Maxwell Type Research Articles

Viscosity of gaseous HFC-125 (pentafluoroethane) under high pressures

This paper reports experimental results lor the viscosity of gaseous HFC-125 (pentafluoroethane) under high pressures. The measurements were carried out with an oscillating-disk viscometer of the Maxwell type at temperatures from 298.15 to 423.15 K and at pressures up to the saturated vapor pressures at each temperature at subcritical conditions or up to 9 MPa at supercritical temperatures. Intermolecular scaling parameters of HFC-125 for the extended corresponding states were determined from the viscosity data at 0.1 MPa. An empirical viscosity equation is proposed to interpolate the present experimental results as a function of temperature and density.

Existence results for steady flow of weakly compressible viscoelastic fluids with a differential constitutive law

In this paper we study flows of viscoelastic weakly compressible fluids having a differential constitutive equation. In both cases, Jeffreys and Maxwell type constitutive equations, we establish a result of existence and uniqueness of solutions. We also show that, when the compressibility goes to zero, then the weakly compressible steady solution goes to the incompressible one.

Boundary element analysis of three-dimensional mixing flow of Newtonian and viscoelastic fluids

The boundary element method (BEM) is implemented for the simulation of three-dimensional transient flows of typical relevance to mixing. Creeping Newtonian and viscoelastic fluids of the Maxwell type are examined. A boundary-only formulation in the time domain is proposed for linear viscoelastic flows. Special emphasis is placed on cavity flows involving simple- and multiple-connected moving domains. The BEM becomes particularly suited in multiple-connected flows, where part of the boundary (stirrer or rotor) is moving, and the remaining outer part (cavity or barrel) is at rest. In this case, conventional methods, such as the finite element method (FEM), generally require remeshing or mesh refinement of the three-dimensional fluid volume as the flow evolves and the domain of computation changes with time. The BEM is shown to be much easier to implement since the kinematics of the elements bounding the fluid is known (imposed). It is found that, for simple cavity flow induced by a rotating vane at constant angular velocity, the tractions at the vane tip and cavity face exhibit non-linear periodic dynamical behavior with time for fluids obeying linear constitutive equations

Dynamical Conductivity of the Dilute Lorentz Gas with Spherically Symmetric Scatterers

The dynamical conductivity of the Lorentz gas with spherically symmetric potentials is studied to lowest order in the density of scatterers. The frequency-dependent friction coefficient is calculated from the Fourier transform of the force–force time-correlation function determined by the dynamics of a single scattering process. The corresponding dynamical conductivity varies with frequency on the scale of the inverse collision time. As an example, the conductivity is calculated for a scattering potential of the Maxwell type.

Spectral Properties of a Transport Operator in a Slab with Integral Boundary Conditions

In this paper, the spectrum of a transport operatorAin a slab with integral boundary conditions of Maxwell type is discussed in its natural spaceL1(G). It is shown that the essential spectrum of the transport operatorAoccupies the left half plane Reλ≤−Σ and there exist only a finite number of eigenvalues of the transport operatorAin each vertical band contained in the right half plane Reλ>−Σ.

Viscosity of Gaseous HFC-134a (1,1,1,2-Tetrafluoroethane) Under High Pressures

The viscosity of gaseous HFC-134a (1,1,1,2-tetrafluoroethane) was measured with an oscillating disk viscometer of the Maxwell type from 298.15 to 398.15 K at pressures up to 5.5 MPa. Intermolecular potential parameters for the Lennard–Jones 12-6 model were determined from the viscosity data at 0.1 MPa. The viscosity equation developed by Krauss et al. was applied to correlate the present viscosity data. In addition, the correlations proposed by Stiel and Thodos and by Lee and Thodos were tested for fitting the experimental viscosity data.

The yield surface of viscoelastic and plastic fluids in a vane viscometer

Vane viscometers are often used to investigate the low shear rate properties of plastic fluids. The shear stress is determined by assuming that the material is held in the space between the vane blades so that it behaves like a rigid cylinder. Experimental evidence supports this assumption and the aim of the present study is to model numerically the yield process in a vane rheometer using viscoelastic and plastic fluids. The finite element method has been used to model the behavior of Herschel-Bulkley (Bingham), Casson and viscoelastic (Maxwell type) fluids. The penalty function approach for the pressure approximation and a rotating reference frame are used together with fine meshes containing more than 1300 elements. The results show that for Herschel-Bulkley (Bingham), and Casson fluids a rotating rigid cylinder of fluid is trapped inside the periphery of the vane, the shear stress is uniformly distributed over the surface of the cylinder. Finally a modified second order fluid is used to simulate the viscoelastic behaviour, anticipated to be an intermediate between the elastic deformation and the plastic flow, to provide a more realistic simulation of the yield process about a vane. In this case, contrast with the concentration of the elastic strain rate at the blade tips, a nearly uniform distribution of the plastic shear rate is still found. This implies that the plastic shear always distributes uniformly during the entire yielding process. Evidently the assumption of uniform shear on a rotating cylinder of material occluded in the blades of a vane is a valid and useful model for many types of fluid possessing a yield stress.

Study of the Free Streaming Operator in Slab Geometry in Dependence of the Boundary Conditions

We study the free streaming operator T Λ in a slab domain with boundary conditions described by a linear matrix operator Λ acting between the'incoming' and'outgoing' particle fluxes. Under suitable assumptions on the entries of Λ, it it is proved that the resolvent operator of T Λ is positive. It is proved also that T Λ is the generator of a positive strongly continuous semigroup, whose type depends on the norm of the entries of Λ. Some examples are given. In particular the case of Maxwell type boundary conditions is studied and the location of the spectrum of T Λ is improved.

Rheological modeling of randomly packed granules with visco-elastic binders of Maxwell type

Abstract This paper focuses attention on the modeling of a particle assembly bonded by a visco-elastic binder material. The inter-particle behavior for two particles with a visco-elastic binder is modeled based on two basic elements, a spring and a dashpot. Different combinations of the basic elements characterize different inter-particle behavior. Here, we mainly consider the viscoelastic binder of Maxwell type. Thus, granular materials can be viewed as a discrete system of particles connected with springs and dashpots. The discrete system can be simulated by an equivalent visco-elastic continuum. The macrorheological behavior of granular materials is derived based on both kinemetic and static methods.

Maxwell型の粘性ダンパーを有するせん断型構造物の地震時指定層間変位に対する剛性設計解列

A new method seismic stiffness design is developed for a shear building with Maxwell type viscous dampers. A sequence of stiffness designs is generated with respect to a sequence of flexibility of spring elements in Maxwell type viscous dampers such that each mean maximum interstory drift would coincide with the specified value subject to a set of spectrum-compatible design earthquakes. With the use of the predominancy of the fundamental participation component, proposed is an approximation formula to evaluate the upper bound for maximum interstory drifts in case that some viscous dampers does not function. Several design examples are presented to demonstrate the usefulness of the proposed design method. The results of time-history response analysis demonstrate the accuracy of this method and the proposed approximation formula.

Rheological Considerations on the Grain-Boundary Sliding of Polycrystalline Ceramics

The grain-boundary sliding and interlocking of polycrystalline ceramics are investigated by means of the model arrays, i.e., two-dimensional arrays of square or hexagonal elastic grains embedded in a contiguous grain-boundary melt. A nonlinear Maxwell type constitutive equation is derived in an universal manner by considering two fundamental processes associated with elastic deformation of grains and squeezing-in/out of a viscous fluid between adjacent grains. The equation applied to creep deformation and stress relaxation yields several important predictions for the nonlinear viscoelastic behavior of polycrystalline ceramics with grain-boundary phase.

The spectrum of a one-velocity transport operator with integral boundary conditions of Maxwell type

In this paper, the spectral properties of the one-velocity transport operator and the streaming operator with integral boundary condition of Maxwell type in a sphere are considered. It is proved that the streaming operator and the transport operator are the infinitesimal generators of positive Co semigroups.

On the type ofC o-semigroup associated with the abstract linear viscoelastic system

In this paper, we give an estimate for the type of semigroup associated with an abstract equation of linear viscoelasticity when the memory kernel decays exponentially. In particular, when the kernel is of Maxwell type, we prove that the spectrum determined growth property holds. Moreover, the type of the semigroup is explicitly expressed by a formula which depends on the parameters of the kernel and the minimum spectrum point of the corresponding elastic operator.

Viscosity of Gaseous Nitrous Oxide from 298.15 K to 398.15 K at Pressures up to 25 MPa

The viscosity of gaseous nitrous oxide was measured using an oscillating disk viscometer of the Maxwell type from 298.15 K to 398.15 K at pressures up to 25 MPa. The results were fitted to an empirical equation as a function of temperature and density. The Chung and Lee−Thodos correlations were tested to fit the experimental viscosity values.

Kerr–Schild gravitational fields in matter and the Kerr-interior problem in general relativity

Stationary Kerr–Schild gravitational fields in the interior of elastic–solid bodies are considered. It turns out that the Einstein field equations for such systems split into two parts: a ‘‘differential’’ part which may be written as a linear partial differential equation of the Maxwell type for a suitably defined, three-dimensional Euclidean vector and an ‘‘algebraic’’ (generally nonlinear) part which allows the calculation of the stresses supporting the bodies. These results are applied to the problem of finding the sources of the Kerr space–time, and a new class of solutions of the Einstein field equations is found. Such solutions describe sources of the Kerr metric composed by an elastic body and a shell distribution of elastic stress energy located on the matching surface. Some explicit examples of ‘‘half local’’ (singular) Kerr–Schild sources of the Kerr space–time are also given.

Gas Viscosity of Difluoromethane from 298.15 to 423.15 K and up to 10 MPa

Chlorodifluoromethane (HCFC-22) has been used mostly as a refrigerant for air-conditioning systems, but it is scheduled to be phased out by 2030 due to its ozone depletion properties. Difluoromethane (HFC-32) has no ozone depletion potential (ODP) since there are no chlorine atoms in the molecule and has been considered as a substitute for HCFC-22. The gas viscosity of difluoromethane was measured using an oscillating disk viscometer of the Maxwell type from 298.15 to 423.15 K at pressures up to 10 MPa. The results were fitted to an empirical equation as a function of temperature and density. Intermolecular force constants of the Lennard-Jones 12-6 potential were determined. In addition, the experimental density was compared with the calculated values from various equations of state previously reported.

Semigroup properties of the streaming operator with multiplying boundary conditions

Abstract We study the one-dimensional streaming operator in a slab domain with boundary conditions of Maxwell type. By using techniques of the theory of semigroups of linear operators in a L1 space context, we prove that the streaming operator is the infinitesimal generator of a strongly continuos semigroup, even if the boundary is “particle multiplying”. This semigroup is positive, quasi-bounded and obviously not contractive.

Dynamic light scattering of CTAB:NaSal threadlike micelles in the semidilute regime. II. effect of surfactant concentration

Dynamic light scattering measurements are made on networks formed by elongated threadlike micelles of cetyltrimethylammonium bromide (CTAB) in aqueous sodium salicylate (NaSal) solutions at 25°C. The surfactant concentrationCD of the samples is varied from 0.006 to 0.3 M and the ratio of the salt concentrationCs toCD is fixed at unity. The time correlation functionAq (t) of light intensity scattered from the solutions exhibits transition from the unimodal to the bimodal distribution of the decay rate Γ at aroundCD=0.05 M. The dependence of the first cumulant Γe on the scattering vectorq for the samples withCD≦0.03 M is described by the dynamic scaling law. The cooperative diffusion coefficientDc is obtained from extrapolation of Γe/q2 for the samples withCD≦0.03 M and of Γf/q2 forCD≧0.05 M where Γf is the first cumulant from the fast mode. TheDc is found in proportion toCD0.45, being in agreement with the theoretical prediction for a rigid rod in the semidilute regime by the scaling law. The decay rate Γs characteristic of the slow mode is independent ofq, and Γs−1 roughly agrees with the mechanical relaxation time τ estimated from a fit of the dynamic viscoelastic data of the same samples by a Maxwell type of model with the single relaxation time τ.

THE FREE STREAMING OPERATOR WITH MAXWELL TYPE BOUNDARY CONDITIONS IN ASYMMETRIC SOBOLEV SPACES

Some properties of the free streaming operator T with Maxwell type boundary conditions are studied in this paper. The domain D(T) is assumed to be contained in a suitable asymmetric Sobolev space. The norm of the element f is defined in such a space by the sum [Formula: see text], where ‖ ‖1 is the usual L1 norm and c is a constant. It is proved that T generates a contraction semigroup, which preserves positivity.

On the flow past a needle in a cylindrical tube

In this paper, the uniform flow past a needle placed at the centre-line of a tube is analysed for a class of constitutive equations of the Maxwell type using a finite element implementation of the explicitly elliptic momentum equation (EEME) formulation. In the coupled finite element approach, the Galerkin method is applied to the modified momentum equations and the continuity equation, while the treamline upwind Petrov-Galerkin method is applied to the constitutive equations of the viscoelastic fluids. For the power-law and the Phan-Thien-Tanner (PTT) fluids, an asymptotic analysis valid for slender needles is also given. The flow is of practical importance since it forms the basis of an existing commercial viscometer. The viscometer would provide the true shear stress-shear rate relationship if the nominal shear rate is given by KU/R, where U is the falling speed of the needle, R is the radius of the tube, and K is a constant. For the PTT model and the geometry used in this paper, this constant is approximately 4, which is also the value for power-law fluids with power-law index n = 1 3 .