Global Analysis of the Flows of Fluids with Pressure-Dependent Viscosities

 To describe the flows of fluids over a wide range of pressures, it is necessary to take into account the fact that the viscosity of the fluid depends on the pressure. That the viscosity depends on the pressure has been verified by numerous careful experiments. While the existence of solutions local-in-time to the equations governing the flows of such fluids are available for small, special data and rather unrealistic dependence of the viscosity on the pressure, no global existence results are in place. Our interest here is to establish the existence of weak solutions for spatially periodic three-dimensional flows that are global in time, for a large class of physically meaningful viscosity-pressure relationships. (Accepted May 1, 2002) Published online November 15, 2002 Communicated by S. S. ANTMAN     

Circular shearing and torsion of generalized neo-Hookean materials

In this paper, the authors study circular shearing and torsionin generalized power-law neo-Hookean materials. For specialvalues of the power-law exponent, explicit exact solutions canbe established. In general, the governing equation is nonlinearand has to be solved numerically. This notwithstanding, somequalitative features of the general solutions can be discussed.The results corresponding to the neo-Hookean material can beobtained by setting the power-law exponent to unity. For valuesof the power-law exponent close to 0.5, a pronounced boundarylayer type of solution is found.     

Electron Transfer Reactions of Photochemically Generated Ruthenium(III)–Polypyridyl Complexes with Methionines

The oxidation of methionine (Met) plays an important role during biological conditions of oxidative stress as well as for protein stability. Ruthenium(III)–polypyridyl complexes, [Ru(NN)₃]³⁺, generated from the photochemical oxidation of the corresponding Ru(II) complexes with molecular oxygen, undergo a facile electron transfer reaction with Met to form methionine sulfoxide (MetO) as the final product. Interaction of [Ru(NN)₃]³⁺ with methionine leads to the formation of >S^+● and (>S∴S<)⁺ species as intermediates during the course of the reaction. The interesting spectral, kinetic, and mechanistic study of the electron transfer reaction of four substituted methionines with six [Ru(NN)₃]³⁺ ions carried out in aqueous CH₃CN (1:1, v/v) by a spectrophotometric technique shows that the reaction rate is susceptible to the nature of the ligand in [Ru(NN)₃]³⁺ and the structure of methionine. The rate constants calculated by the application of Marcus semiclassical theory to these redox reactions are in close agreement with the experimental values.     

Discrete large eddy simulation

IntroductionIn previous worksll,2], we discussed several issues associated with the standard version oflarge eddy simulation (LES) such as filtering and averaging. By the standard version, we meanthe traditional practice of first constructing a set of field equations of motions for turbulentmotion and then discretizing the equations to suit computational simulations.In this paper, we revisit the issue of large eddy simulation with a view towards improvingthe filtering procedure that is used i…     

Stress softening, strain localization and permanent set in the circumferential shear of an incompressible elastomeric cylinder

Corresponding author, email huntley{at}umich.edu A constitutive theory for elastomeric materials has recentlybeen developed according to which stress is generated by differentmicromechanisms at different levels of deformation. When thedeformation is small, the stress is given by the usual theoryof rubber elasticity. As the deformation increases, some junctionsof the macromolecular microstructure rupture. Junctions thenre-form to generate a new microstructure. The constitutive equationallows for continuous scission of the original junctions andformation of new ones as deformation increases. The macromolecularscission causes stress reduction. The formation of new microstructuresresults in permanent set on release of external load. The present work considers a hollow circular cylinder composedof such a material, also assumed to be incompressible and isotropic.The cylinder is fixed rigidly at its inner surface and undergoesaxisymmetric deformation due to a uniform axial moment appliedat the outer surface. There develops an outer zone of materialwith the original microstructure and an inner zone of materialhaving undergone macromolecular scission, separated by a cylindricalinterface, the radius of which increases with the rotation ofthe outer surface. The shear deformation distribution, moment-rotationresponse and permanent set on release of moment are determined.It is found that microstructural scission can lead to higherlevels of shear deformation near the inner surface of the cylinderthan in the case of purely elastic response. It is also seenthat a residual state of high shear deformation can arise ina thin layer of material at the inner boundary of the cylinder.