On the existence and bifurcation of minimal normal modes

Minimal normal modes (MNMs) are defined as non-linear normal modes which give a true minimum to Jacobi's Principle of Least Action. It is shown that for a certain class of two degree of freedom non-linear conservative systems, MNMs generically occur in pairs. The nature of both generic and non-generic bifurcations of MNMs is derived and illustrative examples are given.     

Slow viscoelastic radial flow between parallel disks

A perturbation analysis is presented for the steady-state radial flow of a third-order fluid between two parallel disks. The results include previous perturbation analyses in which various other rheological models were used. The pressure drop needed to maintain the radial flow is less than that for the Newtonian creeping-flow solution because of fluid inertia and shear-thinning viscosity, whereas the normal stresses have the opposite effect. Possible use of the “radial flow viscometer” for experimental evaluation of second-order constants is also discussed. Finally, molecular stretching in the flow system is examined using the elastic dumbbell model for a polymer molecule.     

Rheology of coal suspensions

Proper design of operations encountered in preparation, transport and employment of suspensions like coal slurries and coal-oil mixtures require an accurate knowledge of their rheological behaviour.Such concentrated suspensions generally exhibit non-Newtonian behaviour (shearthinning) which is more pronounced at higher coal concentrations. The nature of the dispersing medium influences the aggregation state of the disperse phase and, consequently, affects the stability and the rheology of the systems. In the present paper coal suspensions prepared with different dispersing media and covering a wide range in solid phase concentration are studied, by using a rotational coaxial cylinders viscometer.Different models have been taken into consideration for correlating experimental data. In particular, in order to describe the dependence of viscosity on shear rate and solid phase concentration, the suitability of the model suggested by Smith and Bruce is evaluated. Accordingly, the aggregation state of the disperse phase as well as its dependence on shear rate and dispersing medium can be estimated.     

A study of the shear viscosity of human whole saliva

Summary A model R-18 Weissenberg Rheogoniometer operating in the continuous shear mode was used to generate shear viscosity vs. shear rate data on male and female human whole saliva. These data were found to accurately follow the Sisko model, , whereµ is the shear viscosity at shear rate is the asymptotic shear viscosity at infinite shear rate, andK andn are constants. Data were collected on the effects of food, coffee, caffeine, and aspirin as functions of time. Studies were also made on the effects of emotional stress, donor sex and age.The saliva viscosity increased with time and then decreased to the basal value for most ingested materials. Emotional stress was found to elevate the saliva viscosity. On the other hand, no significant difference was found between the average saliva viscosities of male and female groups. Also, no significant effect of donor age was detected.

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Zusammenfassung Mit Hilfe eines Weissenberg-Rheogoniometers (Typ R-18) wurden bei stationärem Betrieb Scherviskositätskurven in Abhängigkeit von der Schergeschwindigkeit für den Speichel von Männern und Frauen gemessen. Man fand, daß sich die Meßwerte hinreichend genau durch ein Sisko-Modell, , beschreiben lassen, woµ die Scherviskosität bei der Schergeschwindigkeit die asymptotische Scherviskosität bei unendlich großer Schergeschwindigkeit sowieK undn weitere Konstanten bedeuten. Diese Messungen verfolgten die Wirkung von Nahrung, Kaffee, Coffein und Aspirin als Funktion der Zeit. Untersucht wurde weiterhin der Einfluß von emotionaler Spannung, sowie Geschlecht und Alter der Spender.Die Speichelviskosität stieg bei den meisten eingenommenen Stoffen mit der Zeit zuerst an, um danach wieder auf den Normalwert abzusinken. Ebenso fand man, daß emotionale Spannung eine Viskositätserhöhung hervorruft. Dagegen wurden bei Gruppen von Männern und Frauen keine signifikanten Unterschiede gefunden, und ebenso wurde kein gesicherter Einfluß des Alters festgestellt.

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With 4 figures and 6 tables     

The elastic behaviour of gels during the structure formation process

Summary A simple modification of the stress-strain relation for a normal viscoelastic material has been derived for a gel with temporary structural bonds which is subjected to small deformations during gelation. This shows that the storage modulus should separate into two parts, one dependent on frequency and the other on the time for which the gel has been allowed to set. The loss modulus should depend only on frequency. These theoretical results, and others concerning creep under constant stress are in general agreement with observations on a number of gels. Exceptions occur, however, in the period immediately after preparation (before continuous structure has formed) and also after long periods of time during which irreversible changes can have occurred. Certain anomalies appear when the basic assumption of the theory are applied to structure formation in gels with permanent bonds, and a possible resolution of these is suggested.

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Zusammenfassung Es wird eine einfache Modifikation der Spannungs-Dehnungs-Beziehungen normaler viskoelastischer Stoffe abgeleitet, durch die das Verhalten eines Gels mit temporärer Bindungsstruktur bei kleinen Deformationen während des Geliervorgangs beschrieben werden kann. Diese sagt voraus, daß der Speichermodul in zwei Teile aufspaltet, wobei der eine von der Frequenz und der andere von der Erstarrungszeit des Gels abhängt. Dagegen sollte der Verlustmodul nur von der Frequenz abhängig sein. Diese theoretischen Voraussagen, sowie die daraus abgeleiteten Folgerungen bezüglich des Kriechens unter konstanter Spannung, stimmen durchweg mit den an einer Anzahl von Gelen gemachten Beobachtungen überein. Abweichungen kommen dagegen in der Zeit unmittelbar nach der Herstellung vor (bevor sich eine durchgehende Struktur gebildet hat) und nach einer so langen Zeitspanne, daß irreversible Strukturänderungen entstanden sein können. Gewisse Anomalien treten in Erscheinung, wenn die Grundvoraussetzungen der Theorie auf die Strukturbildung bei Gelen mit permanenten Bindungen angewendet werden. Hierfür wird eine mögliche Deutung vorgeschlagen.

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With 3 figures     

Combined influence of the Reynolds number and localised wall suction on a turbulent boundary layer

This paper considers the effect the Reynolds number has on a turbulent boundary layer that is subjected to concentrated suction, applied through a short porous wall strip. The response of the skin friction coefficient to suction is strongly modulated by the momentum thickness Reynolds number R ₀. The magnitude and wavelength of the variation of the skin friction decrease as R ₀ increases. Measurements clearly show that it is the combination of R ₀ and the suction rate that controls the boundary layer response. Relaminarisation of the near-wall flow, which occurs just downstream of the suction strip when =5.5 and R ₀=660, could not be achieved at higher Reynolds numbers. It is suggested that the ratio R ₀/ should not exceed a (as yet undetermined) critical value if pseudo-relaminarisation is to occur. The mean velocity profiles differ from the undisturbed profile for all the values of R ₀ and considered here. Although the redistribution of the turbulent kinetic energy among the normal Reynolds stresses is affected by , a variation in R ₀ does not appear to alter the effect of on this redistribution.     

Jet column modes in both a plane jet and a passively modified plane jet subject to acoustic excitation

Use is made of acoustic excitation to enhance the coherent vortical structures that form in both a plane jet and a passively modified plane jet. The Strouhal number for the preferred mode based on the nozzle height of the jet is found to be unaffected by the passive modification. The existence of the jet column mode of stable pairing in the excited plane jet is unambiguously confirmed. Measurements in the excited and modified plane jet show that the passive modification suppresses this mode. Finally, the work shows the existence of a new mode of stable pairing. Both time- and phase-averaged measurements are presented to examine this mode.     

Temperature spectra from a turbulent thermal plume by ultrasound scattering

This paper reports the results of a study on temperature inhomogeneities conducted on a thermal plume by using ultrasound scattering as a non-intrusive measurement technique. The plume rises from a metallic disk which can be heated up to 800 °C. The working fluid is air at atmospheric pressure. In the measurement technique, an incoming ultrasound wave is emitted towards the thermal plume. The incident wave is scattered because of non-linear couplings with the flow instabilities present in the measurement region. The scattered wave carries information about those flow instabilities. The technique allows for the retrieving of this information. The shape of the obtained spectrum of temperature fluctuations as a function of wave vector modulus is consistent with previous theoretical analysis. Three qualitatively different regions were identified: first, a production region characterized by a q² law; secondly, a region with behavior as per q⁻³ associated with a buoyancy region and; finally, a dissipation region associated with a q⁻⁷ law. These spectral regions characterize the energy transfers mechanisms among the length scales of flow investigated here. A coefficient of anisotropy γ was defined to analyze anisotropic features of the flow.     

Determining stress intensity factors in orthotropic composites from far-field measured temperatures

We demonstrate the ability to determine stress intensity factors in orthotropic materials directly from measured temperatures away from the crack and using far-field expressions for the stresses. This is advantageous, recognizing that recorded thermoelastic data can be very unreliable near the tip of a crack. In addition to singular terms that govern in the immediate vicinity of the crack tip, the present series expressions for the stresses contain higher-order finite terms. Little measured input information is needed and data acquisition positions can be selected largely at the user's discretion.