Dispersion de Taylor généralisée à un fluide à propriétés physiques variablesGeneralized Taylor dispersion for heterogeneous fluid

The investigation of non-reactive miscible solute dispersion in a vertical Hele–Shaw cell is considered. An asymptotic method is used to extend Taylor model to the case of the fluid density, the dynamic viscosity and the molecular diffusion coefficient are solute concentration-dependent. It is demonstrated that the averaged variables over the gap are governed by a convection–dispersion equation in which the dispersion tensor is concentration-dependent. To cite this article: C. Felder et al., C. R. Mecanique 332 (2004).     

Rheology and microstructure of gluten and soya-based o/w emulsions

Highly concentrated oil-in-water (o/w) emulsion stabilised by means of gluten and soya protein isolate (SPI) at low pH have been characterized by means of linear dynamic viscoelasticity and droplet size distribution analysis (DSD). The microstructure of these emulsions has been characterized at a colloidal level by using confocal laser scanning microscopy (CLSM) and light microscopy (LM). These emulsions always exhibited a behaviour characteristic of highly flocculated emulsions with a mechanical spectrum showing a well-developed plateau region. DSD results generally showed log normal bimodal profiles. Microstructure images revealed occurrence of a close packing of droplets with a broad distribution of sizes participating in the formation of a three dimensional flocculated network. The Mason model of elasticity of compressed emulsions has been used to correlate viscoelastic and microstructural parameters giving adequate fitting but underestimating the elastic properties obtained for the highest concentration of gluten. These deviations may be explained in terms of an enhancement of the elastic network formed in the aqueous phase in which the glutenin fraction must play an important role. Paper presented at the Annual European Rheology Conference (AERC) 2005, April 21-23, Grenoble, France.     

A fluidic-muscle driven force-controlled parallel platform for physical simulation of virtual spatial force-displacement laws

Described in this paper is a six-legged Stewart-Gough parallel platform driven by a relatively new type of fluidic muscles. The advantage of the platform is that it is virtually free of stick-slip effects. Thus, the device is well-suited for fine-tuned force control and for physical simulation of virtual force-displacement laws. The legs of the platform are of type RRPS and are equipped with a coaxial coil spring and a fluidic muscle providing push and pull forces. Each leg is equipped with a force sensor, a pressure sensor, and a magnetostrictive position encoder. The control for the platform consists of six control loops for the six operated actuators with model-based force control comprising individual gas models as well as the rubber nonlinearities for each leg. The control law also includes the gas flow in the proportional directional control valve in 3/3-way function. The present paper describes the basic architecture of the platform, the dynamic models, as well as testbed results for the existing fluidic-muscle parallel platform DynaHex. It is shown that the presented control scheme leads to a stable force control of the platform for quasi-static motion. As an application, the device will be employed in fields of biomechanics, as well as in general environments requiring physical simulation.     

Inhomogeneous inverse problem in finite elasticity

For a class of materials for which the principal strain directions always coincide with the principal stress directions one can determine the stress field in an inhomogeneously deformed body from given boundary conditions and a known strain field without knowing the constitutive equations. Each point of the inhomogeneously deformed body contains information such as that derived from an individual homogeneous identification test. The practically important two-dimensional case leads to a problem of solving a linear hyperbolic system where two differential equations describe the principal stress components. The problem can be reduced to that of integration along characteristics.Under a certain globality condition the existence, uniqueness, and correctness of the solution are guaranteed in the whole test piece. It is shown that the globality condition is closely related to whether or not the test piece is isotropic and elastic. The influence of experimental error on the correctness of problem formulation is discussed.

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Abstrakte Für die Klasse der Materialen, für welche die Grundspannungsrichtungen und die Grundverformungsrichtungen gleich sind, kann man das Spannungsfeld in einem inhomogen deformierten Körper für gegebene Randbedingungen und einem bekannten Verformungsfeld ohne Kenntnis der detailierten Form der Dehnungs-Spannungsgleichung bestimmen. Jeder Punkt des inhomogen deformierten Körpers liefert dieselbe Information wie ein individueller homogener Test. Der praktisch wichtige zweidimensionale Fall führt zu einem Problem der Lösung eines linear hyperbolischen Systems von zwei Differentialgleichungen für die Grundspannungskomponenten. Das Problem kann auf die Integration entlang der Charakteristik des Systems reduziert werden.Unter einer Bedingung der Globalität das die Existent, Eindeutigkeit und Richtigkeit der Lösung in der ganzen Testprobe gewährleistet sind. Es wird gezeigt, dass diese Globalitätsbedingung damit zusammenhängt eng, ob die Testprobe isotrop und elastisch ist. Der Einfluss der experimentellen Fehler auf die Richtigkeit der Formulation des Problems wird auch analysiert.

     

A CFD comparative study of bubble break-up models in a turbulent multiphase jet

In this paper several bubble break-up models are compared. They have been implemented in the CFX-4.4 fluid dynamic commercial code, which uses the population balance equations for describing liquid/gas multi-phase flows. The models have been assessed against published experimental data, obtained for air bubble break-up within a turbulent water jet. The model of Martínez-Bazán, based on purely kinematics arguments, has shown better agreement with the experimental data. The capabilities of using these models coupled to a CFD code for multiphase flow prediction in industrial applications have been demonstrated.     

Shape and structure recovery of an LCP droplet under a large step strain: observation and stress calculation

Shape recovery of a droplet of liquid crystalline polymer (LCP) hydroxypropylcellulose in a matrix of poly(dimethyl siloxane) subjected to a step shear strain has been studied via optical microscopy. Just after application of a large strain, the LCP droplet shape is flat ellipsoid, and then the droplet takes cylindrical shape and band texture perpendicular to the flow direction appears. The band texture fades away before emergence of poly-domain structure. In the final process with the shape of spheroid, poly-domain structure recovers very slowly. Except for the final process, the shape change is identical with that of isotropic droplet at strains smaller than 3, when the LCP viscosity in Region II is taken as an equivalent viscosity for normalization. For a 20:80 blend, the excess relaxation modulus is calculated based on the Doi-Ohta theory, taking account of the distribution of droplet size and compared with experimental modulus data.     

Bitumen/polyethylene blends: using m-LLDPEs to improve stability and viscoelastic properties

The stability and the rheological properties of blends of a 60/70 penetration-grade bitumen with conventional HDPEs and metallocene catalysed LLDPEs (m-LLDPE) are investigated. Considerably better stability results are obtained using m-LLDPEs instead of conventional polyethylenes, allowing one to avoid phase separation of the emulsion-like system during storage at high temperature. Thermodynamical interaction between bitumen and polyethylene is discarded as a cause of the observed difference, because the solubility parameter is practically the same for all the investigated polyethylenes. The result is explained on the basis of the lower melt elasticity of m-LLDPEs (attributed to their narrow molecular weight distribution), which facilitates the drop breakup during mixing process. The modification of bitumen with any of the m-LLDPEs considered in this work gives a new material with considerably improved viscoelastic properties.     

A well posed problem in singular Fickian diffusion

We prove that the problem of solving $$u_t = (u^{m - 1} u_x )_x {\text{ for }} - 1< m \leqq 0$$ with initial conditionu(x, 0)=φ(x) and flux conditions at infinity \(\mathop {\lim }\limits_{x \to \infty } u^{m - 1} u_x = - f(t),\mathop {\lim }\limits_{x \to - \infty } u^{m - 1} u_x = g(t)\) , admits a unique solution \(u \in C^\infty \{ - \infty< x< \infty ,0< t< T\} \) for every φεL¹(R), φ≧0, φ≡0 and every pair of nonnegative flux functionsf, g ε L _loc ^∞ [0, ∞) The maximal existence time is given by $$T = \sup \left\{ {t:\smallint \phi (x)dx > \int\limits_0^t {[f} (s) + g(s)]ds} \right\}$$ This mixed problem is ill posed for anym outside the above specified range.     

General solution of the two-dimensional heat equation for two concentric domains of different material

The general solution of the two-dimensional heat equation is given for two concentric domains consisting of different materials; it is represented as integrals over the given source and boundary distribution multiplied by a Green's function. The Green's function in this problem is given for any (linear) boundary condition of Sturm-Liouville type with constant coefficients. Examples are evaluated for source free problems with uniform initial temperature distribution and a boundary condition which corresponds to constant external temperature. Numeric evaluations show the development of the temperature distribution with time in compounds heated from outside and also for an isolated electric conductor which is cooled from outside after it has been heated by a short circuit.

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Allgemeine Lösung der zweidimensionalen Wärmeleitgleichung für zwei konzentrische Kreisbereiche verschiedener Materialien

Zusammenfassung In dieser Arbeit wird die allgemeine Lösung der zweidimensionalen Wärmeleitungsgleichung für zwei konzentrische Kreisbereiche mit unterschiedlichen Materialeigenschaften angegeben. Diese ist als quellenmäßige Darstellung gegeben, d.h. als Integral über die Wärmequellen im Inneren und am Rand und über die Anfangsverteilung, wobei alle mit der zugehörigen Greenschen Funktion multipliziert werden. Die angegebene Greensche Funktion gilt für alle beliebigen (linearen) Randbedingungen vom Sturm-Liouvilleschen Typ mit konstanten Koeffizienten. Es werden für quellenfreie Probleme mit homogener Anfangstemperatur und konstanter Außentemperatur Beispiele berechnet. Numerische Berechnungen zeigen die zeitliche Entwicklung der Temperaturverteilung für Zweischichtenanordnungen, welche von außen erwärmt werden, und für einen isolierten elektrischen Leiter, welcher nach einer Erhitzung durch Kurzschluß von außen gekühlt wird.

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Nomenclature a diffusion constant, m²/s - c specific heat for constant pressure, W_s/kgK - d₁ inner diameter, m - d₂ outer diameter, m - l length of the construction element, m - J_m, Y_m Bessel functions of m-th order - r, polar coordinates; m, rad - t time, s - T₀ initial temperature, K - T_e external temperature of the medium surrounding the compound, K - T(r, , t) temperature field - _n n-th eigenvalue of the characteristic equation - thermal conductivity, W/mK - (r, , t) heat source density, Ws/m⁵ - mass density, kg/m³