Onset of oscillatory thermocapillary convection in systems with a deformable interface

Oscillatory interfacial instability is investigated with allowance for the deformation of the interface. The possibility of two types of oscillations being excited is established. One of these is similar to the well-known type in systems with a plane interface, while the other is determined by the oscillations of the deformable surface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 11–16, July–August, 1991.     

On a non-linear system for shape memory alloys

A non linear system modelling phase changes in metallic alloys is studied. Two existence, uniqueness and regularity results are established in the reversible or irreversible setting. The technique uses non linear semi-groups theory and a fixed point method.     

Elastic properties of obliquely wound composites with a damaged matrix

Special Design and Technological Office, Institute of Mechanics, Academy of Sciences of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 25, No. 2, pp. 82–89, February, 1989.     

Rheological models with microstructural constraints

Rheological models of complex fluids with a physically restricted microstructure are analyzed to obtain general classes of dynamical evolution equations for these materials. These classes insure that the appropriate mathematical constraints, associated with each type of physical restriction, are consistently incorporated into the corresponding model development. Describing the microstructure of the complex fluid with a second-rank tensor variable, a general class of dynamical evolution equations is derived for three physically meaningful constraints associated with constancy of the invariants of this microstructural tensor. The physical rationale for each of these constraints is discussed, and a corresponding set of constrained dynamical evolution equations is derived in general terms. Abdellatif Ait-Kadi passed away suddenly during the course of this research. The surviving authors express their gratitude to Abdellatif for our many hours of productive work and companionship.     

Solving the Stress Problem for a Finite Cylinder by the Schwarz Method with Hybrid Approximations

An axisymmetric elastic problem is solved by a heterogeneous numerical scheme of the alternating Schwarz method based on the finite- and boundary-element methods. The Schwarz method and the modified scheme are compared. A relaxation parameter is used to accelerate the iterative process     

The effect of “creep acceleration” in the theory of viscoelasticity

A particular case of constitutive relations in the Pobedrya nonlinear theory of viscoelasticity is considered. It is shown that these relations can be used in the problem of describing the material softening under pulsed loading.     

Numerical simulation of effects of flow maldistribution on heat and mass transfer in a PEM fuel cell stack

A 3D numerical study was carried out to analyze flow, heat and mass transfer first in a single half-cell cathode channel of proton exchange membrane (PEM) fuel cell. From practical point of view, it is necessary to put the appropriate number of cells in a stack. Hence, the above study on a single half-cell is extended to a stack of channels. Due to stacking, the assumption of uniform flow distribution would no longer hold true. Therefore, the channel flow-maldistribution is considered. The water formed at the active surface due to the electrochemical reaction diffuses through the porous layer and eventually enters the gas flow duct. The higher gas velocities in the duct result in faster water vapour removal which leads to a lower value of water vapour into the duct and hence a lower Nusselt number.     

On the finite deformation of a sector plate

Summary In this paper an investigation is given into the behaviour of the stress singularity which occurs in the linear theory of elasticity at the deformation of a sector plate, if finite deformations are considered. It is assumed that for very small deformations Hooke's law is valid, and only in the neighbourhood of the singularity Hooke's law has to be extended. This extension is not unique. It is shown that for two different strain-energy functions, which have the same asymptotic expansion for infinitesimal deformations, the behaviour of the solutions is quite different. One of the strain-energy functions leads to a bounded solution, while the solution, obtained from the other one becomes singular for the case of contraction. As it cannot be expected that it will be possible to decide on an experimental basis about the right extension, an assertion about the difference in smoothness of solutions to problems in linear and non-linear theory cannot be given. An open question is raised: whether or not the requirement of regularity for this kind of problems in non-linear theory can be posed as a restriction on the admissible energy functions.     

The investigation of the dynamic visco-elastic functions of printing inks

Summary Measurements of the dynamic rigidities and viscosties of some inks have been made in the frequency range 0.01 to 25 c. p. s. in the linear region. The dependency of the visco-elastic properties on concentration of pigment and added solvent is discussed. The dynamic mechanical properties of non-thixotropic inks are found to be distinct from those of thixotropic inks.

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Zusammenfassung Es wurden Messungen der dynamischen Steifigkeiten und Viskositäten verschiedener Tinten im Frequenzbereich zwischen 0,01 und 25 Hz im linearen Bereich durchgeführt. Es wird die Abhängigkeit der viskoelastischen Eigenschaften von der Pigmentkonzentration und dem Lösungsmittelgehalt diskutiert. Es zeigt sich, daß die dynamisch-mechanischen Eigenschaften nichtthixotroper Tinten sich deutlich von denen thixotroper Tinten unterscheiden.

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Turbulence time scales in mixing box experiments

Laboratory experiments are performed to examine eddy time scales in turbulence generated by an oscillating grid in homogeneous fluid using tanks with varying depth and fixed high aspect ratio horizontal cross-section. For high ratios of depth to width, a mean circulation develops in the form of a pair of counter-rotating vortices. In a new technique, pearlescent dye is employed to measure eddy time scales and to determine their power law scaling dependence on the distance from the oscillating grid. Two scaling regimes are observed, one near the source of turbulence and one at intermediate depths. At intermediate depths, the scaling exponent is found to increase if the total fluid depth is larger. We discuss the significance of these results on the use of the law-of-the-wall scaling in the upper oceanic mixed layer.