Electrical Conductivity of Rocks under Shock Compression

The electrical conductivity of silicate rocks (quartzite, granite, and dry and wet tuffs) under single shock–wave loading is measured. It is shown that even at a shock–wave pressure of 20 GPa, the conductivity of rocks changes by several orders of magnitude compared to the initial value (10^–9 — 10^{–12 –1} · m^–1 for dry rocks) and reaches 0.01 ^–1 · m^–1 for quartzite and granite and 0.1 — 1.0 ^–1 · m^–1 for tuff. As the shock–wave amplitude increases from 20 to 60 GPa, the electrical conductivity increases by further one or two orders of magnitude. The experiments with rocks did not reveal a drastic change in electrical conductivity similar to the that observed for silicon dioxide (fused quartz) at a pressure of about 40 GPa.     

A torsional creep apparatus

Summary This paper describes a torsional creep apparatus for the determination of the creep compliance in shear as a function of time. The instrument is suitable for the measurement of compliances below 5·10^–8 m²/N, in the time range between 1 and 10⁵ seconds. Within five minutes and with an accuracy of 1 C, the temperature of the specimen can be adjusted to any value between –175 and –200 C. From the torsional creep measurements can be calculated the dynamic shear modulus and the corresponding damping. The lowest damping, determined in this way, is several times 10^–3.

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Zusammenfassung Ein Apparat zur Messung des Torsions-Kriechverhaltens wird beschrieben. Das Instrument ist zur Bestimmung von Nachgiebigkeiten kleiner als 5·10^–5 m²/N im Zeitbereich zwischen 1 und 10⁵ Sekunden geeignet. Die Temperatur der Probe läßt sich innerhalb 5 Minuten und mit einer Genauigkeit von 1 C auf jeden Wert zwischen –175 und –200 C einstellen. Aus der gemessenen Kriechfunktion können der dynamische Schubmodul und die dynamische Dämpfung berechnet werden. Eine untere Grenze für die Dämpfung, die man auf diese Weise noch bestimmen kann, ist einige Male 10^–3.

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The work was partly sponsored by the Office of Naval Research, Washington, D. C., under contract number N 62558-3884.     

Rheologische Eigenschaften gesunder Synovialflüssigkeiten

Zusammenfassung Die rheologischen Eigenschaften gesunder menschlicher Gelenksflüssigkeiten im Geschwindigkeitsgefällebereich vonD = 10^–3-10³ s^–1 wurden untersucht. Es wurden die Scherviskosität und die erste Normalspannungsdifferenz gemessen. Gesunde Synovialflüssigkeiten besitzen hohe Anfangsviskosität (~40 Pa · s) und zeigen eine starke Abhängigkeit vom Geschwindigkeitsgefälle. Der SchermodulG ist im Gegensatz zu pathologischen Proben niedrig und über weite Bereiche konstant. Die längsten Relaxationszeiten betragen 5–10 s. Die kritische Konzentration, bei der Netzwerkbildung einsetzt, beträgt 0,75 10^–3 g/ml. Die Proben lassen sich zu einer Masterkurve vereinigen, die als verallgemeinertes Fließgesetz für gesunde Synovia aufgefaßt werden kann. Eine Untersuchung über die zeitliche Abhängigkeit der post-mortem-Synovia zeigt, daß innerhalb von 12 Stunden keine nennenswerten Veränderungen eintreten.

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The rheology of healthy human synovial fluids has been investigated at a shear-rate between 10^–3-10³ s^–1. Shear viscosity and first normal-stress difference were measured. Healthy synovial fluids show high zero-shear viscosity (about 40 Pa · s) and a strong shear rate dependence. The modulusG is constant over a large range, in contrast to pathological samples. The longest relaxation times are 5–10 s. The critical concentrationc _cr , at which entanglement occurs is about 0.75 10^–3 g/ml. The samples can be represented by a master-curve, which may be regarded as the constitutive equation of healthy synovial fluids. An investigation of the time dependency of synovial fluids indicated no changes within 12 hours post mortem.

Herrn Prof. Dr. DDr. h. c. O. Kratky zum 80. Geburtstag mit den besten Wünschen gewidmet.     

Viskositätsmessungen bei kleinen Schergefällen

Zusammenfassung Große, stark strukturierte Moleküle können Konformationswechselzeiten haben, die in der Größenordnung der Deformationsperiode bei der Scherung der Moleküle in Lösung liegen, wenn das Geschwindigkeitsgefälle kleine Werte annimmt. Es werden einige Viskosimeter beschrieben, die zur Untersuchung verdünnter Lösungen in einem Geschwindigkeitsgefälle-Intervall von 10^–2–10⁴ sec^–1 geeignet sind. Anhand von Messungen an DNA wird gezeigt, daß bei Geschwindigkeitsgefällen von 10 sec^–1 noch starke Strukturviskosität auftreten kann.

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Summary Large strongly structured molecules may have change of constellation times comparable to the deformation period in shearing the molecules in solution, if the shear rate assumes low values. Several viscometers are described, which are suitable for the investigation of diluted solutions in a shear rates range of 10^–2–10⁴ sec^–1. With the help of measurements with DNA, it is shown that strong shear dependence is observed for shear rates of 10 sec^–1.

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Vorgetragen auf der Rheologen-Tagung in Darmstadt am 7. und 8. Juni 1971

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Diese Arbeiten wurden von der DFG im Rahmen des SFB 41 Mainz-Darmstadt unterstützt, wofür wir herzlich danken.     

Dynamic measurements on polymer solutions and melts

Summary An apparatus for the measurement of the dynamic viscosity is described. In a coaxial cylinder geometry forced vibrations are executed in the frequency region from 2·10^–4 to 50 cycles/sec. Fluids with a wide range of viscosities (10^–1 to 10⁷ poise) can be measured. A number of experimental results obtained on dilute solutions and melts of polymers are given and compared with results of the molecular theories.

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Zusammenfassung Es wird ein Gerät für die Messung der dynamischen Viskosität beschrieben. Innerhalb eines koaxialen Zylindersystems werden im Frequenzgebiet von 2 · 10^–4 bis 50 Hz erzwungene Schwingungen ausgeführt. Messungen an Flüssigkeiten sind in einem weiten Viskositätsbereich (10^–1 bis 10⁷ Poise) möglich. Einige Messungen an verdünnten Lösungen oder Schmelzen von Hochpolymeren werden mitgeteilt und mit Voraussagen molekularer Theorien verglichen.

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Paper read at the Annual Meeting of the German Rheologits, Berlin-Dahlem, May 20–21, 1968).     

Shear creep and recovery of a technical polystyrene

The torsional creep and recoverable bahaviour of a technical polystyrene is reported over seven orders of magnitude of the value of the compliance from 10^–8 to 10^–1 Pa^–1 and over more than seven decades in time. The results for the recoverable compliance J_R (t) reveal a dispersion region seen between the glass transition and the steady-state recoverable compliance J_e. The limiting value of the final dispersion J_e = 4.7 · 10^–4 Pa^–1 indicates a broad molecular-weight distribution. The steady-state recoverable compliance J_e is independent of the temperature. The temperature dependence of the final dispersion was found to be indistinguishable from that of viscous flow. However, this temperature dependence differs significantly from that of the glass-rubber transition. A proposal has been made for the construction of creep compliance and recoverable compliance over an extended time scale.     

Dynamics of Brownian particles in a turbulent channel flow

Turbulent channel flows with suspended particles are investigated by means of numerical simulations. The fluid velocity is computed by large eddy simulation. Motion of small graphite particles with diameter of 0.01–10 m, corresponding to the Schmidt number, Sc, of 2.87 × 10²–6.22 × 10⁶ and the particle relaxation time in wall unit, _p⁺, of 9.79 × 10^–5–4.51, is computed by Lagrangian particle tracking. Relation between the particle relaxation time and the computed deposition velocity is found to be in good agreement with an empirical relation. The statistics of the particle motion in the vicinity of the wall are studied. Clear differences are found in dynamical behavior of particles with different sizes. Medium size particles show a strong dependence on the structure of the fluid flow, while small and large particles are considerably less sensitive.     

Extensional flow of polystyrene melt

Summary The extensional flow of molten polystyrene was studied in the strain rate range of 7.8×10^–4 sec^–1 to 2.2×10^–2 sec^–1 at a test temperature of 300F (149 C) Extensional viscosity was compared to shear viscosity measured at the same degree of stress and temperature and found to be from 3 to 350 times greater in magnitude but much less stress dependent.     

Effect of longitudinal riblets on the aerodynamic characteristics of a straight wing

The results of balance aerodynamic tests on model straight wings with smooth and ribbed surfaces at an angle of attack =–4°–12°, Mach number M=0.15–0.63, and Reynolds number Re=2.4·10⁶–3.5·10⁶ are discussed. The nondimensional riblet spacings ⁺, which determines the effect of the riblets on the turbulent friction drag, and the effect of riblets on the upper and/or lower surface of a straight wing on its drag, lift, and moment characteristics are estimated.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 33–38, March–April, 1995.     

Direct measurement of static yield properties of cohesive suspensions

A technique of yield stress investigation based upon the combined use of two devices (an applied stress rheometer and an instrument for measuring the propagation velocity of small amplitude, torsional shear waves) is described. Investigations into the low shear rate rheological properties of illitic suspensions are reported for shear rates, typically, in the range 10^–4— 10^–1 s^–1 under applied stresses in the range 0.01 — 10 Nm^–2 and involving shear strains between 10^–1 and 10^–4. Results are presented which demonstrate that the technique does not invoke the excessive structural disruption of material associated with applied shear rate based methods (direct and otherwise) and the widely encountered problem of wall slip at the surface of rotational measuring devices is avoided using miniature vane geometries. Results are compared with those obtained using smooth-walled cyclindrical measuring devices in both applied stress and applied shear rate instruments.Yield measurements are considered in relation to the structural properties of the undisturbed material state and shear moduli obtained by studying the propagation of small amplitude (10^–5 rad), high frequency (~ 300 Hz) torsional shear waves through the test materials are reported. Experimental techniques and instrument modifications to permit these measurements are described.     

An appraisal of rheological models as applied to polymer melt flow

Summary An attempt is made at giving an appraisal of some representative rheological models of both differential and integral type, using the standard rheological measurements of six polymer melts. Experimental data obtained were the steady shear viscosity and the first normal stress difference by means of aWeissenberg rheogoniometer over the range of shear rates: 10^–2 ~ 10 sec^–1, and by means of aHan slit/capillary rheometer over the range of shear rates: 10 ~ 10³ sec^–1. Also measured by means of theWeissenberg rheogoniometer were the dynamic viscosity and dynamic elastic modulus over the range of frequencies: 0.3 × 10^–2 ~ 3 × 10² sec^–1. Rheological models chosen for an appraisal are theSpriggs 4-constant model, theMeister model, and theBogue model.It is found that the capability of the three models considered is about the same in their prediction of the rheological behavior of polymer melts in simple shearing flow. It is pointed out however that, due to the ensuing mathematical complexities, the usefulness of these models is limited to the study of flow problems associated with simple flow situations. Therefore, in analysing the complex flow situations often encountered with various polymer processings, the authors suggest use of the empirical models of the power-law type for both the viscosity and normal stress functions.With 11 figures, 4 schemas and 1 table     

Airflow behind strong shock front with account for nonequilibrium ionization and radiation

We consider the gas state behind a shock wave front in air with a velocity v10 km/sec. Nonequilibrium ionization and radiative transport are taken into account. We take into consideration the real air spectrum — the numerous lines, bands, and continuua. Account for the radiation leads to an integrodifferential system of equations for which a solution method is developed. As a result we obtain the gas parameter profiles behind the shock wave, which are affected by the relaxation processes and radiative cooling. The calculations were made for v=10–16 km/sec and a pressure p=10^–5–10^–2 atm ahead of the front.In order to obtain realistic results, we consider only the gas layer bounded by the shock and a surface parallel to it. It is assumed that the gas bounded by these planes is not irradiated from without. In this formulation still another defining parameter appears—the distancel between the planes. The calculations were made forl=1–100 cm.     

Numerical investigation and self-similar solutions of the glacier-ocean interaction problem

The mathematical modeling of the heat and mass transfer processes in glaciers is an effective means of investigating and predicting their development. A full explanation of the problem of constructing appropriate mathematical models is given in [1–5]. By analyzing the equations involved [3, 6] it is possible to establish the principal factors and dimensionless numbers determining glacier dynamics and provide justification for neglecting the secondary terms. In particular, a simplified closed system of differential equations for the detailed calculation of all the hydrodynamic characteristics of the glacier can be obtained for K_hj « 1 up to O(K _h ² ), where K_h is the ratio of the vertical and horizontal scales of the ice mass investigated (K_h 10^–4–10^–6). In this case many of the qualitative characteristics of glacier dynamics are preserved even in one-dimensional models within the subisothermal approximation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 3–7, September–October, 1986.     

The Use of Fick's Law for Modeling Trace Gas Diffusion in Porous Media

Two models for combined gas-phase diffusion and advection in porous media, the advective-diffusive model (ADM) and the dusty-gas model (DGM), are commonly used. The ADM is based on a simple linear addition of advection calculated by Darcy's law and ordinary diffusion using Fick's law with a porosity–tortuosity–gas saturation multiplier to account for the porous medium. The DGM applies the kinetic theory of gases to the gaseous components and the porous media (or dust) to develop an approach for combined transport due to diffusion and advection that includes porous medium effect. The ADM and Fick's law are considered to be generally inferior for gas diffusion in porous media, and the more mechanistic DGM is preferred. Under trace gas diffusion conditions, Fick's law overpredicts the gas diffusion flux compared to the DGM. The difference between the two models increases as the permeability decreases. In addition, the difference decreases as the pressure increases. At atmospheric pressure, the differences are minor (<10%) for permeabilities down to about 10^–13 m². However, for lower permeabilities, the differences are significant and can approach two orders of magnitude at a permeability of 10^–18 m². In contrast, at a pressure of 100 atm, the maximum difference for a permeability of 10^–18 m² is only about a factor of 2. A molecule–wall tortuosity coefficient based on the DGM is proposed for trace gas diffusion using Fick's law. Comparison of the Knudsen diffusion fluxes has also been conducted. For trace gases heavier than the bulk gas, the ADM mass flux is higher than the DGM. Conversely, for trace gases lighter than the bulk gas, the ADM mass flux is lower than the DGM. Similar to the ordinary diffusion variation, the differences increase as the permeability decreases, and get smaller as the pressure increases. At atmospheric pressure, the differences are small for higher permeabilities (>10^–13 m²) but may increase to about 2.7 for He at lower permeabilities of about 10^–18 m². A modified Klinkenberg factor is suggested to account for differences in the models.     

Interferometric study of natural convection in rectangular air cavities of various orientations

The results of an experimental investigation into the temperature profiles and heat transfer associated with natural convection in rectangular air cavities are presented, the angle of inclination varying from 0 (heating at the bottom) to 180° (heating at the top). The range of Rayleigh numbers was R=2.68·10³–2.57·10⁵, and n=H/d=5.06–18.3. The investigation was carried out by an optical method, using an IZK-454 interferometer. For a horizontal orientation of the cavity the heat-transfer data satisfy the relation N=0.216 R^0.25, for a vertical orientation N=0.144 R^0.3h^–0.129, where N is the Nusselt number. In the region of an inclination of 30° the heat transfer passes through a maximum under all conditions studied.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 89–93, July–August, 1972.     

Thermal effect of a freely expanding gas jet on a flat plate

An experimental investigation was made into the thermal effect of a single gas jet on a plate at Mach numbers of the nozzles in the range 2–6.1, specific heat ratio = 1.4, total pressure difference up to 6·10⁷, gas temperature 450–520 °K in the forechamber, and pressure in the forechamber (10–20)· 10⁵ Pa. The proposed dimensionless numbers made it possible to obtain generalized dependences of the distribution of the heat flux to the plate on the conditions of the problem. A method of approximate calculation of the heat fluxes is proposed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 119–126, July–August, 1981.     

An automated dynamic viscometer with air bearing and inductive transducers for angular displacement detection

A dynamic viscometer is described, with which the dynamic moduli in the frequency range from 2 × 10^–3 to 10 Hz can be determined for liquids with 10^–3 Pa< |G ^* | <10² Pa. Due to the application of an air bearing and inductive transducers for the detection of the angular displacement of both the drive and the measuring cylinder a sensitive apparatus has been made. Very small strains (₀ 10^–3) can be applied and only a small amount of sample (4 ml) is needed. The operation of the apparatus is fully computer-controlled, thus, long runs at various frequencies and temperatures are possible without operator intervention. The theoretical background, calibration procedure, and operation window are described. A presentation of some measurements on two polyisoprene/polystyrene triblock copolymer solutions concludes the work.     

Forced capillary breakup of liquid jets

The characteristics of the forced capillary breakup (FCB) of liquid jets have been investigated over a broad range of variation of the breakup parameters: jet orifice diameter (34–527 m), flow rate (10^–5–1 cm³/sec), and excitation amplitude and frequency. The theory is compared with experiment.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 53–61, March–April, 1988.The authors are grateful to E. V. Ametistov for his constant interest and assistance.     

Supersonic molecular beams production and temperature distribution in free expanding jets

Summary A supersonic molecular beam production system is described in which a continuous flux of Argon molecules can be produced as high as4 · 10 ¹⁸ molecules sterad^–1 sec^–1 in a vessel where the background pressure can be kept below10 ^–6 mmHg using relatively little cryo and diffusion pumping facilities. The beam intensity is measured at different stagnation pressures as a function of nozzle-skimmer separation and skimmer diameter. The results are compared with the existing theories, and information is obtained on the radial temperature distribution in the free expanding jet.

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Sommario Si descrive un apparecchio per la produzione di fasci molecolari supersonici nel quale, facendo uso di stazioni di pompaggio, a diffusione e criogenico, relativamente modeste, si può produrre un flusso continuo di molecole di Argon di4 · 10 ¹⁸ molecole sterad^–1 sec^–1 in un ambiente in cui la pressione di fondo è mantenuta inferiore a10 ^–6 mmHg. Vengono riportate misure di intensità del fascio, a diversi valori della pressione nell'ugello, in funzione della distanza ugello-primo collimatore e del diametro del primo collimatore. I risultati vengono confrontati con le teorie esistenti e dal confronto si ottiene informazioni sulla distribuzione della temperatura radiale nei getti in espansione libera.

     

Radiative heat transfer in an emitting,absorbing, and scattering compressed layer

The aim of the paper is to investigate the screening of radiation from the high-temperature part of the compressed layer by the two-phase ablation products of a graphite axisymmetric body moving under the following conditions through a hypersonic air flow: V = 12–18 km/sec, p_s = 10⁵ Pa, R = 1–3 m, and /₀ = (2.54–5.73)·10^–4. Steady and unsteady sublimation regimes of graphite ablation with strong blowing are considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 94–103, March–April, 1984.