An extension of Reiner's “Deborah Number” concept to a Wide field of rheological investigations

Summary Reiner defined a numeric, which he called theDeborah Number to represent the ratio of a relaxation time to a natural (observation) time. This implies aMaxwell model but is readily extended to complete relaxation spectra. Similar Numbers are proposed for retardation times and also for some conditions of coagulation thixotropy and for data from certain psychophysical experiments.     

Influence of molecular weight upon drag reduction by polymers

Summary Drag reduction measurements have been made with samples of polyethyleneoxide and polyacrylamide with relatively narrow molecular weight distributions obtained by fractionation of commercial polymers. Relationships between the polymer molecular weight and the concentration required to give the same drag reduction have been determined. The influence of polymer degradation upon these relationships has been investigated.Molecular weight distributions of commercial polymers have been determined and their influence upon the drag-reducing properties is noted.The influence of wall shear stress has been investigated over the range 1.0 × 10² - 4.5 × 10³ dyn/cm². The results with unfractionated polymers were found to be consistent with other results in the literature.     

Modeling and simulation of martensitic phase transitions with a triple point

A framework for modeling complex global energy landscapes in a piecewise manner is presented. Specifically, a class of strain-dependent energy functions is derived for the triple point of Zirconia (ZrO₂), where tetragonal, orthorhombic (orthoI) and monoclinic phases are stable. A simple two-dimensional framework is presented to deal with this symmetry breaking. An explicit energy is then fitted to the available elastic moduli of Zirconia in this two-dimensional setting. First, we use the orbit space method to deal with symmetry constraints in an easy way. Second, we introduce a modular (piecewise) approach to reproduce or model elastic moduli, energy barriers and other characteristics independently of each other in a sequence of local steps. This allows for more general results than the classical Landau theory (understood in the sense that the energy is a polynomial of invariant polynomials). The class of functions considered here is strictly larger. Finite-element simulations for the energy constructed here demonstrate the pattern formation in Zirconia at the triple point.     

Equilibrium shapes of strained islands with non-zero contact angles

The equilibrium morphology of a strained island on an elastic substrate is determined. The island is assumed to partially wet the substrate (Volmer-Weber growth) and thus makes a non-zero contact angle with the surface. Both isotropic and anisotropic misfit strain are allowed. Two- and three-dimensional equilibrium island shapes are determined by using expressions for the elastic strain energy in the small-slope approximation. In this limit, the problem can be reduced to a singular integral-differential equation for the island thickness. We find that when there is a non-zero contact angle, all island shapes, for a given ratio of the elastic stress to surface energy, attain a form that is independent of the specific contact angle under an appropriate scaling. We show that for islands with non-zero contact angles, as the island volume increases, the shape approaches the geometry of a completely wetting island. But when the volume decreases, these islands approach a point while islands with a zero contact angle, approach a finite length line segment of zero volume. Multiple-hump equilibrium shapes are found. Single-humped islands are shown to have a lower chemical potential than multiple-humped islands, implying that they are the most stable. This conclusion is shown to be consistent with a stability analysis of the two-dimensional case. The effects of a tetragonal misfit strain on the three-dimensional island shape is investigated.     

DPIV study of near-stall wake-rotor interactions in a transonic compressor

Wake-rotor interactions at near-stall conditions are studied using digital particle image velocimetry (DPIV) in a transonic compressor at the Compressor Aero Research Lab (CARL) at Wright-Patterson Air Force Base. The wake generators (WGs) are designed to simulate wakes of highly loaded stators without producing flow swirl. Flow visualization, instantaneous, and average velocity field data are presented for near-stall compressor operating conditions. These results describe the interaction of the wake shed from the upstream WG with the downstream potential field of the rotor leading edge for two axial spacings at 75 and 90% span. The advantage of ensemble averaging is demonstrated when operating at challenging conditions such as near-stall, which poses special difficulties in obtaining DPIV data. Ensemble averaging, which is possible because of a natural phase locking provided by the blade potential field, allows robust statistics.     

Transversality between invariant manifolds of periodic orbits for a class of monotone dynamical systems

We consider a special class of monotone dynamical systems and show that in this special class the stable and unstable manifolds of two hyperbolic periodic orbits always intersect transversally. The proof is based on the existence of a family of positively invariant nested cones.This paper is dedicated to Jack Hale on the occasion of his 60th birthday.     

Dilute polymeric solutions close to bounding surfaces: Shear stresses in equilibrium

The problem of a dilute polymer solution in equilibrium close to a wall, an edge, and a corner, respectively, is studied theoretically. Detailed knowledge of the rheology in these regions is needed in order to obtain the proper boundary conditions for bulk variables. It is interesting to see that shear stresses are predicted, whose origin is based on the intramolecular (elastic) interaction between the beads.     

Finite deformation and stability behaviour of spherical inflatables subjected to axi-symmetric hydrostatic loading

This paper deals with the large deflection and stability behaviour of inextensible spherical air-supported membranes subjected to an accumulating ponding fluid. It is assumed that ponding fluid is available to fill an initial axi-symmetric deformation around the apex and that due to such accumulation deflections increase until under certain conditions collapse of the structure occurs.The problem is reduced to a set of differential equations which are solved numerically to determine the parameters defining the deflected wrinkled shape of the membrane. A simple expression for use in design of such structures is obtained and the results presented in non-dimensional graphic form.