Variational approach for the flow of Ree–Eyring and Casson fluids in pipes

The flow of Ree–Eyring and Casson non-Newtonian fluids is investigated using a variational principle to optimize the total stress. The variationally obtained solutions are compared to the analytical solutions derived from the Weissenberg–Rabinowitsch–Mooney equation and the results are found to be identical within acceptable numerical errors and modeling approximations.

Approximate Solution of Momentum Transfer in System Generalized Newtonian Fluid-Fluidized Bed of Spherical Particles Using Modified Rabinowitsch-Mooney Equation

The modified Rabinowitsch-Mooney equation together with the corresponding relations for consistency variables has been adopted for approximate solution of momentum transfer between generalized Newtonian fluid with laminar flow and surface of fluidized bed of spherical particles inclusive of wall surface. The solution has been concretized for a fluid characterized by power-law and Ellis flow models in the creeping flow region. The range of values of ratios of particle diameter to column diameter and that of porosity values e in which the suggested relation satisfactorily agrees with experimental results for pseudoplastic fluids have been delimitated experimentally.

Rubber Elasticity in the Range of Small Uniaxial Tensions and Compressions. Results for Poly(Dimethylsiloxane)

Results of uniaxial tension and compression experiments are reported on crosslinked poly(dimethylsiloxane) networks in the unswollen state over the range 0.5<α−1<1.2 , where α is the extension ratio. Curves representing the reduced force [ƒ]=ƒ(V0/V)1/3(α−α−2)−1 plotted against α−1 can be approximated by straight lines for 0.5<α−1<0.9, in agreement with the phenomenological Mooney equation. As α−1 approaches 1, however, they tend to level off and continue into the α−1>1 region with decreasing slope. These results are in agreement with the predictions of recent elasticity theories that incorporate the effect of junction-chain entanglements in the elastic free energy.

The mechanics of rubber elasticity

The mechanical properties of a rubber may conveniently be represented in terms of the strain energy W , which in Rivlin’s notation is expressed as a function of the strain invariants I 1 and I 2 . The experiments of Rivlin & Saunders indicated that ∂ W /∂ I 1 was approximately constant while ∂ W /∂ I 2 varied with I 2 , in contrast to the Mooney equation, according to which both ∂ W /∂ I 1 and ∂ W /∂ I 2 are constant. More recently it has been proposed by Valanis & Landel that W may be expressible in terms of separate functions w ( λ i ) of the principal extension ratios λ i This hypo­ thesis appears to be borne out experimentally, and gives promise of a more accurate analysis of experimental measurements. Application to recent data enables w ( λ i ) to be expressed as an explicit algebraic function, from which it appears that the earlier conclusions of Rivlin & Saunders require some modification in detail.

On the Mechanical Behavior of the Orthotropic Cord-Rubber Composite

The effective elastic properties of the cord-rubber composite are deduced from the principle of virtual work. Such a composite must be compliant in the noncord directions and therefore undergo large deformations. The Rivlin-Mooney equation is used to derive the effective Poisson's ratio and Young's modulus of the composite and as a basis for their measurement in uniaxial tension.