Nonlinear rheological behavior of a concentrated spherical silica suspension

Linear and nonlinear viscoelastic properties were examined for a 50 wt% suspension of spherical silica particles (with radius of 40 nm) in a viscous medium, 2.27/1 (wt/wt) ethylene glycol/glycerol mixture. The effective volume fraction of the particles evaluated from zero-shear viscosities of the suspension and medium was 0.53. At a quiescent state the particles had a liquid-like, isotropic spatial distribution in the medium. Dynamic moduli G^* obtained for small oscillatory strain (in the linear viscoelastic regime) exhibited a relaxation process that reflected the equilibrium Brownian motion of those particles. In the stress relaxation experiments, the linear relaxation modulus G(t) was obtained for small step strain (0.2) while the nonlinear relaxation modulus G(t, ) characterizing strong stress damping behavior was obtained for large (>0.2). G(t, ) obeyed the time-strain separability at long time scales, and the damping function h() (–G(t, )/G(t)) was determined. Steady flow measurements revealed shear-thinning of the steady state viscosity () for small shear rates (< ^–1; = linear viscoelastic relaxation time) and shear-thickening for larger (>^–1). Corresponding changes were observed also for the viscosity growth and decay functions on start up and cessation of flow, + (t, ) and _– (t, ). In the shear-thinning regime, the and dependence of ₊(t,) and _–(t,) as well as the dependence of () were well described by a BKZ-type constitutive equation using the G(t) and h() data. On the other hand, this equation completely failed in describing the behavior in the shear-thickening regime. These applicabilities of the BKZ equation were utilized to discuss the shearthinning and shear-thickening mechanisms in relation to shear effects on the structure (spatial distribution) and motion of the suspended particles.Dedicated to the memory of Prof. Dale S. Parson     

Comparison of Calculated and Experimental Data on Supersonic Flow past a Circular Cylinder

The supersonic perfect-gas flow past a circular cylinder is studied on the basis of a numerical analysis of the time-dependent two-dimensional Reynolds equations using a differential q– turbulence model with reference to the experimental conditions. The calculations are carried out at Reynolds and Mach numbers Re=2× 10⁵ and M=1.1, 1.3, and 1.7 and the experimental investigations at Re=1.62×10⁵–2×10⁵ and Mach numbers on the interval 0.7 M 1.7. The calculated and experimental data on the pressure coefficient distribution over the cylinder surface, the location of the separation point on the surface, and the pressure drag coefficient are compared.     

Diffusion of moisture in deformable porous media. Anisotropic fibrous materials

This paper presents a study on the deformation of anisotropic fibrous porous media subjected to moistening by water in the liquid phase. The deformation of the medium is studied by applying the concept of effective stress. Given the structure of the medium, the displacement of the solid matrix is not taken into account with respect to the displacement of the liquid phase. The transport equations are derived from the model proposed by Narasimhan. The transport coefficients and the relation between the variation in apparent density and effective stress are obtained by test measurements. A numerical model has been established and applied for studying drip moistening of mineral wool samples capable or incapable of deformation.Nomenclature D mass diffusion coefficient [L²t^–1] - e void fraction - g gravity acceleration [Lt^–2] - J mass transfer density [ML^–2t^–1] - K hydraulic conductivity [Lt^–1] - K _s hydraulic conductivity of the solid phase [Lt^–1] - K ^* hydraulic conductivity of the deformable porous medium [Lt^–1] - P pressure of moistening liquid [ML^–1 t^–2] - S degree of saturation - t time [t] - V speed [Lt^–1] - X horizontal coordinate [L] - Z vertical coordinate measured from the bottom of porous medium [L] - z z-coordinate [L] Greek Letters porosity - ₁ total hydric potential [L] - _g gas density [ML^–3] - ₁ liquid density [ML^–3] - ₀ apparent density [ML^–3] - _s density of the solid phase [ML^–3] - density of the moist porous medium [ML^–3] - external load [ML^–1t^–2] - effective stress [ML^–1t^–2] - bishop's parameter - matrix potential or capillary suction [L] Indices g gas - 1 moistening liquid - p direction perpendicular to fiber planes - s solid matrix - t direction parallel to fiber planes - v pore Exponent * movement of solid particles taken into account     

Non-Markovian diffusion process in polymers and stretched exponential relaxation

In this contribution, we model the long-time behaviour of the desorption from an LDPE sheet, using non-Markovian random walks. It is shown that the mass of penetrant in the final stage of desorption decays as t ^–m , where m is proportional to the exponent of the probability distribution (t) t ^–(1+u), 0 < v < 1. Furthermore, it is shown that this model may lead to the so-called mechanical stretched exponential relaxation, and that Wagner's memory function can be obtained as a special case.Presented at the second conference Recent Developments in Structured Continua, May 23–25, 1990, in Sherbrooke, Québec, Canada     

Rheological properties of skim milk gels at various temperatures; interrelation between the dynamic moduli and the relaxation modulus

The rheological properties of rennet-induced skim milk gels were determined by two methods, i.e., via stress relaxation and dynamic tests. The stress relaxation modulusG _c (t) was calculated from the dynamic moduliG andG by using a simple approximation formula and by means of a more complex procedure, via calculation of the relaxation spectrum. Either calculation method gave the same results forG _c (t). The magnitude of the relaxation modulus obtained from the stress relaxation experiments was 10% to 20% lower than that calculated from the dynamic tests.Rennet-induced skim milk gels did not show an equilibrium modulus. An increase in temperature in the range from 20° to 35 °C resulted in lower moduli at a given time scale and faster relaxation. Dynamic measurements were also performed on acid-induced skim milk gels at various temperatures andG _c (t) was calculated. The moduli of the acid-induced gels were higher than those of the rennet-induced gels and a kind of permanent network seemed to exist, also at higher temperatures. G storage shear modulus,N·m^–2; - G loss shear modulus,N·m^–2; - G _c calculated storage shear modulus,N·m^–2; - G _c calculated loss shear modulus,N·m^–2; - G _e equilibrium shear modulus,N·m^–2; - G _ec calculated equilibrium shear modulus,N·m^–2; - G(t) relaxation shear modulus,N·m^–2; - G _c (t) calculated relaxation shear modulus,N·m^–2; - G ^*(t) pseudo relaxation shear modulus,N·m^–2; - H relaxation spectrum,N·m^–2; - t time,s; - relaxation time,s; - angular frequency, rad·s^–1. Partly presented at the Conference on Rheology of Food, Pharmaceutical and Biological Materials, Warwick, UK, September 13–15, 1989 [33].     

Experimental investigation of return currents in electrogasdynamic flows

An investigation is made of return electric currents in electrogasdynamic flows for laboratory sources of unipolar charged particles. These currents play an important role in the process of airplane electrification as a result of the work of jet engines. Models have been built, making it possible to study the behavior of return currents outside and inside an axisymmetric electrogasdynamic flow, in the absence (single-contour source) and the presence (double contour source) of an external annular neutral jet. It is shown that a rise in the return current J^– outside an electrogasdynamic jet is accompanied by a decrease in the take-off current J °. A decrease in the relative distance L from the source to an external grounded surface and an increase in the ratiov of the velocity of the external neutral jet to the velocity of the electrogasdynamic flow lowers J^– in both grounded and insulated models; in the latter case, where J ° J°0, there is an appreciable return current outside the jet. With an increase in the potential of the source from =0 to the floating potential, the current J^– rises, attaining a maximum, and then decreases. This effect is observed also when J^–=0 in both grounded and insulated models. For the case L–1,v=1, the theoretical and experimental dependences of J^– on the potential of the source , retarding the charged particles of the flow under transitional conditions, are in satisfactory agreement.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 127–134, January–February, 1978.In conclusion, the authors thank A. B. Vatazhin for his interest in the work, and A. P. Strekal and V. F. Kudryashov for their participation in the experiments.     

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.     

Development of a full-field planar Mie scattering technique for evaluating swirling mixers

A full-field planar optical diagnostic technique for studying mixing in swirling flows is described. Results were obtained using this technique to provide planar mixing information by seeding a simulated fuel stream with aluminum oxide particles, then inferring concentration from Mie scattering intensity distributions. This facility and measurement technique are unique for several reasons. First, they allow spatial variations in laser sheet energy to be corrected for on a shot-to-shot basis. Second, they allow experiments to be performed for swirlers with practical fuel and oxidizer flow rates, i.e. on the order of 150 g/s (0.33 lbm/s). Finally, they allow full size swirler models to be evaluated, with the entire exit plane imaged simultaneously. Representative results are presented as false color images of the planar mixing fields. These images allow rapid assessment of the mixing process and its changes with variations in operating conditions or swirler geometry.List of Symbols C seed particle concentration, m^–3 - mean component of seed particle concentration, m^–3 - C fluctuating component of seed particle concentration, m^–3 - C ^* time averaged ratio of rms particle concentration fluctuations to average particle concentration, dimensionless - d _p particle diameter, m - I laser energy after passing through the flow, J/m² - mean laser energy, J/m² - I ₀ laser energy before passing through the flow, J/m² - L _v eddy length scale, m - l laser beam path length, m - U _v eddy velocity scale, m/s - V diode voltage reading after passing through the flow, V - mean diode voltage, V - V ₀ diode voltage reading before passing through the flow, V - absorptivity, m² - _rel relative equivalence ratio, dimensionless - fluid viscosity, Ns - _p particle density, kg/m³ - Stokes number= _p / _f , dimensionless - _f flow time scale, s - _p particle response time, s     

Rheologie pathologischer Gelenkflüssigkeiten

Zusammenfassung Zur Charakterisierung der Lösungsstruktur pathologischer Synovialflüssigkeiten wurden parallel rheologische Untersuchungen sowohl im Bereich konzentrierter als auch verdünnter Lösungen durchgeführt. Durch die Berücksichtigung der Scherabhängigkeit der Grenzviskositätszahl [] und Messung bei niedrigen Schergeschwindigkeiten (D 2,9 10^–3 – 4,6 s^–1) errechneten sich höhere Molekulargewichte der Hyaluronsäure (HA) als bisher angegeben. Für entzündliche Gelenkergüsse betragen sie (2,4–12,0) 10⁶, für nicht entzündliche (3,1–11,4) 10⁶ und sind damit gegenüber der normalen Synovia mit 16,2 10⁶ erniedrigt. Unterschiedlichek _SB-Werte sprechen zusätzlich für eine stärkere Verknäuelung der HA-Makromoleküle in der pathologischen Synovia.Durch Ermittlung der kritischen Polymerkonzentration der HA sowie der Verhängungszahlenv aus Anlaufmessungen konnten quantitative Aussagen zum makromolekularen Netzwerk getroffen werden. Die normale Synovia entspricht einem sehr engmaschigen und dichten Netz, aber auch in den pathologischen Gelenkflüssigkeiten ist die HA nicht im Sinne einer Partikellösung isoliert, sondern bildet ein, wenn auch lockeres Netzwerk mit wesentlich niedrigerer Verhängungszahl. Eine Erniedrigung der Viskosität und Elastizität isolierter HA weist darauf hin, daß molekulare Wechselwirkungen zwischen HA und anderen Makromolekülen in der Synovialflüssigkeit für das rheologische Verhalten von wesentlicher Bedeutung sind. Relaxationszeitmessungen in Ruhe und unter Scherung zeigten eine vermehrte Segmentbeweglichkeit des Netzwerkes der pathologischen Synovia als Folge der HA-Konzentrationsabnahme und/oder Molekulargewichtsverminderung.

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Summary Rheological investigations were done in concentrated as well as diluted solutions to characterize the solution structure of pathological synovial fluids. By looking at the shear rate dependence of [] at low shear rates (D 2,9 10^–3 – 4,6 s^–1) higher molecular weights were determined than reported before. The so determined molecular weights of hyaluronic acid (HA) are in the range ofM = 2,4 10⁶–12 10⁶ g/mol in inflammatory joint diseases and in non-inflammatory in a range ofM = 3,1 10⁶–11,4 10⁶ g/mol and therefore both are lower than in normal synovial fluids,M = 16,2 10⁶ g/mol. Additional distinctk _SB-values indicate a compacter coil of HA macromolecules in the pathological synovial fluid.Quantitative statements can be made to the macromolecular network structure by determination of the critical HA polymer concentration and the number of entanglements resulting from prestationary measurements. The normal synovial fluid is comparable with a very narrow-meshed and dense network, but also in the pathological synovial fluid the HA is not isolated like in a particle solution but forms a much looser entanglement network structure. The reduction of viscosity and elasticity of isolated HA indicate that molecular interactions between HA and other macromolecules in synovial fluid are of essential significance for the rheological behaviour. Measurements of relaxation time at rest as well as shear conditions show a higher segment-flexibility of macromolecular network structure resulting from a reduction of HA-concentration and/or molecular weight in the pathological synovial fluid.

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D Schergeschwindigkeit - D _K D-Koordinate des Tangentenschnittpunktes der Fließkurve - t _k Knickzeit (Relaxationszeit) - scheinbare Viskosität (Scherviskosität) - ₀ Anfangs-, Nullviskosität - _rel relative Viskosität - _sp spezifische Viskosität - _red = _sp/c reduzierte Viskosität - [] Grenzviskositätszahl (Staudinger-Index) - A Flächenmaß der master-curve - G ₀ Ruheschermodul - G _s Schermodul der strömenden Lösung - _N = ₁₁ – ₂₂ erste Normalspannungsdifferenz - ₁₂ Schubspannung - ₀ scheinbare Relaxationszeit der ruhenden Lösung - scheinbare Relaxationszeit der strömenden Lösung - v Verhängungszahl - M Molekulargewiht - s ₂₀ Sedimentationskoeffizient bezogen auf 20°C - s ₂₀ ⁰ Sedimentationskoeffizient bezogen auf 20°C bei unendlicher Verdünnung (c 0) - c Hyaluronsäure-Konzentration - c _krit kritische Hyaluronsäure-Konzentration - c _p Protein-Konzentration - _äqu Dichte äquivalenter Kugeln - Dichte des Mediums im Kegel/Platte-Spalt - Winkelgeschwindigkeit - R Radius von Kegel und Platte des Meßsystems - r Korrelationskoeffizient - p Signifikanzniveau Herrn Prof. Dr. med.Fritz Hartmann zu seinem 60. Geburtstag gewidmet.Mit 14 Abbildungen und 5 Tabellen     

Peessure intensification on the front of a shock wave propagating in a heterogeneous system

An increase in pressure in the wave front as compared to the pulse initiating the wave has been observed experimentally in a study of shock-wave propagation in aqueous suspensions of bentonite [1]. In suspensions in which the solid phase is in the form of colloidal size particles =10^–7–10^–8 m of the mineral montmorillonite with mass content c=6%, with multishock loading an intensification of this effect from experiment to experiment was observed [2]. In order to study the principles involved in this anomalous intensification of pressure on the shock wave front, as well as to clarify the effect of the nature of the material in the dispersed phase, experiments were performed with particles of another broad class of clay-like minerals — kaolinite.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 86–92, September–October, 1986.     

A three-parameter model describing the behaviour of a viscoelastic liquid in a tangential annular flow

A three-parameter model describing the shear rate-shear stress relation of viscoelastic liquids and in which each parameter has a physical significance, is applied to a tangential annular flow in order to calculate the velocity profile and the shear rate distribution. Experiments were carried out with a 5000 wppm aqueous solution of polyacrylamide and different types of rheometers. In a shear-rate range of seven decades (5 10^–3 s^–1 < < 1.2 10⁵ s^–1) a good agreement is obtained between apparent viscosities calculated with our model and those measured with three different types of rheometers, i.e. Couette rheometers, a cone-and-plate rheogoniometer and a capillary tube rheometer. a physical quantity defined by:a = {1 – ( / ₀)}/ ₀ (Pa^–1) - C constant of integration (1) - r distancer from the center (m) - r ₁,r ₂ radius of the inner and outer cylinder (m) - v _r local tangential velocity at a distancer from the center (v _r = _r r) (m s^–1) - v ₂ local tangential velocity at a distancer ₂ from the center (m s^–1) - shear rate (s^–1) - local shear rate (s^–1) - ₁ wall shear rate at the inner cylinder (s^–1) - dynamic viscosity (Pa s) - _a apparent viscosity (_a = / ) (Pa s) - _a1 apparent viscosity at the inner cylinder (Pa s) - ₀ zero-shear viscosity (Pa s) - infinite-shear viscosity (Pa s) - shear stress (Pa) - _r local shear stress at a distancer from the center (Pa) - ₀ yield stress (Pa) - ₁, ₂ wall shear-stress at the inner and outer cylinder (Pa) - _r local angular velocity (s^–1) - ₂ angular velocity of the outer cylinder (s^–1)     

Couple on a rotary oscillating sphere in a dusty gas

Rotary oscillations of a sphere about its vertical diameter in an infinite expanse of viscous, incompressible fluid with imbedded identical spherical particles are studied. The problem is solved by the method of separation of variables and explicit expressions for the velocity of fluid particles and the couple experienced by the sphere due to fluid stresses are obtained. The couple is expressed in terms of two parameters and graphs have been drawn to represent the variation in these parameters and some interesting conclusions are made.Nomenclature u ⁵ velocity of fluid particles - v ⁶ velocity of dust particles - P ⁵ pressure - ⁶ fluid density - t ⁹ time - m mass of a dust particle - N number density of dust particles - k ⁵ Stokes resistance coefficient - ³ viscosity - ⁶ kinematic viscosity - ⁷ particle relaxation time - ⁴ frequency of oscillation of the sphere - f ⁹ mass concentration of the dust particles     

On physical criteria for the selection of wood for soundboards of musical instruments

In order to develop criteria for the physical evaluation of wood for soundboards of musical instruments, measurements were made of dynamic Young's modulusE, static Young's modulusE, internal frictionQ ^–1 in longitudinal direction, and specific gravity for numerous species of broad-leaved wood. From the results obtained, including those of our previous paper on coniferous wood [1], it was found that the suitability of wood for soundboards could be evaluated by the quantity ofQ ^–1/(E/), and that there were very high correlations betweenQ ^–1/(E/) andE/, and betweenE andE, regardless of wood species. Consequently, it becomes possible to select practically any wood suitable for soundboards by using the value ofE/, which can be measured easily, and it was derived that the relation betweenE/ andQ ^–1 of wood could be expressed by an exponential equation regardless of wood species.     

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.     

The relaxation of concentrated polymer solutions

The focus of this paper is on the viscoelastic properties of concentrated polymer solutions and polymer melts. Dynamic mechanical measurements were performed on various polystyrene/ethylbenzene solutions with polymer concentrations ranging from 40% up to 100% and temperatures from Tg+30°C up to 70°C (230°C for polymer melts). The basis polymers are two commerical grade polystyrenes (BASF) with M _W = 247 kg/mol and 374 kg/mol, respectively. To avoid solvent loss due to evaporating during the measurements, a special sealing technique was used.A phenomenological model which describes quantitatively the relaxation spectrum of concentrated polymer solutions from the flow regime up to the glass transition regime is developed. The relaxation data of the respective polymer melt and the glass transition temperature of the solution are the only input parameters needed. The temperature dependence is described by a universal, concentration invariant WLF-equation. The relaxation spectra are divided into two parts accounting for the entanglement and the segmental relaxation modes, respectively. The relaxation strength related to the flow and entanglement regime scale with c ^2.3, whereas the segmental relaxation strength does not alter with concentration. All relaxation times change with concentration proportional to c ^3.5. Flow curves can be calculated from these relaxation spectra and thus, our results are useful for engineering applications.Roman Symbols a _T Time temperature superposition shift - factor - a _c Time concentration superposition - shift factor in the flow regime - a _c Time concentration superposition - shift factor in the glassy regime - b _T Modulus temperature superposition - shift factor - b _c Modulus concentration shift factor - in the flow regime - b _c Modulus concentration shift factor - in the glassy regime - B Virial coefficients - c Polymer mass fraction kg/kg - c ₁ WLF-parameter - c2 WLF-parameter K - g Relaxation strength of a relaxation Pa mode - G(t) Relaxation modulus Pa - G Storage modulus Pa - G Loss modulus Pa - GN Plateau modulus of linear flexible Pa polymers - (x) Delta function: (0) = 1, - (x<>0)=0 - h() Damping function - H() Relaxation spectrum Pa - J ₀ ^N Recoverable compliance Pa^–1 - m Mass kg - M _c Critical molecular weight kg/mol - M _e Entanglement molecular weight kg/mol - M _w Weight average molecular weight kg/mol - M Number of datapoints - n Scaling exponent - N Number of discrete relaxation modes - T Temperature °C - T _g Glass transition temperature °C - V Volume 1 Greek Symbols Scaling exponent - _f Thermal expansion coefficient K^–1 - Scaling exponent - Shear deformation - Shear rate s^t–1 - Relaxation time s - _c Characteristic relaxation time of thes Cross model - _e Entanglement relaxation time s - Viscosity Pa s - ₀ Zero shear viscosity Pa s - ₀ First normal stress coefficientPa s2 - Segmental friction coefficient - Frequency rad/s Indices f Flow and entanglement regime - g Glass transition regime - i Count parameter - p Polymer - ref Reference state - s Solvent Dedicated to Prof. Dr. J. Meissner on the occasion of his retirement from the chair of Polymer Physics at the Eidgenössische Technische Hochschule (ETH) Zürich, Switzerland     

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.     

Measurement of the Coefficient of Transverse Dispersion in Flow Through Packed Beds for a Wide Range of Values of the Schmidt Number

Experimental values of the coefficient of transverse dispersion (D _T) were measured with the system 2-naphthol/water, over a range of temperatures between 293K and 373K, which corresponds to a range of values of viscosity () between 2.83×10^–4 Ns/m² and 1.01×10^–3 Ns/m² and of molecular diffusion coefficient (D _m) between 1.03×10^–9 m²/s and 5.49×10^–9 m²/s. Since the density () of water is close to 10³ kg/m³, the corresponding variation of the Schmidt number (Sc=/D _m) was in the range 1000 – 50. More than 200 experimental values of the transverse dispersion coefficient were obtained using beds of silica sand with average particle sizes (d) of 0.297 and 0.496mm, operated over a range of interstitial liquid velocities (u) between 0.1mm/s and 14mm/s and this gave a variation of the Reynolds number (Re=du/) between 0.01 and 3.5.Plots of the dimensionless coefficient of transverse dispersion (D _T/D _m) vs. the Peclet number (Pe_m=ud/D _m) based on molecular diffusion bring into evidence the influence of Sc on transverse dispersion. As the temperature is increased, the value of Sc decreases and the values of D _T/D _m gradually approach the line corresponding to gas behaviour (i.e. Sc 1), which is known to be well approximated by the equation D _T/D _m=1/+ud/12D _m, where is the tortuosity with regard to diffusion.     

Spherical particle sedimentation along an inclined plane at high Reynolds numbers

At high Reynolds numbers (10²Re _p <10⁵), the gravity-driven motion of a solid spherical particle along an inclined surface in a Newtonian liquid at rest was studied experimentally. The parameters which determine the particle drag coefficient and its relation with the hydrodynamic force component normal to the wall were obtained.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 105–112, July–August, 1996.     

Fourier transform mechanical spectroscopy of the sol-gel transition in zirconium alkoxide ceramic gels

The gelation of a ceramic precursor, zirconium alkoxide, has been studied using dynamic oscillatory measurements. The gelation time is controlled by varying the concentrations of zirconium propoxide, hydrolysis with water, and acetylacetone concentration which acts as a chelating ligand. Gelation times were varied from minutes to months. The gelation time varied with zirconium concentration to the –10 power, hydrolysis to the –7 power, and ligand concentration of the –17 power. The sol-gel transition was monitored using the criteria of Winter in which GG ⁿ and tan () = tan . It is shown that the use of multiple superimposed sinusoidal waves to simultaneously measure the moduli at several frequencies is faster than using individual frequency sweep experiments. The selection of rate and strain criteria for brittle network gels is discussed in detail.     

Material functions generated by the complex viscosity

Based on the complex viscosity model various steady-state and transient material functions have been completed. The model is investigated in terms of a corotational frame reference. Also, BKZ-type integral constitutive equations have been studied. Some relations between material functions have been derived. C ^–1 Finger tensor - F[], (F ^–1[]) Fourier (inverse) transform - rate of deformation tensor in corotating frame - h(I, II) Wagner's damping function - J (x) Bessel function - m parameter inh (I, II) - m(s) memory function - m _k, n_k integers (powers in complex viscosity model) - P principal value of the integral - parameter in the complex viscosity model - rate of deformation tensor - shear rates - [], [] incomplete gamma function - (a) gamma function - steady-shear viscosity - ^* complex viscosity - , real and imaginary parts of ^* - ₀ zero shear viscosity - ⁺, ₁ ⁺ stress growth functions - ^–, ₁ ^- stress relaxation functions - (s) relaxation modulus - ₁(s) primary normal-stress coefficient - ø(a, b; z) degenerate hypergeometric function - ₁, ₂ time constants (parameters of ^*) - frequency - extra stress tensor