Flows formed after the passage of a discontinuous wave over a bottom drop

The solvability of the problem of the flow formed after a discontinuous wave has passed over a bottom drop is studied within the framework of the first approximation of shallow water theory. Solutions in which the total energy of the flow is either conserved or lost at the drop are considered. Stable self-similar solutions of five qualitatively different types are derived and their domains of existence are determined in the dimensionless parameter plane.     

Diffusion effects on the interfacial tension of immiscible polymer blends

Most methods of measuring the interfacial tension between two immiscible polymers are based on the analysis of the shape that a drop of one polymer immersed in the other one exhibits under the action of flow or gravity. In such a situation, the small, yet nonzero mutual solubility between the two polymers acts toward mass transfer between the drop and the surrounding fluid. In this work, diffusion effects on the interfacial tension of the pair polyisobutylene/polydimethylsiloxane have been investigated by drop deformation under shear flow. When the drop was made of polyisobutylene, drop size decreased with time due to diffusion. Drop shrinkage was associated with a significant increase in interfacial tension, until an apparent plateau value was reached. The effect was attributed to a selective migration of molecular weights, which would act to enrich the drop with higher molar mass material. To support such an interpretation, drop viscosity was evaluated by drop shape analysis and it was actually found to increase with time. In some cases, the ratio between drop and continuous phase viscosity became higher than the critical value for drop breakup in shear flow. Upon inverting the phases (i.e., when the drop was made of polydimethylsiloxane), no significant transient effects were observed. In the light of these results, the problem of what are the correct values of interfacial tension and viscosity ratio for a polymer blend of a certain composition will also be discussed. Received: 25 January 1999 Accepted: 24 May 1999     

Mechanisms of martensitic transformations in boron nitride and conditions of their development

Abstract

The dependence of the pressure threshold of martensitic transformations on the disordering degree of starting structures is considered for graphite-like BN into diamond-like BN modifications transitions. The effect of loading conditions on transformation mechanisms of rhombohedral BN into zinc blende or wurtzite modifications is analyzed also. Analytical relations obtained allow to explain the experimental data and to predict a behavior of various graphite-like structures under different p, T conditions.     

On the deformation of linear r-fields

We study the question: For which (r,n) can a linear r-field on the (n-1)-sphere in an n-dimensional real linear space be deformed through a continuous path of linear r-fields into an orthonormal r-field. We provide complete answers for the cases: (r,n)=(2,4),(3,4), and provide several partial results for the cases (r,n)=(2,2m), where m is an even integer satisfying m4. Characterizations of linear r-fields are pivotal in the investigation.     

A fundamental solution to the Cauchy problem for a fourth-order pseudoparabolic equation

The Cauchy problem for a fourth-order pseudoparabolic equation describing liquid filtration problems in fissured media, moisture transfer in soil, etc., is studied. Under certain summability and boundedness conditions imposed on the coefficients, the operator of this problem and its adjoint operator are proved to be homeomorphism between certain pairs of Banach spaces. Introduced under the same conditions, the concept of a θ-fundamental solution is introduced, which naturally generalizes the concept of the Riemann function to the equations with discontinuous coefficients; the new concept makes it possible to find an integral form of the solution to a nonhomogeneous problem.     

Flow of viscoelastic fluids between plates rotating about distinct axes

We discuss the flow of BKZ fluids in an orthogonal rheometer. Some analytical results are proved, and numerical solutions are obtained for the Currie model. These solutions show a boundary layer behavior at high Reynolds numbers and the possibility of discontinuous solutions or nonexistence at high Weissenberg numbers.     

Rheology and microstructures formation of immiscible model polymer blends under steady state and transient flows

Viscoelastic properties of model immiscible blend were studied here under steady state condition at different initial conditions and transient flow conditions. The flow‐induced microstructure has been studied on these model blends. For this system, the elastic properties of the blend are mainly governed by the interface. Measurement of the dynamic modulus and of the first normal stress difference, both reflecting this enhanced elasticity, have been used to prove the blend morphology. The dynamic moduli after cessation of shear flow, the mean diameter of the disperse phase as generated by the shear flow, have been calculated using the model of Palierne. A procedure based on a direct fitting of the dynamic moduli with the model is compared with the one that uses a weight relaxation spectrum. On the other hand, the steady state normal stress data have been related to the morphology of the blend by means of Doi and Ohta model. The specific interfacial area is found to be inversely proportional to the ratio of interfacial tension over shear stress for the blend. The flow behavior during transient shear flow was also discussed. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3519–3533, 2005     

Microdeformation behavior in nanotemplated epoxy thermosets: A study with in situ tensile deformation technique in transmission electron microscopy

Microdeformation behavior in nanostructured block copolymer‐toughened epoxy resins, or templated epoxy thermosets, was studied using an in situ tensile deformation technique performed directly in a transmission electron microscope. The observed microdeformation modes were found to correlate well with the macroscopic mechanical properties of the materials. In the order of decreasing macroscopic fracture toughness, the microdeformation modes were observed to change from large uniform plastic deformation over an extensive area, to localized plastic deformation bands, to little plastic deformation observed in the most brittle material. A similar trend was also observed when samples of the same material were tested at different temperatures, reflecting changes in the deformation mechanism as a function of temperature. Structural defects were observed in nanotoughening phases when plastic deformation was observed. The implication of the observed microdeformation modes to the macroscopic toughening mechanisms is discussed in the context of the micromorphology of the nanometer sized toughening phases and parameters of the epoxy matrix chemistry such as bromination, molecular weight, and interfacial miscibility. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 393–406, 2009     

Sliding mesh algorithm for CFD analysis of helicopter rotor–fuselage aerodynamics

The study of rotor–fuselage interactional aerodynamics is central to the design and performance analysis of helicopters. However, regardless of its significance, rotor–fuselage aerodynamics has so far been addressed by very few authors. This is mainly due to the difficulties associated with both experimental and computational techniques when such complex configurations, rich in flow physics, are considered. In view of the above, the objective of this study is to develop computational tools suitable for rotor–fuselage engineering analysis based on computational fluid dynamics (CFD). To account for the relative motion between the fuselage and the rotor blades, the concept of sliding meshes is introduced. A sliding surface forms a boundary between a CFD mesh around the fuselage and a rotor‐fixed CFD mesh which rotates to account for the movement of the rotor. The sliding surface allows communication between meshes. Meshes adjacent to the sliding surface do not necessarily have matching nodes or even the same number of cell faces. This poses a problem of interpolation, which should not introduce numerical artefacts in the solution and should have minimal effects on the overall solution quality. As an additional objective, the employed sliding mesh algorithms should have small CPU overhead. The sliding mesh methods developed for this work are demonstrated for both simple and complex cases with emphasis placed on the presentation of the inner workings of the developed algorithms. Copyright © 2008 John Wiley & Sons, Ltd.