an instantaneous flow stoppage of a truly incompressible fluid in an inelastic pipe, the pressure rise would be infinite. Finite compressibility of the flmd and elasticity of the pipe limit the pressure rise to a finite value. The Joukowstd formula gives the maximum pressure... 

Thus, the pipe friction chart for a Newtonian fluid (Figure 3.3) may be used for shearthinning power-law fluids if Remit is used in place of Re. In the turbulent region, the ordinate is equal to (R/pu2)n 0 fn5. For the streamline region the ordinate remains simply R/pu2, because Reme has been defined so that it shall be so (see equation 3.140). More recently, Irvine(25j has proposed an improved form of the modified Blasius equation which predicts the friction factor for inelastic shear-thinning polymer-solutions to within 7 per cent. 

Research Centers (IUCRC), 24 395 Inelastic mean free path (IMFP), 24 87 Inert fluids, 11 877 properties of, 11 879 Inert gas dilution, 11 456 Inert gases, 13 456 17 376-377. See also Helium- group elements Noble gases narcotic potency and solubility of, 17 377 Inert gas generators, 17 280 Inertial confinement fusion targets, microcapsules as, 16 460 Inertial impaction, in depth filtration theory, 11 339... 

In the case of a flowing fluid the mechanical pressure is not necessarily the same as the thermodynamic pressure as is the case in a static fluid. The pressure in a flowing fluid is defined as the average of the normal stress components. In the case of inelastic fluids, the normal stress components are equal and therefore, with the negative sign convention, equal to the pressure. It is for this reason that the pressure can be used in place of the normal stress when writing force balances for inelastic liquids, as was done in Examples 1.7-1.9. 

Turbulent flow of inelastic non-Newtonian fluids in pipes... 

A stability analysis made by Ryan and Johnson (1959) suggests that the transition from laminar to turbulent flow for inelastic non-Newtonian fluids occurs at a critical value of the generalized Reynolds number that depends on the value of The results of this analysis are shown in Figure 3.7. This relationship has been tested for shear thinning and for Bingham... 

Measurements suggest that the pressure loss for laminar flow of power law fluids through a sudden contraction is not significantly different from that for Newtonian flow [Skelland (1967)]. This statement applies to inelastic power law fluids in the case of elastic liquids, very high contraction pressure losses occur as discussed in Section 3.10. 

Intraocular pressure. The fixed distances of the refractive surfaces from the retina are maintained because the inelastic sclera is under a constant intraocular pressure of 20-25 mm. Hg. This pressure is maintained by a balance between the production and escape of the intraocular fluid. The mechanism appears to be as... 

For inelastic fluids exhibiting power-law behaviour, the bed expansion which occurs as the velocity is increased above the minimum fluidising velocity follows a similar pattern to that obtained with a Newtonian liquid, with the exponent in equation 6.31 differing by no more than about 10 per cent. There is some evidence, however, that with viscoelastic polymer solutions the exponent may be considerably higher. Reference may be made to work by Srimvas and Chhabra(15) for further details. 

Physically, the Brillouin spectrum arises from the inelastic interaction between a photon and the hydrodynamics modes of the fluid. The doublets can be regarded as the Stokes and anti-Stokes translational Raman spectrum of the liquid. These lines arise due to the inelastic collision between the photon and the fluid, in which the photon gains or loses energy to the phonons (the propagating sound modes in the fluid) and thus suffer a frequency shift. The width of the band gives the lifetime ( 2r)-1 of a classical phonon of wavenumber q. The Rayleigh band, on the other hand, represents the... 

Most of the models assume that neutral-species transport can be represented with either a well-mixed model or a plug flow model. The major drawback to these assumptions is that important inelastic rate processes such as molecular dissociation are usually localized in space in the reactor and are often fast compared with rates of diffusion or convection. As a result, the spatial variation of fluid flow in the reactor must be accounted for. This variation introduces a major complication in the model, because the solution of the nonisothermal Navier-Stokes equations in multidimensional geometries is expensive and difficult. 

Lun, C. K. K., Savage, S. B. and Jeffery, D. J. (1984). Kinetic Theories for Granular Flow Inelastic Particles in Couette Flow and Slightly Inelastic Particles in a General Flow Field. J. Fluid Mech., 140, 223. 

The same statement can be made about inelastic non-Newtonian fluids, such as the Power Law fluid, from a mathematical solution point of view. In reality, most non-Newtonian fluids are viscoelastic and exhibit normal stresses. For fluids such as those (i.e., fluids described by constitutive equations that predict normal stresses for viscometric flows), theoretical analyses have shown that secondary flows are created inside channels of nonuniform cross section (78,79). Specifically it can be shown that a zero second normal stress difference is a necessary (but not sufficient) condition to ensure the absence of secondary flow (79). Of course, the analyses of flows in noncircular channels in terms of constitutive equations—which, strictly speaking, hold only for viscometric flows—are expected to yield qualitative results only. Experimentally low Reynolds number flows in noncircular channels have not been investigated extensively. In particular, only a few studies have been conducted with fluids exhibiting normal stresses (80,81). Secondary flows, such as vortices in rectangular channels, have been observed using dyes in dilute aqueous solutions of polyacrylamide. Interestingly, these secondary flow vortices (if they exist) seem to have very little effect on the flow rate. 

The experimental and theoretical literature on instabilities in fiber spinning has been reviewed in detail by Jung and Hyun (28). The theoretical analysis began with the work of Pearson et al. (29-32), who examined the behavior of inelastic fluids under a variety of conditions using linear stability analysis for the governing equations. For Newtonian fluids, they found a critical draw ratio of 20.2. Shear thinning and shear thickening fluids... 

Early modeling of these processing flows was aimed at the fluid mechanics of the flow field and was based on a temperature-independent inelastic fluid rheology. Though illustrative, this could never capture the real essence of processing problems or behavior. Formal attempts to write down and solve a full set of coupled equations for temperature-sensitive elasticoviscous fluids led to intractable complexity, for which even the most modern computers offered no panacea. 

Viscoelasticity was introduced in Section 11.5. A polymer example may be useful by way of reeapitulalion. Imagine a polymer melt or solution confined in the aperture between two parallel plates to which it adheres. One plate is rotated at a constant rate, while the other is held stationary. Figure 11-3la shows the time dependence of the shear stress after the rotation has been stopped, r decays immediately to zero for an inelastic fluid but the decrease in stress is much more gradual if the material is viscoelastic. In some cases, the residual stresses may... 

Kim M. E., R. A. Brown and R. C Armstrong," The roles of inertia and shearthinning in flow of an inelastic liquid through an axisymmetric sudden contraction," J. Non-Newtonian Fluid Mech., 13 (1983) 341-364. 

Ofoli, R. Y., Morgan, R. G., and Steffe, J. F. 1987. A generalized rheological model for inelastic fluid foods. J. Texture SUid. 18 213-230. 

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