Viscous Flow Theory Research Articles

Viscous boundary layer between the solar wind and cometary plasmas

The interaction between the solar wind and cometary ionospheres downstream from the subsolar region is modeled in terms of viscous MHD flow theory. Calculations of the flow stremalines within the mixing region indicate that, as a result of viscous action, both the solar wind particles and the cometary material should be gradually directed towards the interior of the plasma wake to reinforce the formation of a type 1 tail. This behavior supports the notion that a transverse force acting on cometary plasma particles is actually responsible for the collapse of tail ray structures as suggested by Opik (1964), Wurm (1968, 1975) and Wurm and Mammano (1972).

The hot pressing of an alloy based on (Ti, Cr)B 2 and a study of its properties

An experimental study of the densification process for powder mixtures of (Ti, Cr)B 2 with metal additives was carried out and the dependence of the relative density of hot-pressed samples on the temperature, the time and the applied pressure was obtained. An analysis was made of the densification process for the (Ti, Cr)B 2-based alloy using the volume viscous flow theory for a porous solid; the creep parameters in the non-porous state were determined and the optimal conditions for the preparation of the (Ti, Cr)B 2-based alloy were established. The structure, the specific electrical resistance, the hardness and the ultimate compressive strength were studied and it was found that the (Ti, Cr)B 2-based alloy may be a good wear-resistant material.

Simple calibrated gas feed system

Constant calibrated gas flow is needed in vacuum processes such as plasma etching and sputtering. It is shown that capillary tubes combined with a simple pressure regulator can give satisfactory results. Typical calibrations for different capillary lengths, diameters, and for different gas types (A, N(2), H(2), He, CH(4), CCl(2)F(2), CHClF(2)) are given. Agreement with viscous flow theory is good, and over a 100:1 range in flowrate the resettability and variability in flowrate varies from +/-2% to +/-20%.

The effect of thermal history and strain rate on the mechanical properties of diethylenetriamine‐cured bisphenol‐A‐diglycidyl ether epoxies

AbstractThe tensile mechanical properties of diethylenetriamine (DETA)‐cured bisphenol‐A‐diglycidyl ether (DGEBA) epoxies prepared from 9, 11 and 13 phr DETA are reported as a function of thermal history, strain‐rate and test temperature. These epoxies exhibit macroscopic yield stresses and >10% ultimate elongations. The mechanical properties of these epoxies exhibit a free‐volume dependence as a function of thermal history. Annealing below Tg causes an increase in the macroscopic yield stress and a decrease in the ultimate elongation, whereas quenching from above Tg lowers the yield stress and increases the elongation. These mechanical property modifications are shown to be reversible with reversible thermal–anneal cycles. The activation volumes associated with Eyring's theory for stress‐activated viscous flow for the DGEBA‐DETA epoxies are within the range of values (9–12 nm3) reported for noncrosslinked polymers. These observations suggest that the DGEBA‐DETA epoxies are not as highly crosslinked as would be expected from normal addition reactions of epoxide groups with primary and secondary amines. The formation of lower crosslink density networks is discussed in terms of potential chemical reactions.

Note on an integral equation of viscous flow theory

The integral equation encountered by Van de Vooren and Veldman in a problem of viscous flow was recently solved by Brown by use of the Wiener-Hopf technique. In this note Brown's solution is re-derived by a different, function-theoretic method.

Kinetic theory of nonlinear viscous flow in two and three dimensions

On the basis of a nonlinear kinetic equation for a moderately dense system of hard spheres and disks it is shown that shear and normal stresses in a steady-state, uniform shear flow contain singular contributions of the form ¦X¦3/2 for hard spheres, or ¦X¦ log ¦X¦ for hard disks. HereX is proportional to the velocity gradient in the shear flow. The origin of these terms is closely related to the hydrodynamic tails t−d/2 in the current-current correlation functions. These results also imply that a nonlinear shear viscosity exists in two-dimensional systems. An extensive discussion is given on the range ofX values where the present theory can be applied, and numerical estimates of the effects are given for typical circumstances in laboratory and computer experiments.

On an integral equation of viscous flow theory

The integral equation encountered by van de Vooren and Veldman [1] in their study of the Knudsen region near the leading edge of a flat plate is solved by the method of Wiener and Hopf. This exact solution yields the values of certain arbitrary constants which were not determined in [1].

Hydromechanics of low-Reynolds-number flow. Part 4. Translation of spheroids

The problem of a uniform transverse flow past a prolate spheroid of arbitrary aspect ratio at low Reynolds numbers has been analysed by the method of matched asymptotic expansions. The solution is found to depend on two Reynolds numbers, one based on the semi-minor axis b, Rb = Ub/v, and the other on the semi-major axis a, Ra = Ua/v (U being the free-stream velocity at infinity, which is perpendicular to the major axis of the spheroid, and v the kinematic viscosity of the fluid). A drag formula is obtained for small values of Rb and arbitrary values of Ra. When Ra is also small, the present drag formula reduces to the Oberbeck (1876) result for Stokes flow past a spheroid, and it gives the Oseen (1910) drag for an infinitely long cylinder when Ra tends to infinity. This result thus provides a clear physical picture and explanation of the ‘Stokes paradox’ known in viscous flow theory.

Slender-body theory for slow viscous flow

Slow flow of a viscous incompressible fluid past a slender body of circular crosssection is treated by the method of matched asymptotic expansions. The main result is an integral equation for the force per unit length exerted on the body by the fluid. The novelty is that the body is permitted to twist and dilate in addition to undergoing the translating, bending and stretching, which have been considered by others. The method of derivation is relatively simple, and the resulting integral equation does not involve the limiting processes which occur in the previous work.

Glass temperature, formation and stability of Fe, Co, Ni, Pd and Pt based glasses

The thermal behavior of a number of metallic glasses, particularly (Pd 1 − x Ni x ) 1 − y P y systems, has been investigated. The composition dependence of T g and the mode of crystallization of the PdNiP glasses change abruptly at a critical phosphorus content, y c, near the eutectic. Below y c, the glasses exhibit multiglass transitions, an indication of phase separation. The tendency towards phase-separation and consequently the destabilization of the PdNiP glasses near the eutectic composition renders further support to the previous proposition that the destabilization of crystalline mixtures rather than the stabilization of the liquid phase is responsible for the stability of metallic glasses. The effect of alloying on the glass temperature will also be discussed using the entropy theory of viscous flow.

On uniqueness questions in the theory of viscous flow

On uniqueness questions in the theory of viscous flow

Solutions in terms of homogeneous harmonic functions in three-dimensional elastostatics and the viscous flow theory

The paper presents the mean-stress approach to integration of differential equations in elastostatics and the theory of a viscous medium in steady slow flow. This method in the general formulation is used to the derivation of new uncoupled forms of the solution, in particular-expressed by homogeneous harmonic functions. It is shown that in spherical coordinates the boundary conditions arc uncoupled both for displacement and stress as well. As an example, the problem of a fixed elastic spherical inclusion (or obstacle) is studied.

Mean-stress approach to integration of differential equations in elastostatics, and the Neuber-Papkovich and Galerkin representations

The mean-stress approach proposed by the author for integration of differential equation in elastostatics is applied to derivation of uncoupled solutions. In particular, the Neuber-Papkovich and Galerkin representations are analysed and adapted for use in elastostatics of incompressible bodies and in theory of slow steady viscous flow. It is shown that in multiply-connected regions, both representations may lead to many-valued solutions unless the special integral conditions are satisfied identically.

On a theory of laminar flow in channels of a certain class. II

This paper continues (and concludes) the mathematical analysis begun in (8) of a formal theory of viscous flow in channels with slowly curving walls. In that paper, the theory was shown to yield strict asymptotic expansions, in powers of the small curvature parameter, of exact solutions of the Navier-Stokes equations, but the proofs were restricted to a set of Reynolds numbers and wall divergence angles that is distinctly smaller than the set on which the formal approximation is defined. In the present paper, we study in more detail a certain linear, partial differential operator TN, the invertibility of which is essential to the proofs. This operator is shown to be invertible (and the formal theory is thereby justified) on a parameter domain that is much larger than and may well be the whole of . A key step is to associate with TN a family of operators that approximate TN locally and have much simpler coefficients.

Creep in the hot pressing of titanium diboride powder

1. An experimental study was made of the densification of a technical titanium carbide powder and a titanium carbide powder washed free from iron, and the effects of temperature, time, and applied pressure on the relative density of hot-pressed titanium carbide specimens were determined. 2. The experimental data obtained are analyzed in the light of the theory of volume viscous flow of solids, and it is shown that creep of particles is responsible for densification in the hot pressing of titanium carbide powder. The creep is controlled by a dislocation climb mechanism. 3. It is demonstrated that contamination by iron substantially reduces the energy of activation for the creep of titanium carbide. 4. The magnitude of effective Laplacian pressure in porous titanium carbide produced by hot pressing is assessed.

Hot pressing of oxides of the iron group metals

1. A study was made of the hot pressing of oxides of the iron group metals in powder form, and the effects were determined of temperature, process time, and applied pressure on their relative density. 2. It is shown that the densification of powders of these oxides can be described within the frame-work of the theory of volume viscous flow of porous solids. 3. It was established that the deformation rate of particles of these oxide powders in hot pressing obeys the law έ∼σ, i.e., is proportional to the applied pressure. 4. The energy of activation for the creep of oxide powder particles in hot pressing and the micro-hardness of oxide specimens produced by this method were determined.

Kinetics of the hot pressing of titanium and tungsten carbide alloys cemented with niobium

1. A study was made of sintering kinetics in the hot pressing of TiC-Nb and WC-Nb cermets containing 25, 50, and 75 at. % of binder metal. It was established that the highest relative density (0.93–0.96 and 0.94–0.97%) in the hot pressing of TiC-Nb and WC-Nb cermets is attained at temperatures of 2100–2375 and 2100–2300°C, respectively, a pressure of 300 kg/cm2, and a holding time of 10–15 min. 2. Experimental data on densification kinetics in the sintering of TiC-Nb and WC-Nb cermets were processed within the framework of the theory of volume viscous flow of porous solids, and the energy of activation for the sintering process was calculated. It was found that the hot pressing process comprises a transient and a steady-state creep stage and that the energy of activation for sintering of TiC-Nb and WC-Nb alloys decreases with rise in the amount of the metallic component.

The Mathematical Theory of Viscous Incompressible Flow. By O.A. Ladyzhenskaya. Revised 2nd edition (translated from the Russian by R. A. Silverman). Pp. xviii, 224. (Gordon & Breach, New York.)

The Mathematical Theory of Viscous Incompressible Flow. By O.A. Ladyzhenskaya. Revised 2nd edition (translated from the Russian by R. A. Silverman). Pp. xviii, 224. (Gordon & Breach, New York.)

Three-dimensional viscous flow of fissile materials during high-temperature swelling under the influence of inert gases

It was shown that the theory of three-dimensional viscous flow for porous solids may be used to describe the swelling of irradiated fissile materials; the kinetics of swelling were analyzed in the framework of this theory. The condition stipulating the minimum rate of energy dissipation regulates the process of swelling in such a way that the creep of the material takes place under steady-state conditions at a constant effective pressure. The process of swelling ends when there is no longer any excess free energy and when all the sources of point defects have been exhausted.

Vacuum hot pressing of metal powders under the action of ultrasonic vibrations

1. Using the theory of volume viscous flow of porous material, an analysis was carried out of the powder densification process, as a result of which it was established that ultrasonic vibrations raise the effective pressure in hot compaction. 2. The application of ultrasonic vibrations during the steady-state stage of powder particle creep in hot pressing accelerates creep and temporarily disturbs steady-state flow. 3. In hot pressing, the creep rate of iron and nickel powder particles is proportional to the square of the stress; it is shown that creep under these conditions is controlled by the dislocation climb process. 4. It was established that the efficiency of ultrasonic vibrations decreases with rise in temperature.