Elongational properties and molecular structure of polyethylene melts

Summary The viscosity and the recoverable strain in the steady state of elongation have been measured on several polyethylenes of different molecular structures. The elongational viscosity as a function of tensile stress runs through a more or less pronounced maximum in the nonlinear range whereas in the linear range the Trouton viscosity is reached. For low density polyethylenes it could be demonstrated that the maximum of the steady-state elongational viscosity and the elasticity expressed by the steady-state compliances in shear and tension sensitively increase if the molecular weight distribution is broadened by the addition of high molecular weight components. A variation of the weight average molecular weight does only shift the elongational viscosity curve but leaves its shape unchanged. Two of the four high density polyethylenes investigated do not show a maximum of the steady-state elongational viscosity, for the others it is less pronounced than in the case of low density polyethylenes. The influence of branching on the elongational behaviour of polyethylene melts in the steady-state and the transient region is qualitatively discussed.With 11 figures and 4 tables     

Le jet libre immergé d'un fluide viscoélastique

Résumé Les auteurs étudient le jet libre laminaire bidimensionnel d'un fluide viscoélastique obéissant à une loi de comportement semiempirique. Ils appliquent la méthode de raccordement des développements asymptotiques afin de déterminer le profil de vitesses à l'intérieur du jet, et l'entraînement du fluide extérieur. Les résultats obtenus illustrent l'influence de l'élasticité sur le champ de vitesse et la présence d'un gradient de pression à l'intérieur du jet. Les lignes de courant obtenues montrent que le fluide externe est aspiré vers l'axe du jet.

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Summary A two-dimensional laminar free jet of a viscoelastic fluid following a semiempiric constitutive equation is studied. The method of matching asymptotic expansions is applied to determine the velocity profiles inside the jet and the entrainment of the external fluid. The results thus obtained highlight the influence of elasticity on the velocity field and the presence of a pressure gradient inside the jet. The streamlines obtained show that the external fluid is sucked in towards the axis of the jet.

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Zusammenfassung Es wird der laminare zweidimensionale Freistrahl einer viskoelastischen Flüssigkeit, die einem halbempirischen Stoffgesetz folgt, untersucht. Asymptotische Entwicklungen werden aneinandergefügt, um die Geschwindigkeitsverteilung in der Strahlströmung und die Ansaugkraft der äußeren Flüssigkeit zu bestimmen. Die erzielten Ergebnisse zeigen den Einfluß der Elastizität auf die Geschwindigkeitsverteilung und das Bestehen eines Druckgradienten innerhalb der Strahlströmung. Die abgeleiteten Stromlinien zeigen weiter, daß die äußere Flüssigkeit zur Strahlachse hin angesaugt wird.

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A ₁;A ₂;A ₃ tenseurs de Rivlin-Ericksen - A constante définie par [27] - D domaine d'écoulement - f ₁();f ₀() fonctions définies par la transformation [20] - I tenseur unité - J nombre adimensionnel [12] - L longueur de référence - M flux total d'impulsion [19]m: µ/ - N _Re nombre de Reynolds - N _w nombre de Weissenberg - n indice de comportement - p pression - s indice de comportement «élastique» - T tenseur des contraintes - U ₀ vitesse de référence - u, v composantes du vecteur vitesse - x, y coordonnées cartésiennes - Y coordonnée de «couche limite» [9] - Z variable complexe - angle entre les parois de la fente - paramètre de perturbation - variable affine [20] - () fonction définie par [2c] - coefficient d'élasticité - fonction de viscosité [2a] - µ indice de consistance - masse volumique - ; fonctions de courant - fonction définie par [2b] - 2ème invariant principal du tenseurA ₁ Avec 7 figures     

Numerical modeling of carbon monoxide neutralization by metered water injection into a high-temperature mixture of combustion products

A closed mathematical model of the flow of a two-phase mixture consisting of evaporating water droplets and a chemically reacting multicomponent gas is described. The effect of the real droplet heating and evaporationkinetics on the gas-phase chemical reactions in a mixture of combustion products is studied within the framework of this model.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 96–106, November–December, 1993.     

Allowance for the unsteadiness of the flow in determining the critical cavitation number for marine propellers

A method of estimating the critical cavitation number for marine propeller blades is proposed. This method is based on the reduction of the three-dimensional unsteady problem to the three-dimensional steady problem and a series of two-dimensional unsteady problems.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.1, pp. 78–85, January–February, 1993.The authors are grateful to S. V. Kaprantsev for assisting with the experiments.     

Interaction of two spherical particles in a steady flow of viscous fluid when the Reynolds number is not small

The problem of the interaction of two or more particles moving in a viscous incompressible fluid at small Reynolds numbers (Re 1) has been well studied. The linearity of the Stokes equations makes it possible to develop effective methods of solution of the problem for two and many particles [1]. If the Reynolds number is not small, the inertia forces in the Navier-Stokes equations cannot be ignored, and the problem becomes nonlinear, i.e., much more complicated. The present note is devoted to the problem of the interaction of two spherical particles in a steady uniform flow of a viscous incompressible fluid when the Reynolds number is not small. Asymptotic expressions are obtained for the interaction forces between the particles when the distances between them are large compared with their radius.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 142–144, May–June, 1983.     

Further studies on dynamic crack branching

The newly derived dynamic-crack-branching criterion with its modifications is verified by the dynamicphotoelastic results of dynamic crack branchings in thinpolycarbonate, single-edged crack-tension specimens. Successful crack branching was observed in four specimens and unsuccessful branching in another. Crack branching consistently occurred when the necessary conditions ofK _I =K _{I b} =3.3 MPa \(\sqrt m\) and the sufficiency condition ofr _o =r _c =0.75 mm were satisfied simultaneously. In the unsuccessful branching test, the necessary condition was not satisfied sinceK _I was always less thanK _{I b} .     

Turbulent flow of dilute emulsions

An equation is obtained to determine the coefficient of hydraulic drag of dilute emulsions by using the turbulent viscosity concept and the phenomenon of quenching turbulent pulsations. The results of the theory are compared with experiment.     

Method of calculating the contours of aerodynamic nozzles with transition through the velocity of sound

The existing methods of constructing an “ideal” contour (i.e., a contour without taking account of viscosity) for aerodynamic nozzles has a number of drawbacks: they are extremely unwieldly and are not versatile and, moreover, they give in practice an impairment of the flow uniformity, caused by nonconformity of the true flow in the transonic region assumed in the solution, as only the hypersonic flow region is usually calculated. In this paper, a method is proposed for calculating the ideal contours of aerodynamic nozzles with transition through the velocity of sound, which is free from these drawbacks. Cauchy's problem is solved numerically by the method in [1]. A specially corrected pressure distribution, obtained experimentally [2], is used as the initial distribution. Examples of the calculation are given for the ideal contours of plane, axisymmetrical and annular aerodynamic nozzles.     

Boundary turbulence in weak polymer solutions

The construction of a semiempirical method for determining boundary turbulence close to a wall (based on the theory of similarity, dimensional analysis, and certain hypotheses regarding mixing paths) is considered; also considered is the generalization of this method to the case of the turbulent flow of weak polymer solutions in the neighborhood of both smooth and rough surfaces.     

Motion of a solitary wave over a submerged ridge

The two- and three-dimensional motion of a stationary wave in a layer of liquid with a variable depth was studied earlier by Grimshaw [1, 2], who showed that if the unperturbed state of the liquid were a state of rest, then a certain integrated quantity characterizing the energy of the wave (referred to one element on the leading edge of the wave) was conserved during the motion. In the present investigation (which is based on this property) we shall establish the shape of the wave front for the case of steady motion over an infinite submerged cylindrical ridge; we shall present a model describing a wave of limiting amplitude and shall consider the transient perturbation of the steady-state solution. We should note that one particular case (the motion of a straight front, orthogonal to the axis of the ridge, in a direction parallel to this axis) was considered by another method in [3].