ALBERT

Notes: Summary Sequences of hemispheric five day mean minimum brightness mosaics are used to plot the variation in the Antarctic pack ice edge for three summer seasons and to locate extremes at particular dates. Average and extreme areas of sea ice over the hemisphere are measured as a function of time. The geographical distribution of major polynyas is shown and the decay pattern of sea ice in the main continental embayments is described and found to show considerable similarity in each season. Some evidence is shown that apparent substantial differences in ice extent between October 1st, 1969 and the corresponding date in 1970 are qualitatively consistent with observed variations in the strength of the southern westerlies in October of both years.

Notes: Summary Quantitative radiance measurements from NASA's ATS-3 geosynchronous satellite have been used to develop and test a statistical forecst method to predict air terminal weather over the very short range (0–6 hours) time period. Results from more than 800 hourly weather situations at a wide range of U. S. weather stations show that the parameters of ceiling and total opaque cloud cover can be specified or predicted with skill, exceeding peristence forecasts for time periods greater than two hours. Statistical predictions based on satellite data alone are much better than those based on some 500mb upper air parameters tested. The potential global applications of the satellite data-based forecasts can apparently be improved by the use of certain criteria, such as region of interest, in developing and applying the multiple regression equation. Considering the present status of objective short range weather forecasting, these first results using geosynchronous satellite data demonstrate a new potential for improved forecasts at this scale.

Notes: Summary The results of thunderstorm observations made with local lightning flash counters at Poona during 1967–1969 are presented. A positive correlation between the average total count when the count exceeds 20 per hour on a 5V/m counter, and the number of days per month when thunder is heard has been established. The diurnal and seasonal variations in thunderstorm activity are described. It is seen that although a single isolated storm can vitiate the normal pattern of thunderstorm activity in a month or season, a long term statistical average can be taken with a greater degree of confidence as a better index of electrical activity than the current aural method of observation of thunderstorms.

Notes: Summary This paper is concerned with a study of the atmospheric electrical conditions and processes at 700 up to 3000 m a. s. l. during precipitations of the most varied kind. The relation between potential gradientE or, respectively, point discharge currenti po , and precipitation current densityI pr may be represented by regression lines whose character during steady precipitations is independent of the kind of precipitation or altitude a. s. l. The precipitation rate plays only a subordinate part and does not control the character of the above mentioned relations. During steady precipitations the polarities ofE,I pr andi po are determined by the physical state of the precipitations. During snowfall,E andi po are positive,I pr is negative; during rainfall, the opposite signs apply. The sign reversal takes place when snow particles melt in free fall, which, as an average, takes place at +1.1° C. The well-known mirror image effect applies as a rule rather than an exact law. A number of observations regarding deviations from the strict mirroring of the values indicate that the theory cannot be valid which claims that high primary values ofE would trigger point discharges which, in turn, generate ions that are captured by precipitation, with the result thatE andI pr proceed in a mirror-inverted manner. The truth is that by processes of precipitation electricity,E is primarily influenced, andi po secondarily. The charge on cloud bases, except in thunderstorms, is irrelevant to precipitation electrical processes. In precipitation, the behavior of the atmospheric electrical quantities is governed by the precipitation physical processes in the most immediate vicinity of the observation site. The above mentioned polarities of the atmospheric electric quantities during precipitation are applicable only to steady precipitations. If the atmospheric stability is decreased below a certain threshold value, polarity changes of the atmospheric electrical quantities will occur which have nothing to do with the physical state nor with the electric charge on the cloud base (except in thunderstorms). The frequency of the polarity changes may be presented as a function of the exchange intensity above the station. This relation may be used for practical purposes of determining the degree of turbulence.

Notes: Summary Studies have been made of the charge transfer resulting from the collision and separation of water drops falling in an electric field. The charge transferq was measured for values of field strengthE, impact velocityV, drop radiiR, r, radius ratioR/r, and angle Θ ranging from 0.5 to 80 kV/m, 0.5 to 3 m·sec−1, 200 to 600 μ, 1.0 to 3.0 and 0 to 90 degrees respectively, where Θ is the angle between the field and the line of centres of the drops at the moment of separation. Two uniformly sized drop-streams were ejected from hypodermic needles by modulating the flow of water through them and then collided between a pair of electrodes across which a potential difference existed. The drops coalesced temporarily, swung around each other and separated, each resulting stream being collected in a vessel connected to an electrometer in order to measure the charge. The measured values ofq were generally in good agreement with theoretical values derived from the equationq = 1.1 · 10-10 γ1 E r 2 Cos Θ, where γ1 is a function ofR/r. Calculations based on this equation, the Marshall-Palmer drop-size distribution and established values of separation probabilities of colliding drops showed that collisions between raindrops within electrified clouds will act powerfully to dissipate the existing fields.

Notes: Summary The measured values of electrical parameters of the atmosphere are known to be affected by wind, and days with strong winds (v x 〉6 m s−1) are normally classified as electrically disturbed. While the effect of horizontal wind on the electric field is readily explained in terms of changes in the spacecharge density, it is shown from electrodynamical considerations that the observed effect on the air-earth current cannot always be attributed solely to changes in the local conductivity and electric field. The existence of a vertical current of advection of magnitude ɛ0χ e υ x (∂E z /∂x) is revealed, and shown by calculations to be important (for instance during dust-storms and pointdischarge) when large space-charge concentrations are advected by wind. Since the current of advection is proportional tov x (∂E z /∂x), it is suggested that this parameter rather thanv x be used as a criterion for deciding wind-disturbed measurements of routine fair-weather atmospheric electric parameters.

Notes: Summary The specific ozone destruction rate at the ocean surface was estimated from profile measurements between 1 m and 20 m height above the open sea. The ozone concentration gradient turned out to be independent of the horizontal wind velocity within the instrumental error range. Within the velocity interval of 1 m/sec to 10 m/sec a mean gradient of (0.23±0.12) γ/m for stable stratification and of (0.09±0.018) γ/m for unstable stratification were obtained. Both values base upon an assumed ozone concentration of 100 γ at 25 m altitude. Thus, the vertical flux of ozone and the specific ozone destruction rate of the ocean surface are proportional with the wind velocity. Between the specific ozone destruction rateq and the average wind velocity $$\bar u_{10} $$ at 10 m height the relation $$q = (1.7 \pm 0.6)10^{ - 5} \cdot \bar u_{10} [cm/\sec ]$$ holds. Above 30 m height the results of balloon soundings indicate the mixing ratio ozone/air to be constant with altitude.

Notes: Zusammenfassung Dieser Arbeit liegen tägliche globale Wolkenbeobachtungen der meteorologischen Satelliten ESSA 3 und 5 des Jahres 1967 zugrunde [1], die eine Totalbetrachtung irdischer Wettervorgänge ermöglichen. In der vorliegenden Untersuchung wurden vor allem Wirbelstrukturen behandelt, die zur Bildung von Wolkenspiralen geführt haben. Im Jahre 1967 traten auf der ganzen Erde 405 Wirbel mit Spiralstruktur auf, davon 180 auf der Nordhemisphäre und 225 auf der Südhemisphäre. Als Quellenherde traten auf der Nordhemisphäre Nordatlantik und Nordpazifik hervor, auf der Südhemisphäre ergab sich eine Anordnung der Quellgebiete in Form eines breiten Gürtels, der um den Globus herumläuft. Die Wirbelbahnen verlaufen auf der Nordhemisphäre überwiegend in nordöstlicher, auf der Südhemisphäre in ostsüdöstlicher Richtung. Die Ursprungsgebiete der Wirbelstrukturen in einer Serie sind häufig Wolkenbänder mit einer Länge von 5000 bis 10000 Kilometern. Sie entspringen in der Nähe des Äquators und verlaufen quer über die Meere. Diese Bänder, die quasistationär sind und häufig eine Lebensdauer von drei bis fünf Tagen haben, zeigen über bestimmten Gebieten des Globus eine starke Bündelung. Vor allem treten vier Bündel hervor, die ein „Fischgrätenmuster” bilden. Über dem Atlantik verläuft ein Bündel vom tropischen Mittelamerika nach Nordosten bis zum mittleren Nordatlantik, das „Gegenbündel” von den tropischen Gebieten des Amazonenstromes nach Südosten über Brasilien zum Südatlantik. Über dem Pazifischen Ozean lassen sich ganz ähnliche, vom Äquator nordost- bzw. südostwärts verlaufende Bündel von Langen Wolkenbändern finden. Die vier Bündel weisen auf ganz bestimmte Regionen der Erde hin, die beim Luftaustausch zwischen den Hemisphären von großer Bedeutung sein dürften. Es sind dies besonders zwei Regionen: die erste liegt an der Übergangsstelle vom nordamerikanischen zum südamerikanischen Kontinent, die zweite in der äquatorialen Region zwischen Südostasien und Australien.

Notes: Zusammenfassung Die Bedeutung der verschiedenen Terme der Vorticitygleichung (Advektions-, Divergenz- und Rotationsterm) für die Produktion und Reduktion von Vorticity wird anhand von zwei Wetterlagen untersucht. Mittels der geostrophischen Approximation und einem Verfahren zur Berechnung der Vertikalbewegung wind die räumliche und zeitliche Verteilung jedes Terms berechnet. Es zeigt sich, daß bei einer entwicklungsarmen Wetterlage vor allem der Advektions- und Divergenzterm maßgebend für Vorticityänderungen sind, daß hingegen in den Verlauf einer starken Entwicklung auch der Rotationsterm wesentlich eingreifen kann.

Notes: Summary General circulation parameters in the northern hemisphere are calculated using atmospheric thermal structure obtained from Nimbus III SIRS multi-channel radiance information. The thermal structure up to 10 mb is obtained by using a regression technique with thickness between pressure levels as the dependent variable. General circulation parameters calculated on a daily basis include zonal and eddy available potential energy, and zonal and eddy kinetic energy. A second set of calculations is performed using National Meteorological Center (NMC) grid data. A comparison of the two sets of calculations indicates that, although the energies calculated from the SIRS-derived structure underestimate the actual energies, maxima, minima and trends are well identified. An example of mid-stratospheric energy changes during a breakdown of the polar-night vortex is also given.

Notes: Summary With total ozone sensors on earth-orbitung satellites the ozone distribution over the entire earth may be measured daily. The conclusions from some of the Nimbus III measurements are discussed in this paper. A comparison of time-longitude variations of stratospheric radiance values at 60°S with values of the total ozone indicated that low (high) radiance values correspond very closely with the low (high) total ozone amounts. The speed at which these ozone ‘waves’ progress eastward is greatest in the winter hemisphere. The speed of eastward progression decreases as one approaches the lower latitudes in the winter hemisphere. In the equatorial region the progression of the ozone ‘waves’ appears to be slowly westward. In the Northern Hemisphere the waves progress slowly eastward during summer. The intensity of the ozone ‘waves’ was also observed to change with latitude. These temporal and spatial fluctuations are related mainly to the motion of dynamic tropospheric systems. The extremely tight ozone gradients, which may be seen in the winter hemisphere data, have been shown to be associated with strong baroclinic zones in the lower stratosphere and upper troposphere, which are moving eastward. Assuming uniform zonal velocity we found Rossby wavelengths that varied from 2500 to 3700 km.

Notes: Summary It has been experimentally observed that one-inch thick soil-cement slab (fine-grained soil), upon drying from the top face, first deforms with a concave surface at the top and gradually assumes an opposite curvature with convex surface at the top. The latter shape contradicts the classical analysis ofPickett. A theory whereby the doming can be predicted is proposed in this paper. Moisture migration in the drying slab is determined by the unsaturated capillary flow theory, modified to account for the fact that soil-cement will exhibit hysterisis in the relation between pressure head (capillary tension) and its moisture content. By postulating that moisture tension (stress) results in deformation or shrinkage, a relation between shrinkage and moisture tension is obtained from experimental data. The results seem to violate an intuitive feeling that the exposed top face should shrink more than the sealed bottom face. The creep compliance of soil-cement specimens is determined for a range of humidities from 55–100%. Finite difference techniques have been employed to compute the relaxation modulus from creep compliance which are related throughBoltzmann integral. To include the dependence of the modulus upon a variable humidity field, constitutive law is modified on the basis of time-humidity equivalence hypothesis. Imposing on the theoretical shrinkage distribution, computations for stresses and deflections are made from two points of view: 1. Using the simplifying assumption that the relaxation modulusG(t) does not vary with humidity and 2. allowing for the humidity variation in the transient problem and using a generalG(t, H). The solution from the first point of view is obtained by equivalent shrinkage concept and from the latter by finite element method. The computed deflections not only predict doming but also show good agreement with the observed values. It should be noted that the current theory predicts deflections opposite to those predicted by conventional analysis when the moisture movement is assumed to be governed by diffusion law and shrinkage to be proportional to moisture loss.

Notes: Summary The equations for determining die swell of molten polymers are discussed. The critical conditions for melt fracture and die swell results are combined in order to explain the flow behavior at the onset of instability. It is shown that the factor $$\bar M_z \bar M_{z + 1} /\bar M_w^2 $$ is the most important parameter in die swell and melt fracture studies.

Notes: Résumé Les premiers essais réalisés sur la planche à peindre nous ont permis de chiffrer l'ordre de grandeur des efforts d'application et de mettre en évidence l'importance pour une peinture donnée, du rapport de l'effort normal sur l'effort tangentiel. Cette technique simple peut permettre un contrôle rapide, en cours de fabrication, de la brossabilité d'une peinture. Toutefois la mise au point d'un applicateur automatique éliminant sur les résultats la dispersion due au peintre semble indispensable si l'on veut lier la brossabilité aux caractéristiques rhéologiques d'une peinture.

Notes: Summary In order to investigate the short time response of solid polymers, a high resolution laser interferometer has been employed to observe the detailed structure of stress waves produced by the impact of polymeric plates. From the observed stress waves the loading and unloading stress-strain paths followed by the material can be determined. For the polymer, polymethyl methacrylate, over the stress range from 0–60 kbar such observations have disclosed a stress-strain behavior which exhibits large strain nonlinearities and significant rate-dependence. For stress levels below ≈7 kbar and above ≈40 kbar, rate-effects are of secondary importance and the observed wave profiles may be modeled using a nonlinear elastic description of the material behavior. However, at about 7 kbar, a transition is observed in the dynamic stress-strain behavior which is characterized by greater stress relaxation and significant hysteresis upon unloading. This transition, which we attribute to a yield phenomenon, requires a rate-dependent description of the material behavior to be used in the stress range of approximately 7–40 kbar.

Notes: Summary A simple and reliable relative method to derive the molecular weight distribution of linear polymers is proposed. It is shown that both the zero-shear viscosity,η 0, and the intrinsic viscosity, [η], have a logarithmic dependence on the weight average molecular weight, $$\bar M_w $$ , and the polydispersity, $$Q = \bar M_w /\bar M_n $$ . The coefficients of these relationships can be determined by applying a multiple regression analysis to a series of samples for which $$\bar M_w $$ andQ are known. By making use of the two established relationships, the determination of $$\bar M_w $$ andQ for a given polymer sample reduces to the experimental measurement of itsη 0 and [η]. An analysis has been performed to estimate to what extent experimental errors onη 0 and [η] affect the calculated molecular weight distribution. It has been found that only the experimental error on [η] contributes heavily to the final error on the polydispersity.

Notes: Summary High shear capillary viscometry at 37.8°C (100°F) of concentrated solutions of a series of polyalkylmethacrylate viscosity index improvers in a petroleum lubricating oil is reported. Viscosity average molecular weights of the four polymers varied from 355 000–1650 000 and solution concentrations varied from 2–20 wt.-%. An approximating function based on the error function was computerfit to the complete flow curves by correlating the distribution of apparent viscosity with the product ( $$\dot \gamma $$ τ), the rate of viscous energy dissipation. This gave an estimate of the secondNewtonian viscosity (η ∞ ) and two parameters of the approximating function. The fourth quantity required to completely define the flow curve is the low shear or firstNewtonian viscosity (η 0 ). Representation of the original data was within 2%, by this technique. The parameters of the flow function — the energy level at the inflection point and the slope of the transformed flow function — were found to vary in a regular manner with both molecular weight of the polymer and polymer concentration, expressed as relative viscosity (η rel). The limiting asymptotes of the approximating function —η 0 andη ∞ — could not be treated according to the conventionalHuggins equation, but they were fit adequately by theMartin equation: log(η sp/C)=log[η]+K[η]C. The intrinsic viscosities thus determined for both low shear ([η M ]0) and high shear ([η M ]0) demonstrate aMark-Houwink relationship, i.e., [η M ]0=5.668×10−5 M v 0.660 and [η M ]∞=2.574×10−5 M v 0.0669 so that ([η M ]∞≈[η M ]0/2) over the range studied. The relationship of these results to other reports of high shear viscometry of polymer solutions is discussed.

Notes: Summary A literature survey and an experimental study are presented on the short term strength variation of G.R.P. specimens subjected to the combined effect of loading and different environmental conditions. Findings are as follows: a) Residual longitudinal strength was found to decrease above a preloading level of about 25–35% of the corresponding reference strength — on exposure to hot (80 °C) water, even after an environmental-loading history (E.L.H.) stage of 48 h. b) No reduction in residual longitudinal strength (R.L.S.) was observed on exposure to cold water (22 °C) and to a dry-hot environment (80 °C). Conclusions are as follows: a) Early reduction of the residual strength is conditional on a combination of temperature and humidity, whereas each factor alone does not cause any deterioration, even under high preloading. b) Humidity is the main factor in the onset of internal failure in the glass-fiber phase, the effect being probably due to reduction of the surface energy of the glass by water adsorbed on its surface, accompanied by drastic reduction of its strength (Griffiths theory). Temperature has an indirect effect, accelerating the diffusion process and reducing the time scale for failure initiation.

Notes: Summary One of the main problems in Rheology is the determination of the yield condition for which no satisfactory form seems to exist. If a start is made with the stress tensor field, one soon runs into a number of difficulties. It is therefore better to deal with the geometry of the field. The change from elastic to plastic deformation can be interpreted as a mapping of one space into another, and the yield as an asymptotic sub-space. If the elastic strain field ise ij , whose invariants areJ 1,J 2,J 3, then an asymptotic behaviour may be represented by the existence of a functional relationf(J 1, J2,J 3) = 0, between theJ's, which are independent of one another in the normal part of the field. This does not fix the nature of the functionf, for which we can invoke the additional geometric condition that yielding can result from infinite contraction or expansion of a macro-element. Thus theJacobian of the mapping must take on the singular values zero or infinite. These concepts give rise to the yield condition in the strain tensor field in the form 8J 3 − 4J 2 + 2J 1 → 1. If generalized measure of strain is used, which is necessary for creep problems, this takes the formn 3 J 3 −n 2 J 2 +nJ 1 → 1.n being a real constant, which is equal to 2 for theAlmansi measure. These conditions do not depend on either the isotropicity or homogeneity of the field, and hence should be used for all types of yield conditions.

Notes: Summary The time-dependent behavior of the viscosity of bentonite-water suspensions was studied experimentally inCouette flow for various transitions between constant shear rates. It was found that, in general, the characteristic times become longer as the final shear rate becomes smaller and, for the same final shear rate, as the differences in shear rates become smaller. The characteristic time increases with increasing temperature and decreasing concentration. A discussion of the kinetics of the time dependence is given.

Notes: Summary For viscometric, axial, annular flow, the second normal stress differenceN 2 is related to the difference in normal thrust across the annular space,ΔT rr . Past attempts using this method have yielded values ofN 2 for polymer solutions which are different in magnitudeand opposite in sign from those obtained in other experiments. This inconsistency is attributed to errors resulting from the use of pressure holes in the measurement ofΔT rr , and is supported by a second-order fluid analysis. The present work focuses on the measurement of the effect of pressure hole errors on the determination ofN 2 with aqueous polymer solutions. In the measurement ofΔT rr , simultaneous use is made of both pressure holes and miniature pressure transducers to measure and account for pressure hole errors. Results indicate that hole errors are sufficiently large to reverse the sign of the computedN 2. This technique is therefore suggested as a preferred method for determiningN 2, especially at high shear rates.

Notes: Summary This paper deals with the measurement of the second normal stress difference in a viscoelastic flow in an open semi-circular inclined channel; associated theory is also given. The theory shows that simple correlations exist for the second normal stress difference, the shear stress, and the profile (or the deflection) of the free surface of the flow. It leads to a method for deducing the second normal stress from the measured surface profile. A treatment of surface tension, whose effect has been ignored in previous analyses is given as an integral part of the formulation. Samples of polyisobutylene/cetane and some aqueous solutions of different concentrations were used for measurements using two tubes of different materials and sizes tilted at different angles. The N.B.S. No. 1 nonlinear sample was also tested. Agreements between results for different tube sizes and angles indicate the consistency of the theory and measurements. The results presented here show that the ratio of the second to the first normal stress differences is negative and the functional form of the second normal stress difference is close to a square law in shear stress in the range investigated. Relatively speaking, we find the ratio |N 2 /N 1| to be greater for more dilute solutions. A summary of available data onN 2 is given for polyisobutylene, and reasonable consistency between various investigators is demonstrated for this material. Besides, a correlation ofN 2 for various polymer solutions is also shown.

Notes: Summary The total momentum-energy tensor describing the interaction of a polarizable and magnetizable continuum with an electromagnetic field is constructed on the basis ofLorentz invariance. The equations of balance of energy and momentum are deduced and applied to the study of the magnetooptical, electrooptical and photoelastic behavior of an elastic polarizable and magnetizable isotropic continuum. This model exhibits theCotton-Mouton andKerr effects but thePockels andFaraday rotations don't appear.

Notes: Summary A model to describe bond rupture and fracture in polymeric fibers is described. An experimentally determined distribution in stresses is incorporated with absolute reaction rate theory in the model to predict bond rupture. Model predictions are compared with experimentally determined fracture and free radical concentrations for various loadings. The experimental parameters in the model are discussed and their “best fit” values given. In general, these values are found to compare quite satisfactorily with accepted values from theory or other tests in the literature.

Notes: Summary Apparatus for the measurement of extensional viscosity of polymer solutions is described. The range of extensional strain rates is 100–800 sec−1. Two converging liquid jets of high velocity impinge on a central low-velocity jet, causing the liquid in the central jet to be rapidly stretched. The force causing extension of this jet is measured from the change in reaction on the central capillary nozzle, whilst the initial and final velocities are obtained by jet thrust and photographic methods respectively. The Instron system provides accurately-controlled liquid flowrates and continuous recording of the various forces involved. Tests are reported on polyacrylamide solutions of concentration 0.10% and 0.07%, and on poly (ethylene oxide) solutions of concentration 0.10%. The extensional viscosity of the more concentrated polyacrylamide solution is over 30 poise at an extensional strain rate of 600 sec−1, exceeding the shear viscosity by a factor of 400 (the “Trouton” ratio). For the poly (ethylene oxide) solution, theTrouton ratio reaches 1400 at an extensional strain rate of only 200 sec−1. The results are shown to be consistent with orifice jet thrust data for similar solutions at higher strain rates. The axial stress rises rapidly with increasing extensional strain rate, but there is no evidence of an abrupt increase of stress in the range of strain rates between 102 and 104 sec−1. The triple jet method is of value in giving data for intermediate extensional strain rates and being dependent on fewer assumptions than the orifice jet thrust experiment.

Notes: Summary A unique shear stress-shear rate relationship exists for laminar flow of any time independent substance in a tube, whereas this is not the case for turbulent flow. In order to obtain a unique relationship for turbulent flow, a new approach based on the elementary theoretical interpretation of experimental data is adopted in the present paper. In particular, wall shear stress is found to be a unique function of a new turbulent pseudo shear rate term. In this relationship therè are two parameters which characterize a given substance — the limiting viscosity at high shear rateµ m and a factorα m which takes into account modification of turbulent structure by the non-Newtonian properties. Both of these parameters must be determined experimentally. Methods of predicting pressure gradients and of scaling up are outlined. In applying the approach to suspensions in which the solid phase has a density greater than that of the liquid medium, it may be important to determine the increment in shear stress equivalent to the energy required to maintain the solid particles in suspension. The validity of this approach is confirmed by data for the flow of a variety of substances including kaolin suspensions and Carbopol solutions in tubes ranging in diameter from 1.5 to 20 mm.

Notes: Abstract This paper describes the work carried out to investigate the pore pressures occurring in secondary consolidation. A theoretical approach and an experimental technique was developed in order to conduct the study. By considering compression to occur only due to water leaving the soil it was possible to derive an expression for the dissipation of pore pressure in the secondary phase. By further simplified assumptions which are based on experimental observations, the above general solution was reduced to a simple formula which predicted the observed behaviour of pore water pressures during secondary consolidation.

Notes: Summary The relation of melt viscosity to weight-average molecular weight and branching index has been derived for polydisperse polymers, with the most probable distribution of primary chains, having randomly distributed tri- or tetrafunctional branch points. The results are obtained by an extension of theKilb treatment for the intrinsic viscosity calculations. Numerical values of the viscosity functions are given for selected branching indices.

Notes: Summary A new calculation of the stability of elongational flow of a liquid filament is based on an idealized treatment of the effects of non-uniformity of filament diameter. Two uniform cylindrical filaments of different initial cross-sectional areas are connected by a fictitious deformable clamp which transmits tensile force without interfering with the assumed homogeneous elongational flow of each filament. A uniform tensile force is suddenly applied and kept constant. For a Newtonian liquid, the area ratio rapidly tends to infinity. For a “rubberlike liquid”, the area ratio at first increases but then becomes constant; this suggests that finite deformation of a “Gaussian” molecular network may provide a possible mechanism for “spinnability” at constant temperature and composition.

Notes: Zusammenfassung Mit dem hier vorgestellten Rheometer ist man in der Lage, den häufig interessierenden Anfangsbereich der Fließkurve nicht-Newtonscher Flüssigkeiten zu ermitteln. Es konnte theoretisch und am Beispiel einer Reihe von Polymerlösungen gezeigt werden, daß im Bereich sehr niedriger Schergeschwindigkeiten die Beziehungen $$\dot \gamma = \Omega$$ und $$\tau = \frac{M}{{4\pi h \cdot r_{i^2 } }}(1 - \beta )$$ Punkte der Fließkurve liefern. Danach ergibt sich in diesen Fällen ein außerordentlich einfaches Auswertungsverfahren, das auf eine umständliche Bestimmung der Stoff konstanten (beispielsweise mittels Fehlerquadratminimierung) verzichten kann.

Notes: Summary A method is described for measuring the dynamicYoungs Modulus over a range of frequencies for muscle with various static loads. The results of measurements on the Ox Sternomandibularis muscle before and during the development of rigor mortis are presented. These show that the muscle behaves as an extremely non-linear viscoelastic material with properties that depend on both the conditions of measurement and the storage conditions prior to measurement.

Notes: Zusammenfassung Bei der zur Bestimmung des Torsionsmoduls aus erzwungenen Schwingungen an rechteckförmigen Stahlsaiten beobachteten wir eine sehr starke Abhängigkeit dieser Werte von der ProbenvorspannungP v . Weiterhin zeigte sich experimentell, daß diese Abhängigkeit um so stärker in Erscheinung tritt, je größer das Verhältnis von Probenbreite zu -dicke ist. In diesem Bericht wird gezeigt, daß dieser Befund durch ein beim Torsionsversuch auftretendes Zusatzdrehmoment zu deuten ist; dieses ist durch eine Dehnungsverteilung innerhalb des Prüflings bedingt, die ihrerseits dadurch entsteht, daß bei der Tordierung die Prüflings-„Fasern“ um so stärker gedehnt werden, je weiter sie vom Drehpunkt entfernt sind. Experimentell zeigte sich bei Stahlsaiten, daß dieser Effekt bei kreisförmigen Querschnittsflächen weniger ausgeprägt ist. Für rechteckförmige Prüflinge ergab sich ein kritisches Seitenverhältnis von ca. 20. Oberhalb dieser Grenze wurde ein Vorspannungseinfluß beobachtet, der sich während des Versuches in einer Abhängigkeit der Resonanzfrequenz von der Probenvorspannung bemerkbar macht.

Notes: Summary In the present paper, we have undertaken a comparative study of the flow behaviour of two types of fluids —Eringen's mioropolar fluid andStokes' couple stress fluid — in a simple oscillatory flow. This study was undertaken with a view to see if the close resemblance of the flow behaviour of these two fluids in steady shearing flows was maintained even in time dependent flows. We find that the flow behaviour of these two fluids are widely different in oscillatory motion.

Notes: Summary In the present paper we have made a study of simple shearing flows in three polar fluids — (i) the model ofCondiff andDahler, (ii) the model ofEringen, and (iii) the model ofStokes. We have investigated in detail the components of stress, equations governing the motion and boundary conditions in the above fluids in flows induced by motion of boundaries or a pressure gradient. By means of tables, we have studied the common features of these fluids and related the fluid parameters involved in each case.

Notes: Summary A method of defining tensor fields associated with a given continuum is presented and applied to the description of rheological variables for a continuous material moving and deforming in space. Three different types of tensor field are defined and compared: body fields, space fields, andCartesian space fields. A bold-face notation is introduced for body tensor fields and its relation to other authors' notations for space fields is presented. Body fields give the simplest description of rheological states because body stress and body metric tensor fields, unlike space stress and strain tensor fields, are independent of the orientation of material elements relative to directions fixed in space.

Notes: Summary The problem of a rigid punch pressed against and moved on the surface of an elastic or viscoelastic layer is studied. It is shown that the governing equations reduce to the same integral equation for the elastic contact problem. Two particular motions of the punch are considered. In the first case the punch moves at a constant speed along a straight line on the surface of a viscoelastic layer. In the second case the punch moves at a constant speed along a circular path. Finally, the special case of a punch moving on a layer of a standard linear viscoelastic solid is studied. The equation is identical to a punch of modified shape pressed on an elastic layer.

Notes: Résumé Dans ce travail, on étudie l'effetFaraday dans le cadre de la mécanique des milieux continus. On se base sur les équations deMaxwell, ainsi que sur les bilans de quantité de mouvement et d'énergie interne pour un continu polarisable et magnétisable sous la forme obtenue parG. Mayne etPh. Boulanger (4). A ces équations on adjoint des équations constitutives où l'on introduit, en plus des variables qui caractérisent un diélectrique élastique, les dérivées par rapport aux temps de la déformation, de la polarisation et de la magnétisation. Grâce à une linéarisation des équations autour d'un état d'équilibre, on étudie la propagation des ondes planes électromagnétiques et mécaniques dans la direction d'un champ magnétique constant. Cette étude met en évidence l'effetFaraday ainsi qu'un effet analogue pour les ondes mécaniques transversales.

Notes: Summary The micropolar fluid defined by the constitutive equations ofEringen (3, 4) is to be considered. This fluid is characterized by describing the motion of the fluid elements by two kinematic fields: The velocity field and the spin field. The corresponding equations of motion are specialized for boundary layer flow. A similar solution can be given for “flow near stagnation” as outer flow. Concerning the flow properties of the polar fluid two parameters are of main interest: First, the ratio of boundary layer thickness to characteristic length scale of the fluid elements; secondly, a parameter describing the coupling between velocity and spinfield. The solution is discussed comparing the behaviour of the micropolar fluid to that of aNewtonian liquid.

Notes: Summary The present work is concerned with the microrheology of a 2-dimensional fibrous system. A mathematical model is proposed that contains the aspects of bonding between fibres. The notion of three measuring scales, as well as the concept of a “Material Functional” that reflects the geometrical and rheological properties of the network is introduced in the analysis. The deformation kinematics is treated first for single fibres and then the fibre-fibre interaction by using a generalised force concept is considered. A formal presentation of the material functional required for the characterization of the fibrous network response is given.

Notes: Summary It has been known for some time that the molecular orientation of liquid crystals can be affected by the presence of a temperature gradient.Stewart reported in 1936 that, whenp-azoxyanisol was placed in a vertical temperature gradient, the orientation adopted was vertical when the higher temperature was at the bottom and horizontal when the higher temperature was at the top. The continuum theory for nematic liquid crystals, proposed byLeslie, is used to explain this phenomenon. An examination of the stability of the static orientation adopted by the director in the presence of a vertical temperature gradient shows that the stable orientations are either vertical or horizontal, as found experimentally.

Notes: Summary 1. Use of the generalized nonlinearMaxwell equation with due account for two members of relaxation time spectrum shows a good agreement between the theoretical and experimental torsion diagrams and creep curves over a large time range. 2. Calculation of maximum tangential stresses by an approximate method, based on experimental torsion diagram, obtained as a result of rod testing, gives such values that practically coincide with the values calculated with two members of relaxation time spectrum. 3. Constants of polymers, determined on the basis of experimental torsion diagrams, obtained as a result of rod testing, may be used for the evaluation in the first approximation of two relaxation constants of polymers (G ∞,2 andη 0G.2 * ) corresponding to younger component of spectrum.

Notes: Summary The curing reactions of an epoxy-anhydride and a rubber vulcanization system were followed by rheological means. Dynamic shear measurements were used to follow the reaction. The rheological quantities were related to the reaction kinetics of the systems. From these relations, overall activation energies, reaction orders and rate constants were interpreted from the data. These compare favorably with results reported in the literature. The cures of several diallyl phthalate compounds were also examined with dynamic shear measurements. The results correlated well with thermoset molding experience.

Notes: Summary In a previous paper (1) proposals were made for the equations which govern the mechanical behaviour in plane strain of an ideal incompressible granular material. In this paper tentative suggestions are made for the extension of this theory to compressible granular materials. The material is envisaged as a mixture of an ideal gas and solid particles. The state of an element of the mixture is determined by its overall density and the mass and volume concentrations of the constituents. It is proposed that the material satisfies a flow condition which relates the two principal invariants of the stress (in two dimensions) and the density. The condition for the stress equations to be hyperbolic is obtained, and for the hyperbolic case a natural interpretation is obtained for the angle of internal friction. For the kinematic behaviour it is proposed that the deformation consists of superposed shearing deformations on the stress characteristic surfaces, as described in (1), together with a superposed dilatation. The equations describing this behaviour are expressed in characteristic form. They reduce to the equations given in (1) when the density is constant.

Notes: Summary The shape of the free surface of a second order fluid, enclosed between vertical concentric cylinders with the inner cylinder rotating with angular velocityΩ, is calculated. The calculation uses a perturbation procedure in which, for slow flows, the boundary conditions on the free surface are transformed to boundary conditions on the fixed horizontal surface obtained whenΩ is zero. The results are tested experimentally.

Notes: Summary Considering the analogy of a liquid surface to a stretched membrane, the theory of large elastic deformations is used to calculate the deformed shapes of sessile and pendent liquid drops of some polymers. In particular, the liquid drops are treated as highly deformable liquid-filled membranes that follow a neo-Hookean constitutive equation. Since, with the advent of sophisticated pressure transducers, it is easier to measure pressure accurately than to determine the curvature of the liquid drop geometry, the problem is formulated in terms of the pressure prescribed at the tip of the liquid drop with a varying hydrostatic pressure. The governing equations consisting of a non-linear ordinary differential equation and aVolterra type integral equation are solved numerically on a digital computer. Based on the solution of the governing equations, a procedure to estimate the surface tension of a polymer from the shape factor versus pressure curves is illustrated. Also, by increasing the pressure and by balancing the vertical component of the surface tension against the weight of a pendent liquid drop the size of a drop separated from a liquid column is predicted.

Notes: Zusammenfassung Im Warren Spring Laboratory wurde ein neues Drehmoment-und Normaldruckmeßsystem entwickelt, das mit Ausnahme des R17 zu den meisten Modellen desWeissenberg-Rheogoniometers paßt. Ein einziges piezoelektrisches Kristallgerät ersetzt die luftgelagerte Torsionsaufhängung und somit die Notwendigkeit einer Preßluftzufuhr, und es ersetzt außerdem das mit Servoeinrichtung versehene Normaldruckmeßsystem. Bei gleichmäßiger Rotationsprüfung erfaßt das Gerät einen weiten Drehmoment- und Druckbereich. Ohne daß Torsionswellen, Normaldruckfedern und/oder Kegeldurchmesser ausgetauscht werden müssen, werden die gleichen Bereiche wie mit dem Standardsystem erreicht. Durch den Normaldruck verursachte etwaige Änderungen der Spaltweite sind dank der Natur dieses Gerätes praktisch bedeutungslos, und die mit Servoeinrichtung versehene Anordnung wird somit überflüssig. Damit entfallen die Schwierigkeiten durch Unempfindlichkeit und Ansprechverzögerung der Anordnung während des Einsatzes bei hochviskosen Materialien. Beim dynamischen Testen sind keine Korrekturen aufgrund der Eigenfrequenz des Gerätes erforderlich, da diese wesentlich höher als die obere Testfrequenz des Instrumentes ist. Im niedrigen Viskositätsbereich sind beim Standardmodell Korrekturen erforderlich. Dank der Torsionsstabilität der Oberplatte werden außerdem höhere Spannungen ermöglicht. Durch die Ansprechgeschwindigkeit des neuen Gerätes werden dynamische Normalkraftmessungen möglich. Es werden einige mit dem neuen und mit dem Standardsystem gewonnene vergleichende Daten einer Reihe von Materialien sowohl für gleichbleibende Rotations- als auch Oszillationstest angegeben.

Notes: Zusammenfassung Es wurde die Abhängigkeit der Haftfestigkeit im System Polymer-Faser von der Geschwindigkeit der Belastung untersucht. Die Versuche wurden mit Metalldraht von 150µm Durchmesser, alkalifreien Glasfasern von 12 und 200µm Durchmesser und wärmehärtenden Polymeren: Epoxidharz, Polyesterharz, siliziumorganischen und Butvar-Phenolharzen durchgeführt. Der Großteil der Messungen erfolgte bei Zimmertemperatur, bei Butvar-Phenol-Polymeren auch bei Temperaturen oberhalb und unterhalb der Zimmertemperatur. Es wurde gefunden, daß die Haftfestigkeit aller untersuchten Systeme eine lineare Funktion des Logarithmus der Belastungsgeschwindigkeit darstellt. Während sich der absolute Wert der Haftfestigkeitτ merklich beim Übergang von System zu System ändert, hängt die Empfindlichkeit vonτ gegenüber der Belastungsgeschwindigkeit wenig von der Natur der Unterlage und des Adhäsivs sowie vom Härtungsregime des Polymers ab. Aus den erhaltenen Daten wurde mittels desBailey-Kriteriums und der Lebensdauerformel vonShurkov die Aktivierungsenergie des adhäsiven Zerstörungsprozesses bestimmt. Es erwies sich, daß die Aktivierungsenergien der adhäsiven und der kohäsiven Zerstörung ähnlich sind.

Notes: Summary The rheological characteristics of synovial fluid have been examined with aWeissenberg Rheogoniometer. Rheological evidence for the existence of a macromolecular complex in normal but not in inflammatory joint fluids has been deduced from experiments with hydrogen bond breaking agents. Further flow experiments with measurements of relaxation time and activation energy for viscous flow appear to support the contention that macromolecular complexes do exist in normal fluid and that dilution alone does not account for their dissolution in inflammatory joint diseases. Proteolytic enzyme extracts from inflammatory synovial fluid appear to have no effect on the flow characteristics of normal synovial fluid. Attempts to identify the nature of the macromolecular complex by analytical ultracentrifugation were not successful. It is concluded that rheological techniques offer a way of investigating macromolecular interactions when classical chemical methods may not be appropriate.

Notes: Conclusion The effect of mechanical working on polyethylene oxide suggests that, although this substance fulfils many of the criteria for an artificial lubricant in human joints, it is unlikely to be successful in vivo over a prolonged period. This is probably due to the weak linkages present. The simplicity of the structure might have led one to think that it would withstand mechanical degradation more satisfactorily than a more complex molecule, but the experiments demonstrate that this is not so. Sodium carboxymethyl cellulose, on the other hand, shows a high degree of resistance to mechanical degradation and a successful artificial lubricant is likely to be closer to this configuration in which bonds are less exposed.

Notes: Zusammenfassung Die Änderung der Viskosität von nativem Blut in Abhängigkeit von Zeit und Druck in einem Kapillarviskosimeter folgen einem bestimmten Schema: bei gesunden Versuchspersonen folgt einem starken Abfall ein Anstieg, bevor die Gerinnung einsetzt. Derartige Untersuchungen sind auch an Blutproben von Patienten, die an gewissen seltenen Krankheiten leiden, besonders solchen mit Mangel an Gerinnungsfaktoren, gemacht worden. Die erhaltenen Beziehungen entsprechen nicht dem normalen Verlauf. Da jedoch zu wenig Patienten zur Verfügung standen, ist es jedoch schwer zu sagen, ob diese Abweichungen für diese Krankheiten typisch sind. An Multiple Sklerose Erkrankten sind genügend Untersuchungen durchgeführt worden. Es ist wahrscheinlich, daß für diese Krankheit ein eigenartig systemloses Verhalten typisch ist. Dieses ist anscheinend unabhängig von der betreffenden Therapie. Es stellt sich nicht ein, wenn es zu schweren Komplikationen im Krankheitsverlauf gekommen ist. Dieser Test ist aber nicht genügend empfindlich für die Frühdiagnose. Nach Beginn der Gerinnung folgen alle normalen und pathologischen Zustände derselben Gleichung für die Gerinnungskinetik, aber natürlich nicht mit denselben Gleichungskonstanten.

Notes: Summary Stiffness is an important subjective phenomenon diagnostically and therapeutically in rheumatic diseases such as rheumatoid arthritis and osteoarthrosis. A quantitative and qualitative assessment of these phenomena have been made by arthrographs which impose a sinusoidal motion on the metacarpo-phalangeal and knee joints respectively and record the torque in relation to the displacement. The reproducibility with the joint in situ and moved is satisfactory. A hysteresis torque/ displacement plot is obtained with both joints. Reflex muscle activity may be measured at the joint, as in myotonia congenita and Parkinsonism. In patients without neuromuscular disorders electromyographic studies have shown that the muscles are electrically silent during sinusoidal motion and that active contraction distorts the tracing. The latter fact may be useful in the evaluation of patients with psychological factors producing muscle tension, which may be decreased with diazepam. Using the cat's wrist joint it has been shown that the passive stretching of muscles accounts for 41 per cent of the stiffness recorded at the joint and the capsule 47 per cent, a finding in keeping with work on the distal interphalangeal joint of the human finger. Stiffness increases with advancing age and decreased temperature. Conversely, warming the joint reduces its stiffness. Articular gelling in patients with osteoarthrosis may be demonstrated after periods of rest and the results suggest that such changes are due to alterations in the periarticular and muscle tissues. The rapid diminution in torque after rest in one position was not detected in normal joints even after longer periods of immobilisation.

Notes: Zusammenfassung Eine Kontinuumstheorie ist kürzlich entwickelt worden, die erwarten läßt, die Eigenschaften der flüssigen Kristalle zu beschreiben. Der Zweck dieser Arbeit ist es, erstens, diese Theorie vorzustellen, und, zweitens, ihre Anwendung auf die Viskosimetrie der nematischen flüssigen Kristalle zu diskutieren. Oftmals benutzt man magnetische Felder in den umfangreichen Experimenten, um die Orientierung der bevorzugten Richtung zu kontrollieren, und daher ist eine Diskussion dieses Falles eingeschlossen.

Notes: Summary The formulation of oil-in-water emulsions which have the mechanical properties of semi-solids, i. e. creams, involves both theoretical and practical problems. One solution is to use combinations of ionic or non-ionic surfactants with a fatty alcohol, as in Emulsifying Wax B. P., Cetrimide Emulsifying Wax B. P. C. and Cetomacrogol Emulsifying Wax B. P. C. By altering the total amount of such a mixed emulsifier in a formulation, the consistency may be varied from liquid to semi-solid. The rheological properties of such emulsions have been explained on the assumption that a viscoelastie network exists in the continuous phase, linking disperse phase globules. The nature, extent and strength of this network controls the flow properties of the system. This theory is discussed with particular reference to the anionic surfactant sodium dodecyl sulphate, the cationic surfactant cetrimide, and the long chain alcohols cetyl and stearyl and their mixtures. The importance of testing at small strains is emphasised e. g. creep and oscillatory testing, and it is shown that continuous shear methods, although theoretically less satisfactory, may also provide useful information.

Notes: Summary The physical decomposition of the system formed when sodium dodecyl sulphate, 1-hexadecanol and water are heated, mixed and cooled could be achieved at an accelerated rate by cycling the storage temperature between 5–7 °C and 20–25 °C. This decomposition caused the formation of “pearliness” and the systems became progressively more fluid with loss in rigidity. The changes in the rheological properties of the systems were investigated at 25 °C using a modifiedWeissenberg Rheogoniometer, anEpprecht Rheomat 15 viscometer, and a concentric cylinder air turbine viscometer. The systems are referred to by a code Rx where x is the molar ratio of 1-hexadecanol to sodium dodecyl sulphate. The systems R1–R10 were examined during temperature cycling for a maximum period of eight days. During this period, the systems R1–R4 progressively increased in consistency when examined in continuous shear using anEpprecht Rheomat 15, concentric cylinder viscometer. System R5 was also examined using anEpprecht Rheomat 15, but after increasing in consistency up to the fourth day, thereafter decreased in consistency. Systems R3 to R10 were investigated in creep mode. For R3 and R4, the compliance progressively decreased over a period of eight days, whereas for systems R5–R8 compliance was found to pass through a minimum about four days after preparation and the start of temperature cycling. Thereafter it increased. For R9 and R10, the creep compliance at one hour increased continuously during the eight day period.

Notes: Summary The theory ofEyring of viscous flow, allows to describe the newtonian surface viscosity of a monolayer containing only one active component. This theory is extended to mixed monolayers with miscible components, allowing to calculate the surface viscosity of a surface mixture if the flow parameters of the single components are known. This theory is experimentally illustrated for the systems senegin/digitonin and cholesterol/phospholipids. The results of the last system are discussed in terms of the property of cholesterol being a liquifier in cell membranes. Next the surface viscosities of dilute cholesterol monolayers penetrated by digitonin are given. In this situation no agreement between theory and experiment is observed, indicating an interaction between these components as already known from other experimental techniques. This increased surface viscosity may be related to the strong hemolytic action of digitonin.

Notes: Summary The stability of oil-in-water emulsions depends ultimately on the physical nature of the oil-water interface. If a hydrocolloid or protein is used as an emulsifying agent an interfacial film is formed at the oil-water interface and this may be liquid or viscoelastic solid in properties. The film is formed by the two processes of diffusion from the bulk to the interface and the formation of secondary intermolecular cross-links. Gelatine solutions of up to 2% w/v were used to form an interface with light liquid paraffin over a restricted range of p h . For the 2% w/v gelatin solutions, the p h range was confined to the acid region p h 2.5–3.2 owing to the onset of gelation of the whole aqueous phase, at room temperature, if the p h was increased numerically above this range. At lower concentrations of gelatin, e. g., 0.5% w/v, the useful p h range could be extended to p h 4. The interfacial rheological properties were examined using the surface rheometer described in a previous paper. Preliminary results showed that, in the case of the 1% w/v gelatin solution at p h 3, the interfacial film was liquid up to the end of the first half-hour after formation. Solid properties then developed. After 4 hs it was possible to carry out a creep experiment on the film which exhibited a longest retardation time of several minutes. Further creep and recovery experiments conducted up to 200 h after the formation of the film clearly showed that the growth of solid properties of the film was continuing. The gelatin interfacial films were considerably more compliant than similar films of acacia Senegal, over a comparative period of time, and at the same bulk concentration. This difference in behaviour can be attributed to differences in the basic molecular structure of the two polymers.

Notes: Abstract The pressure dependencedT g /dP of glass transition temperatureT g has received considerable interest due to its connection with solid state thermodynamic properties and theories of glass transition. Free volume considerations (1, 2) led to an estimate of the pressure effect onT g , showing thatdT g /dP had to depend on thermal expansion and compressibility changes atT g through the equation: [1] $$\frac{{dT_g }}{{dP}} = \frac{{\Delta \beta }}{{\Delta \alpha }}$$ whereΔβ=β e −β g andΔα=α e −α g Later work (3, 4, 5, 6) has shown that eq. [1] is not verified by experimental facts, the ratioΔβ/Δα being much larger than (dT g /dP) exp. Recent analysis of the properties of glasses obtained under different pressures have complicated the situation, showing that the experimental value ofdT g /dP depends, of course, on the polymer usedbut also on the experimental procedure used in its determination. Since it is obvious that in order to measure anyΔT g -value we need to operate on at leasttwo glasses, these should be identical in all properties which could influenceT g except pressure. Any difference in morphology,which could lead to a change in T g at constant pressure, should therefore be avoided in order to get a sound value for the pure pressure effectdT g /dP. To reveal this effect, we have performed (7)dT g /dP determinations on two polymers, polyvinylacetate (PVAC) and polyvinylchloride (PVC), following three different procedures: A. Measurement of the changeΔT g induced by application of a pressure incrementΔP on the liquid polymer (T〉T g ). This is the procedure normally used; the liquid is cooled down at a fixed rate of temperature change (∼5 °C/day) andT g is dilatometrically recorded at 1 atmosphere. Then the polymer is taken again to the liquid state, pressure ΔP is applied and, at the same rate, the system is cooled down isobarically; the newT g is recorded anddT g /dP calculated. B. Measurement of the change ΔTg induced by application of a pressure increment ΔP on the glassy polymer (T〈T g ). Once determinedT g at 1 atmosphere, pressureΔP is applied on the glass, time is given to the system to equilibrate; then the glass is heated isobarically. Intersection of the glassy line to the liquid line in a volume/temperature plot gives the newT g and therefore allows the calculation ofdT g /dP. C. Measurement ofΔT g during the heating of a glass along an isochor (5, 8). Here the polymer glass is heated at constant volume, by application of an increasing pressure at increasing temperatures given by(∂P/∂T) v . By repeating this procedure two times, starting from two different specific volumes of the glass, two values ofT g at different pressures can be recorded anddT g /dP calculated. Table 1 shows the result of this work Polymer A dT g /dP, °C/atm B C PVAC 0.015 0.037 0.022 PVC 0.013 0.038 0.028 Comparison of values for different procedures shows quite convincingly howdT g /dP, at a given heating or cooling rate, is a property not only of the polymer but also of the experiment. Any information which, like the pressure effect onT g , is based on a comparison between two or more glasses, should be therefore carefully analysed in terms of other contributions, besides pressure, to the total change inT g .

Notes: Abstract The temperature-dependence of the viscosity η of a liquid can be described by means of an empirical equation suggested as early as 1921 byVogel: η=A exp.B/(T−T 0), which, besides the temperatureT, contains three adjustable structuredependent parametersA, B andT 0. An equation of the same form is suited for describing the temperature dependence of the most probable relaxation timeτ m in polymers, and can be easily transformed into the socalled WLF-equation, because the empirical parametersB andT 0 are simple functions of the WLF parameters. In many cases, the temperature-dependence of such quantities as mechanical or dielectric relaxation times, viscosities, diffusion coefficients etc, is regarded as a consequence of a thermal activation process ruled by a temperature-dependentGibbs Free Energy of activationΔG. On the basis of this concept both parametersB andT 0, can be related to the more fundamental high temperature limiting value of the activation energyΔH and the parameterT 0 to the temperature at whichΔG becomes infinite. The parameterA is normally taken to be temperature-independent; theoretically, however, it may just as well be temperature-dependent. Although it is difficult to decide from experimental evidence whether this is the case (accurate values over a large temperature range must be available), one should realize that analysis done by means of a temperature-independent pre-exponential factor gives a set of values for the parameters which differ greatly from those found when e.g.A is set proportional toT −1 orT −2. Literature values for the viscosities ofn-paraffins have been statistically analysed. It is concluded that η in theVogel-equation had better be replaced byη T 1.2/ϱ, whereϱ is the density of the liquid. Values are given for the modifiedVogel, WLF and activation parameters of the paraffins and ethylenecopolymers, those for the latter being obtained from our own dielectricτ m measurements. By analogy,τ m would then have to be replaced byτ m T 2.2. However with our dielectric data, such a refinement would not give any great improvement.

Notes: Abstract Since long it is settled that the elasticity of rubber must be attributed to the statistics of the polymer coils. The molecular basis of visco-elasticity, however, remained mysterious and is still considered by many as a complicated problem. In the first years after World War II phenomenological descriptions by means of models composed of springs and dashpots were popular but these models, and also their mathematical transcriptions intoLaplace series, are highly unsatisfactory (restriction to very small deformations, relaxation and retardation spectra, impossibility to account for the cross contractions connected with uniaxial strain, etc.). In the past years several attempts have been made to interprete the spring-dashpot model in terms of molecular structure. The springs have been identified with the entropy elasticity of the polymer coils and the dashpots with an intermolecular friction coefficient. Even if it is assumed that this interpretation should be justified then it is a matter of course that such a theory is afflicted with the same absurdities and frustrations as the spring-dashpot model itself. The necessity of another approach will be urged. As rubber elasticity, which refers always to equilibrium states, is an effect of changes of the reversible entropy, so the viscoelasticity of transient states is effected by changes of the irreversible entropy. The transformation of irreversible elastic energy into heat is essentially an increase of entropy and the rate of this process is entirely determined by the probability of the various states because probability of a state and life time of a state are identical expressions. The introduction of a molecular friction is a misconception.

Notes: Zusammenfassung Die Rolle der Struktur-Theorie des Theologischen Verhaltens nichtlinearer visko-elastischer Flüssigkeiten wurde diskutiert, und es wird eine solche Strukturtheorie für. verschiedene Polymer-Systeme angegeben.

Notes: Summary In continuation of an earlier investigation, the present paper discusses the stress distribution in the inertialess flow of a viscoelastic fluid confined between two plane parallel walls, in which the upper wall moves with a constant velocity while the lower is held at rest with a uniform constant suction applied on its surface. However, the stress field is discussed in detail for the case when the upper wall is also held at rest and the effects arising due to application of suction are pointed out. The most important difference in the behaviour of viscoelastic fluid, compared with that ofNewtonian fluid, lies in the fact that the gradient of the normal stress component in the horizontal direction depends on the distance from the walls. A short discussion has also been provided for the flow in a cylindrical tube with uniform constant suction applied on its surface. Though not evident from general considerations, it is seen that the situation here also is quite similar to that of plane flow.

Notes: Zusammenfassung Die dynamischen Eigenschaften eines Styrol-Butadien-Copolymers und eines Naturkautschuks sind als Funktion einer statischen Vorverstreckung gemessen worden. Die dynamische Viskositätη dieser Polymeren ändert sich nicht bis zu einer statischen Verstreckung von ca. 1,7, und die dynamische Spannungsamplitude ist der Steigung der statischen Spannungs-Dehnungs-Kurve proportional. Der Tangens des Verlustwinkels hängt nicht nur von der dynamischen Viskosität, sondern auch von der dynamischen Spannungsamplitude ab. Er ist deswegen nicht unbedingt von einer statischen Verstreckung unabhängig, wenn auchη konstant ist.

Notes: Zusammenfassung Ausgehend von den ArbeitenFerrys undBirnboims wird ein Schwingungsviskosimeter konstruiert, das statt eines schwingenden Stabes zur Erzeugung des Geschwindigkeitsgefälles ein Rohr verwendet. Elektromechanischer Antrieb wird verwendet. Ein Frequenzumfang von ca. 100–750 Hz wird erreicht. Einige Meßergebnisse werden diskutiert.

Notes: Zusammenfassung Nach der elastohydrodynamischen Theorie der Schmierung hängt die Filmdicke und damit auch Verschleiß und Reibung in hochbelasteten Maschinen vom Viskositäts-Druckkoeffizienten des Schmiermittels ab. Nachdem mit Hochdruck-Kugelfall- und Kapillar-Viskosimetern an chemisch-einheitlichen Substanzen Zusammenhänge zwischen dem Viskositäts-Druckkoeffizientenα und Parametern der Molekülstruktur nachgewiesen werden konnten, wurden im folgenden die drei binären Gemische: Chlorparaffin/Paraffin-Weißöl; Fluorkohlenstoff/Paraffin-Weißöl und Essigsäure/Wasser bis 2 kbar untersucht. Im 1. Gemisch durchläuft die dynamische und die kinematische Viskosität bei Atmosphärendruck bei einer bestimmten Konzentration einMinimum, im 2. Gemisch weist nur die kinematische Viskosität ein Minimum, im 3. Gemisch die kinematische und dynamische Viskosität sowie die Dichte einMaximum auf. In allen drei Fällen tritt im Viskositäts-Druckkoeffizientenα kein Extremwert auf. Bei genügend hohen Drücken verschwinden die Extremwerte der Viskosität. Der Viskositäts-Druckkoeffizient des Gemisches kann somit in erster Näherung aus den Koeffizienten der Komponenten abgeschätzt werden.

Notes: Summary In experiments with water and dilute aqueous solutions of polyacrylamide spurious normal forces were observed. This phenomenon was traced to changes in contact angle between the test liquid and the plates brought about by starting and stopping shear. There are circumstances in which contact angle and surface tension changes with shear could be indistinguishable from true normal forces.

Notes: Summary Among investigations concerning the rheology of spinning materials from melt, or in other terms the problem of “spinnability”, glasses perform an example of fibre forming without crystallization along the spinning way and with surface tension playing an important role. Furthermore glasses show aNewtonian behaviour at least in the upper part of the drawing zone. As the absence of crystallization simplifies the formulation of the governing energy equation, on the other hand, the surface tension makes the applied motion equations quite complex to solve, above all in the two-dimensional analysis. The present paper shows that only a two-dimensional approach can give reliable results on the temperature, velocity and stress distribution in the drawing zone by a comparison of the theoretical and the experimental diameter profile of the forming fibre. The temperature profile has been obtained by a numerical solution of the energy equation, only after gaining experimentally the heat transfer coefficient. The results shown in the one-dimensional analysis cannot be applied in the opper part of the drawing zone. The velocity and stress distribution can be obtained by very complex numerical solutions in the very upper part of the drawing zone where the one-dimensional approach is shown unreliable. This can be thought an asymptotic solution of two-dimensional approach, reliable only after a certain distance of the spinning way from the exit of the nozzle. Furthermore, an analysis of the dimensionless numbers involved in the spinning phenomena brings up some information concerning the instability of the glass jet in comparison with that shown by materials as molten polymers or metals. As far as the rheological behaviour of glasses in the elongational shear rate is concerned, some conclusions can be drawn.

Notes: Summary Formal use of constitutive equations such as that ofOldroyd in the mathematical model of a flow leads, in general, to a higher order differential equation than is obtained for a purely viscous fluid, and so we expect to need more boundary conditions in order to specify the problem completely. (These extra boundary conditions may be thought of as arising from the need to specify what the fluid “remembers” of the flow outside the region of interest.) In flows which are uniform spatially, or uniform with time for a material element, the uniformity will provide the extra information and so no extra conditions are needed. Similarly for confined flows, where no new fluid enters the region of interest, no information about flow outside this region is needed. Here the steady flow of a tubular film of a viscoelastic fluid is studied with the particular aim of examining the effect of these extra boundary conditions in a situation where they may be expected to have some significant influence on the flow as a whole. The flow, while being geometrically complex, is essentially an elongational free-surface flow involving the biaxial stretching of a thin axisymmetric tubular film. Features of the constitutive equations studied are the presence of a non-zero relaxation time and the possibility of a variable viscosity. One effect of the non-zero relaxation time is that a tube of constant radius (possible but unstable for aNewtonian fluid) is not dynamically possible. Preliminary computational results suggest that the effect of the extra upstream boundary conditions is not large, and also have failed to show any major difference between the two generalisations of theMaxwell model which have been used.

Notes: Summary According to linear viscoelastic theory, the expressions for the complex compliance in cyclic shear at angular frequency,ω, and for the creep function are: [1] $$J*\sqrt 2 \left( {j\omega } \right) = J_\infty + 1/j\omega \eta + J_r \chi \left( {j\omega } \right)$$ [2] $$J\left( t \right) = J_\infty + t/\eta + J_r \psi \left( t \right)$$ The normalised functionsχ(jω) andψ(t) are related through the spectrum of retardation times. Recent work in the author's laboratory has shown that for non-polymeric liquidsχ(jω) can be closely represented by the empiricalDavidson-Cole expression used extensively to describe dielectric relaxation: [3] $$\chi \left( {j\omega } \right) = \frac{1}{{\left( {1 + j\omega \tau _r } \right)^\beta }}$$ τ r is a characteristic retardation time parameter and 0 〈β 〈 1. For supercooled liquids,β is typically 0.5, in which case eq. [1] may be rewritten: [4] $$J*\left( {j\omega } \right) = J_\infty \left[ {1 + \frac{1}{{j\omega \tau _m }}} \right] + \frac{{J_r }}{{\left( {1 + j\omega \tau _r } \right)^{\tfrac{1}{2}} }}$$ τ m =ηJ ∞ is theMaxwell relaxation time. Eq. [4] is fitted to experimental results for a number of liquids: the corresponding functionψ(t) in the time domain is found to fit the creep data ofPlazek for 1,3,5-tri-(α-naphthyl) benzene. In practiceτ r 〉τ m below the “Arrhenius temperature” and forωτ r ≫ 1 eq. [4] reduces to the form of theBarlow, Erginsav andLamb equation used previously: [5] $$J*\left( {j\omega } \right) = J_\infty \left[ {1 + \frac{1}{{j\omega \tau _m }}} \right] + \frac{{2J_r }}{{\left( {1 + j\omega \tau _r } \right)^{\tfrac{1}{2}} }}$$ withJ r J ∞ =2(τ r /τ m )1/2. A review is given of available experimental results which confirm the applicability of eq. [4] or, in more approximate form, eq. [5]. It has also been shown that within experimental accuracy: a) J ∞ is a linear function of temperature, and b) G ∞(=1J ∞) is a linear function of pressure. In the case of polymer melts, the behaviour at high frequencies where molecular movements are restricted to small elements of the polymer chain is found to be similar to that observed in non-polymeric liquids, eq. [5]. Additional contributions are found at lower frequencies due to entanglement effects. Results are given of preliminary measurements on a range of polystyrenes of narrow molecular weight distribution.

Notes: Summary This study is devoted to incompressible viscoelastic fluids in which a superposition principle for stress is assumed. In order to respect the material objectivity, this summation of incremental stress, with corresponding memory factor, is operated in a rheological (corotational) frame. Theoretical study for these fluids in viscometric flows was conducted up to explicit solutions. This study shows some impossibility ranges for such flows. The determination of the memory functions from this type of flow involvesFourier transform and so, would need the knowledge of all the kinematic range, and this is impossible. The study in relaxation tests permits the determination of the memory functions. So, we performed these experiments, to get memory functions which were independent of the kinematics. Using the function so obtained, we can compute and predict some experimental results in steady flows; and the comparison between these two results was quite good.

Notes: Summary As the number of rheological and other scientific publications increases considerably year by year, documentation services should be used more extensively. The Deutsche Rheologische Gesellschaft (German Society of Rheology), 1 Berlin 45, Unter den Eichen 87, publishes at regular intervals and for an international reader audience the “Documentation Rheology” which contains a fairly complete collection of relevant literature subdivided into subject groups. The papers listed cover fundamentals of rheology, rheometry, rheological behaviour of polymer melts and solutions, plastics and rubber, metals, pastes, colloids and suspensions, solids, ceramics, concrete, pharmaceutical products and cosmetics, food stuffs, chemical engineering, forming processes, flow processes, mixing processes and so on. The documentation is available at a small charge. It has been published to make better use of the possibilities that lie in a systematic collection, arrangement, exploitation and application of findings achieved and published so far. Methodical and intensified research and development, as well as further rationalization and cost-saving measures in the field of practical application depend on a better utilization of existing findings. The above-mentioned documentation service covers basic research as well as technical application. With the aid of it literature search on general or more specific problems of research and practice can be done quicker and carried out much more easily. Literature search done this way guarantees that a research project will start from the current state of knowledge and that sufficient hints to solutions of practical problems are at hand. Moreover, the preparation and publication of literature reports will initiate a systematic evaluation of the numerous existing publications.

Notes: Summary This paper is an account of the design of a test sample of polystyrene solution which will be distributed to research laboratories interested in participating in a comparison of techniques of measurement of normal stresses through a common sample. Questions of concentration, molecular weight distribution and solvent properties are considered.

Notes: Summary Measurements of the viscometric properties of a thixotropic fuel oil at constant shear rate have shown a reduction of viscosity that has the characteristics of combined long term and short term exponential decay processes. It is possible to evaluate parameters from experimental data for decay processes which combine to represent the observed time dependence of viscosity. At a particular shear rate the time dependence can be represented as: $$\begin{gathered} \mu (t) = \mu _0 - \Delta \mu _1 (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _1 }}} \right. \kern-\nulldelimiterspace} {\lambda _1 }}} ) \hfill \\ - \Delta \mu _2 (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _1 }}} \right. \kern-\nulldelimiterspace} {\lambda _1 }}} ) \hfill \\ \end{gathered} $$ . When measurements are made for a range of shear rates it is found that the time constants,λ 1 andλ 2, are relatively unchanged while the viscosity deficits,Δµ 1 andΔµ 2, and the initial viscosity are shear rate dependent. For a limited shear rate range the nature of this dependency can be expressed as: $$\begin{gathered} \Delta \mu (\dot \gamma ) = \Delta \mu ^1 \dot \gamma ^n \hfill \\ \mu _0 (\dot \gamma ) = \mu _0^1 \dot \gamma ^{n_0 } \hfill \\ \end{gathered} $$ whereΔμ 1 andµ 0 1 are evaluated at $$\dot \gamma = 1$$ and the various indices all lie between 0 and −1. The time dependence of viscosity measured at constant shear rate can then be represented as: $$\begin{gathered} \mu (t) = \mu _0^1 \dot \gamma ^{n_0 } - \Delta \mu _1^1 \dot \gamma ^{n_1 } (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _1 }}} \right. \kern-\nulldelimiterspace} {\lambda _1 }}} ) \hfill \\ - \Delta \mu _2^1 \dot \gamma ^{n_2 } (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _2 }}} \right. \kern-\nulldelimiterspace} {\lambda _2 }}} ). \hfill \\ \end{gathered} $$ With this characterization method long term, short term, time independent and shear rate dependent characteristics of a material can be individually identified.

Notes: Summary This paper describes the coupling of a minicomputer with two rotational rheometers. In the first instance, the computer acquires output data from aWeissenberg Rheogoniometer in oscillatory shear, andFourier-analyzes stress and strain signals. The second instance utilizes a rotational rheometer specifically designed to be controlled by the computer, employing a servo-driven torque motor. The computer-rheometer system is used to analyze steady-state non-Newtonian viscosity and linear viscoelasticity, as well as non-linear dynamic behavior.

Notes: Zusammenfassung Die Schwierigkeiten, die sich bei der Ermittlung rheologischer Stoffeigenschaften bei großen Zähigkeiten und hohen Schergefällen durch die starke Wärmeentwicklung in der Strömung ergeben, können in gewissen Grenzen durch sehr kurze Scherzeiten behoben werden. Es wurde ein Rotationsrheometer gebaut, dessen Antrieb und Meßeinrichtungen extrem kurze Versuchszeiten im Bereich von 10 bzw. 100 Millisekunden zulassen. Das Rheometer ist zur Messung der Schubspannungsfunktion und der beiden Normalspannungsdifferenzen bei Schergefällen bis 104 s−1 und Temperaturen bis 260°C eingerichtet. Aus dem Anlauf- und Bremsverhalten der Flüssigkeit können ferner elastische Parameter bestimmt werden. Es werden erste Ergebnisse mitgeteilt, die an einerCouette-Apparatur mit ähnlichem Antrieb für hochviskoses Siliconöl erhalten wurden. Das Material zeigt während des Anlaufes einen ausgeprägten Strukturzusammenbruch.