Two characterizations of newtonian potential

Summary The sufficient conditions in some propositions of Newton's about gravitation are shown to be necessary also. The problem is expounded in §1, the principal results are presented in §§3, 4, 9, and 10.

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Sommario Si dimostra in alcuni enunciati di Newton sulla gravitazione che le condizioni sufficienti sono anche necessarie. Il problema è esposto nel paragrafo 1, i risultati principali sono presentati nei paragrafi 3, 4, 9 e 10.

     

Rheological model of concrete in the dynamic field

Summary The definition of the rheological model of concrete, or uncracked reinforced concrete, in the field of dynamic stresses sufficiently far from breaking, is here attempted; an aim towards which we had already recently directed a series of investigations to clarify the different aspects of experimental behaviour.Even with gaps in detail, the model found seems to correctely interpret the dissipativemechanism of our material, and it is — contrary to current viscous schematizations — of a prevalently plasto-elastic characteristic, with dampers of asolid-friction type.This work concludes dealing with the experimental determination of the parameters of the model and with particular approximate solutions of motion.

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Sommario Viene qui tentata la definizione del modello reologico del calcestruzzo, o cemento armato non parzializzato, in campo di sforzi dinamici sufficientemente lontani dalla rottura; fine al quale avevamo di recente già indirizzato una serie di indagini, volte a chiarire i diversi aspetti del comportamento sperimentale.Pur con lacune di dettaglio, il modello trovato sembra correttamente interpretare ilmeccanismo dissipativo del nostro materiale, ed è — contrariamente a correnti schematizzazioni viscose — a caratteristica prevalentemente elastoplastica, con smorzatori di tiposolid-friction.Il lavoro si conclude trattando della determinazione sperimentale dei parametri del modello e di particolari soluzioni approssimate del moto.

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The first results of this work were presented at 2° Convegno Nazionale Gruppo di Studio C.N.R. sulle Costruzioni Antisismiche — Camogli (Genova), Nov. 1966 [1].     

A generalized network model for polymeric liquids

A kinetic model was developed for relating the molecular structure and the rheological behaviour of polymer-like materials in which bonds are being created and broken. In particular, the stress contribution of molecules that are not a part of the network was taken account of. In two limiting cases the model introduced here is identical to the transient-network model and the bead-spring model, respectively. Model predictions were interpreted and compared with measurements on an L.D.-polyethylene melt, available from literature, and an S.I.S.-blockcopolymer solution. In both cases information was obtained about the network and the kinetic processes occurring in a state of rest and during steady-shear flow, assuming the model to be valid.     

Suspension of solid particles in a newtonian fluid

We consider the motion of a Newtonian fluid containing solid particles in the case of high concentration (the partial volume of solid is comparable to that of fluid) by using a homogeniztion technique associated with the small parameter ? (the ratio of the particle length to the characteristic macroscopical length). The limit behaviour as ? → 0 is that of fluid with anisotropy properties associated with a microstructure. The evolution equations for the limit flow and for the microstructure are given.     

Rheological properties of suspensions of the green microalga Chlorella vulgaris at various volume fractions

A systematic study of the rheological properties of solutions of non-motile microalgae (Chlorella vulgaris CCAP 211-19) in a wide range of volume fractions is presented. As the volume fraction is gradually increased, several rheological regimes are observed. At low volume fractions (but yet beyond the Einstein diluted limit), the suspensions display a Newtonian rheological behaviour and the volume fraction dependence of the viscosity can be well described by the Quemada model (Quemada, Eur Phys J Appl Phys 1:119–127, 1997). For intermediate values of the volume fraction, a shear thinning behaviour is observed and the volume fraction dependence of the viscosity can be described by the Simha model (Simha, J Appl Phys 23:1020–1024, 1952). For the largest values of the volume fraction investigated, an apparent yield stress behaviour is observed. Increasing and decreasing stress ramps within this range of volume fractions indicate a thixotropic behaviour as well. The rheological behaviour observed within the high concentration regime bears similarities with the measurements performed by Heymann and Aksel (Phys Rev E 75:021505, 2007) on polymethyl methacrylate suspensions: irreversible flow behaviour (upon increasing/decreasing stresses) and dependence of the flow curve on the characteristic time of forcing (the averaging time per stress values). All these findings indicate a behaviour of the microalgae suspensions similar to that of suspensions of rigid particles. A deeper insight into the physical mechanisms underlying the shear thinning and the apparent yield stress regime is obtained by an in situ analysis of the microscopic flow of the suspension under shear. The shear thinning regime is associated to the formation of cell aggregates (flocs). Based on the Voronoi analysis of the correlation between the cell distribution and cell sizes, we suggest that the repulsive electrostatic interactions are responsible for this microscale organisation. The apparent yield stress regime originates in the formation of large-scale cell aggregates which behave as rigid plugs leading to a maximally random jammed state.     

Flows of non‐newtonian fluids with hydraulic jumps

Steady and unsteady waves propagating over the surface of a thin layer of a dilatant fluid moving over an inclined plane, with rheological properties of the fluid described by the Ostwald–de Waele power law, are studied analytically and numerically.     

Flow of a newtonian fluid through a sudden contraction

The full Navier-Stokes equations describing flow through a sudden contraction are solved by an explicit finite-difference method. Streamlines, vorticity distributions, velocity profiles, excess pressure drops, and entrance lengths are calculated as functions of Reynolds number and radius ratio. The results are compared with existing experimental data and the limited theoretical work available.     

Thermal stretching in two-phase porous media: Physical basis for Maxwell model

An alternate yet general form of the classical effective thermal conductivity model (Maxwell model) for two-phase porous materials is presented, serving an explicit thermo-physical basis. It is demonstrated that the reduced effective thermal conductivity of the porous media due to non-conducting pore inclusions is caused by the mechanism of thermal stretching, which is a combination of reduced effective heat flow area and elongated heat transfer distance (thermal tortuosity).     

Rheological predictions of a transversely isotropic fluid model with extensible microstructure

A continuum extensible director theory was formulated to describe the isothermal, incompressible flow of uniaxial rodlike semiflexible liquid crystalline polymers. The model is strictly restricted to material that flow-align in shear, and that, in the absence of flow, are sufficiently far from the nematic-isotropic phase transition. The microstructure of the continuum is described by a variable length director, but the extensibility is finite. The model is an extension of the TIF (Transversely Isotropic Fluid) model of Ericksen (1960). The thermodynamic restrictions on the model parameters are found using the non-negative definiteness of the entropy production. The rheological material functions predicted by the model are calculated for steady simple shear and steady uniaxial extensional flows. In the rigid rod limit the model predictions agree with those of the TIF model, and for the finite extensibility case the model predictions are in agreement with those associated with flexible isotropic polymers: strong non-Newtonian shear viscosity, positive first normal stress differences, recoverable shear of order one, negative second normal stress differences, and a maximum in the steady uniaxial extensional viscosity.     

Rheological structural model of a crack in a viscoelastic composite material

Institute of Mechanics, Academy of Sciences of the Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 28, No. 7, pp. 12–18, July, 1992.     

Rheological characterization in shear of a model dumbbell polymer concentrated solution

We investigate the linear and non-linear rheological behavior in shear of a concentrated solution of ??dumbbell?? polystyrene with long linear backbone and dense short brushes at both ends and compare it with corresponding linear polymers. This type of dumbbells has never been rheologically characterized before. In linear viscoelasticity, the dumbbell polymers show significant differences with conventional linear polymers. In particular, the reptation relaxation of the dumbbell is strongly slowed down. Furthermore, the addition of the side chains increases the friction so that the dumbbell lies above the ?? ₀ vs. number of entanglements relation of linear samples. Transient shear rheology experiments on weakly entangled solutions show a retardation of the chain stretch relaxation of the dumbbell by a factor 2.5 vs. a linear polymer with the same Rouse time. Additionally, a second peak in the transient viscosity is observed at high shear rates.     

Bifurcation phenomena of generalized newtonian fluids in curved rectangular ducts

The bifurcation phenomenon in flow through a curved rectangular duct is investigated in this study. The non-linear equations of motion governing the steady, fully developed laminar flow of an incompressible generalized Newtonian fluid have been solved numerically. Extensive results have been generated in an effort to map the regions of multiple solution in the parameter space of Dean number, Dn, aspect ratio, γ, power-law index, n, and radius of curvature, r. For a Newtonian fluid (n = 1), at a fixed curvature (r = 100), the transition between a symmetric 2-cell and a symmetric 4-cell solution appears to follow a tilted cusp. The extent of the stable, symmetric 2-cell solution surface is critically influenced by the length scale γ. In the non-Newtonian case, at a fixed aspect ratio (γ = 1) and a fixed curvature (r = 100), the flow transition follows that of a fold catastrophe. The influence of the curvature is reasonably well accounted for in Dn. The bifurcation set determined in the Dn-γ space remains qualitatively the same at any value of n or r. These parameters merely shift and/or stretch the equilibrium surface determined by Dn and γ.     

Cattaneo-Christov heat flux model for third-grade fluid flow towards exponentially stretching sheet

The Cattaneo-Christov heat flux in the two-dimensional (2D) flow of a third-grade fluid towards an exponentially stretching sheet is investigated. The energy equation is considered through thermal relaxation. Similarity transformations are accounted to obtain the ordinary differential systems. The converted non-dimensional equations are solved for the series solutions. The convergence analysis of the computed solutions is reported. The graphical results of the velocity and temperature profiles are plotted and elaborated in detail. The results show that the thermal relaxation enhances the temperature gradient while reduces the temperature profile.     

Non linear viscoelasticity of polymeric liquids interpreted by means of a stress dependence of free volume

Summary Several existing data of non-linear viscoelasticity of amorphous polymers aboveT _g are here interpreted by assuming that the free volume changes during the motion. Equations of a stress-temperature equivalence are suggested which favorably compare with the data. It is also shown that the volume variations are sufficiently small to have escaped observation.

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Zusammenfassung Verschiedene vorliegende Meßergebnisse bezüglich des nicht-linear viskoelastischen Verhaltens von amorphen Polymeren oberhalbT _g werden mit Hilfe der Annahme interpretiert, daß das freie Volumen sich bei der Bewegung ändert. Es werden dazu Gleichungen für die Spannungs-Temperatur-Äquivalenz in Ansatz gebracht, die eine gute Anpassung an die Meßdaten ergeben. Ebenfalls wird gezeigt, daß die Volumenänderungen hierbei so klein bleiben, daß sie sich der Beobachtung haben entziehen können.

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With 9 figures     

An empirical constitutive model for complex glass-forming liquids using bitumen as a model material

While extensive research efforts have been devoted to understand the dynamics of chemically and structurally simple glass-forming liquids (SGFLs), the viscoelasticity of chemically and structurally complex glass-forming liquids (CGFLs) has received only little attention. This study explores the rheological properties of CGFLs in the vicinity of the glass transition. Bitumen is selected as the model material for CGFLs due to its extremely complex chemical composition and microstructure, fast physical aging and thermorheological simplicity, and abundant availability. A comprehensive rheological analysis reveals a significant broadening of the glass transition dynamics in bitumen as compared to SGFLs. In particular, the relaxation time spectrum of bitumen is characterized by a broad distribution of long relaxation modes. This observation leads to the development of a new constitutive equation, named the broadened power-law spectrum model. In this model, the wide distribution of long relaxation times is described by a power-law with positive exponent and a stretched exponential cut-off, with parameter β serving as a measure of the broadness of the distribution. This characteristic shape of the bitumen spectrum is attributed to the heterogeneous freezing of different molecular components of bitumen, i.e., to the coexistence of liquid and glassy micro-phases. Furthermore, as this type of heterogeneous glass transition behavior can be considered as a general feature of complex glass-forming systems, the broadened power-law spectrum model is expected to be valid for all types of CGFLs. Examples of the applicability of this model in various complex glass-forming systems are given.     

Thermocapillary instability of the interface between two immiscible liquids in the presence of volume heat sources

The problem of the stability of the interface between two infinite layers of different immiscible liquids is considered. It is assumed that within the liquid a distributed volume heat source, simulating Joule heating, is given. The stability of the rest state with respect to small unsteady disturbances is investigated. The investigation is carried out using the real boundary conditions at the interface between the two liquids rather than the model boundary conditions usually employed in such problems [5]. The problem considered is related to the practical question of the stability of electrolyzer processes. In the present case a possible threshold mechanism of development of oscillations of the electrolyte-aluminum interface is examined. A numerical example with liquid parameters that coincide with those of the electrolyte and aluminum shows that the thermocapillary instability mechanism can, in fact, be the source of surface waves at the electrolyte-aluminum interface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 156–160, September–October, 1990.     

A computer model of hole-pressure measurement in Poiseuille flow of visco-elastic liquids

Summary Liquid-filled holes used for pressure measurements of visco-elastic liquids give rise to systematic hole pressure errors.Tanner andPipkin have presented an analysis for flows of a second-order fluid in which they derive a simple relation between the first normal-stress difference and the hole pressure for flow situations where Reynolds numbers are very small. Implicit in the analysis is the assumption that the streamlines are symmetric about the hole center line. In this paper, using a numerical solution, we investigate the relationship between the hole pressure and the first normalstress difference for a range of Reynolds numbers where inertial effects are not negligible. The ratio of hole pressure to first normal-stress difference is found to vary from 0.25 to 0.16 as the Reynolds number is varied from 1 to 10. Streamline patterns are presented for Poiseuille flow of a second-order fluid over a slot cut into one wall of an otherwise straight channel. Various geometries are considered. The results naturally include those for an incompressible Newtonian liquid at non-zero Reynolds numbers.

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Zusammenfassung Flüssigkeitsgefüllte Bohrungen für Druckmessungen führen bei viskoelastischen Flüssigkeiten zu systematischen Fehlern (hole pressure errors).Tanner undPipkin haben für Strömungen von Flüssigkeiten zweiter Ordnung diesen Effekt analysiert und finden im Falle sehr kleiner Reynoldszahlen eine einfache Beziehung zwischen der ersten Normalspannungsdifferenz und dem Lochdruck (hole pressure). Bei dieser Untersuchung wird implizit von der Annahme Gebrauch gemacht, daß die Stromlinien symmetrisch zur Lochachse verlaufen. In der vorliegenden Arbeit wird unter Anwendung eines numerischen Verfahrens die Beziehung zwischen dem Lochdruck und der ersten Normalspannungsdifferenz für einen Bereich von Reynoldszahlen untersucht, bei dem Trägheitseffekte nicht mehr vernachlässigt werden können. Das Verhältnis von Lochdruck zu erster Normalspannungsdifferenz verkleinert sich von 0,25 auf 0,16, wenn die Reynoldszahl von 1 bis 10 ansteigt. Für die Poiseuille-Strömung einer Flüssigkeit zweiter Ordnung über einer in die Wand eines sonst geradlinigen Kanals eingeschnittene Nute werden Stromlinienbilder dargestellt, wobei unterschiedliche geometrische Verhältnisse betrachtet werden. Die Ergebnisse schließen natürlich den Fall der Strömung inkompressibler newtonscher Flüssigkeiten mit nicht-verschwindender Reynoldszahl ein.

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With 11 figures and 2 tables