Arkadii I. Leonov

Rheology of concentrated dispersed systems in a low molecular weight matrix

Abstract The objective of this paper is to provide a complete theoretical and experimental study of shear rheology for concentrated dispersed systems in low molecular weight matrices. A new theoretical approach based on qualitative microstructural physics and thermodynamical arguments is devel- oped which considers flow, elastic deformations, ruptures and restorations of flocs. The approach was developed to study steady and transient phenomena and has predicted very different behaviours for various systems; one of them was a non-monotonic flow curve. The most remarkable feature of the theoretical model is that it contains no mathematical yield criterion but predicts anisotropic yield values with continuous transition from solid state to flow as a bifurcation. A complete set of experiments in simple shearing was carried out for two different dispersed systems: a granular grease and a water-clay platelet mixture. Also some disturbing phenomena were observed and experimental techniques were developed which made it possible to obtain reliable results. Additionally the clay-water system exhibited a minimum in the flow curve, and all the characteristics peculiar to the evolution from solid state to flow, as predicted by the theory. Despite the short time scale of transition phenomena for the materials tested, the general comparison of experimental results with theory showed good agreement.

On the rheological modeling of viscoelastic polymer liquids with stable constitutive equations

Various approaches to the theology of polymer solutions and melts have resulted in an overabundance of constitutive equations (CEs). None of these equations can describe the entire set of available rheological data in a consistent fashion, even for simple flows. Additionally, almost all the CEs suggested in the literature have recently been determined to be unstable in either the Hadamard or dissipative sense without any physical reason. In this paper, we attempt to describe simple flow data for LDPE Melt I/IUPAC A/IUPAC X, HDPE II. PS I, PIB P-20 and PIB L-80 with a certain class of differential CEs, while complying with the global isothermal stability constraints. For simplicity, only one or two nonlinear parameters additional to the discretized linear viscoelastic spectra are introduced for the description of data.

Stability constraints in the formulation of viscoelastic constitutive equations

Abstract This paper discusses the criteria for both global Hadamard and dissipative stabilities of viscoelastic constitutive equations (CEs) with instantaneous elasticity. In order to formulate as generally as possible the conditions of stability analyses, we used some unified forms for CEs of differential Maxwell-like and factorable single integral types. The obtained criteria formulate the constraints which have to be imposed on parameters or functions in CEs to avoid the unphysical instabilities in the whole range of Deborah numbers, independent of the flow situation. The problem of Hadamard stability for the viscoelastic CEs is reduced to that well known in the theory of nonlinear elasticity where the complete solution of the problem was found recently in an algebraic form. The criteria of dissipative stability, which have been established previously, are also discussed. When applied to many popular viscoelastic models, the combined stability criteria impose a set of such severe constraints that no single integral CE with time-strain separability proposed in the literature, could satisfy them, and only few differential models have proved to be stable.

On the rheological modeling of filled polymers with particle-matrix interactions

In this paper constitutive equations are developed for the rheological description of highly filled polymers in which particle-matrix interactions are more significant than interparticle interactions. At any point in the deformation history the polymer chains are classified as either “free” or “trapped” (to the particles), the total stress being assumed to be the sum of the stresses in these two types of chains. When a load is applied to this system, it is hypothesized that a fraction of the trapped chains becomes free, and that simultaneously some free chains become trapped, with a balance between the two described by a deformation rate dependent kinetic equation. The rheological behavior of the free chains is described by stable nonlinear viscoelastic constitutive equations for unfilled polymers. For the trapped chains similar equations are used, but with the relaxation time in the evolution equation scaled by a scalar “mobility” function of the degree of chain debonding from the particles. All the basic features of highly filled systems such as anisotropic yield stresses, thixotropy, and frozen memory during relaxation can be described by this scheme without using any yield criterion. Preliminary comparisons are made with experimental data in simple shear and simple elongation.

The extended Padé-Laplace method for efficient discretization of linear viscoelastic spectra

The discretization of linear viscoelastic spectra is valuable as a starting point for non-linear viscoelastic modeling. However, obtaining the parameters of the generalized Maxwell model from linear viscoelastic experiments with naive least squares procedures is known to be an ill-posed problem. A novel technique, the Padé-Laplace method was recently elucidated (Fulchiron et al., 1993) for robustly extracting the parameters of the generalized Maxwell model from stress relaxation experiments, without any a priori assumption about the number of Maxwellian modes. We extend this method for obtaining the Maxwellian modes from dynamic data and discuss the relationship between continuous viscoelastic spectra and the Maxwellian modes obtained by this procedure. Furthermore, the applicability of this method with experimental data in limited time/frequency windows is clarified. Finally, a procedure for assembling the discretized spectrum with the Padé-Laplace method applied to both stress relaxation and dynamic data with typical experimental time/frequency cutoffs is developed.

Constitutive equations for viscoelastic liquids: Formulation, analysis and comparison with data

Publisher Summary This chapter discusses the two common classes of viscoelastic constitutive equations (CEs) for polymer melts and concentrated polymer solutions. These are general Maxwell-like and single integral CEs with instantaneous elasticity. The formulation of both classes of CEs are analyzed. The Maxwell-like CEs usually employ some hidden tensor variables with different physical senses. Therefore, in spite of the generality in formulation, their evolution equations and stress relations have different features, depending on the theoretical approach used. Some artifacts related to formulation of the CEs are also exposed. Such an important effect as compressibility is discussed. General results on stability for both classes of CEs is demonstrated, which included stability analyses of both the Hadamard and dissipative types. Results of the stability analyses are applied to popular CEs. The descriptive capability of a class of Maxwell-like CEs is demonstrated, whose formulation satisfies all the stability constraints. The data for equi-biaxial extension is obtained using the lubricated squeezing technique.

Investigations of the rheological behavior of rubber-carbon black compounds over a wide range of stresses including very low stresses

Abstract The rheological properties of gum and carbon black compounds of an ethylene-propylene terpolymer elastomer at 20, 30, 40, and 50 vol.% carbon loadings have been investigated over a very wide range of stresses and shear rates. This was accomplished using (1) a constant shear stress creep instrument, (2) a rotational rheometer and (3) a capillary extrusion rheometer at higher shear rates. The stresses used in the studies included magnitudes leading to shear flow and stresses below the yield value, where rubber compounds exhibit only finite deformation. Much attention was given to measurements of creep and strain recovery at low stresses. The magnitudes of yield stresses obtained from these low stress and recovery experiments are significantly lower than those obtained using standard extrapolation to zero shear rate of higher stresses from rotational and capillary instruments.

On Hadamard-type stability of single-integral constitutive equations for viscoelastic liquids

Abstract This paper studies the Hadamard-type stability of viscoelastic constitutive equations (VECEs) of single-integral type by the analysis of local linear stability against extremely short and fast disturbances. The analysis is quite similar to that previously considered for Maxwell-like VECEs of differential type. The necessary and sufficient conditions for the global stability (i.e. stability for any type of flow and any value of velocity gradient) are obtained in algebraic form for the time-strain separable single-integral VECEs with instantaneous elasticity. These conditions are then applied to the analysis of the stability for some single-integral VECEs proposed in the literature: Oldroyd-Lodge model, some specifications of the Kaye-BK-Z model and two modifications of the VECEs proposed by Wagner. It is shown that apart from very particular cases, both Wagners VECEs are unstable in the Hadamard-type sense, seemingly due to poor (or the absence of any) relations to thermodynamic description.

Non-Markovian Brownian Motion in a Viscoelastic Fluid

A theory of non‐Markovian translational Brownian motion in a Maxwell fluid is developed. A universal kinetic equation for the joint probability distribution of position, velocity, and acceleration of a Brownian particle is derived directly from the extended dynamic equations for the system. Unlike the extended Fokker–Planck equation which corresponds to Mori–Kubo generalized Langevin equation and provides only with calculations of one‐time moments, the universal kinetic equation obtained gives complete statistical description of the process. In particular, an exact generalized Fokker–Planck equation in the velocity space valid for any time instant is derived for the free non‐Markovian Brownian motion. It shows that both the ‘‘master telegraph’’ and the respective kinetic equations, obtained in the molecular theory of Brownian motion, are type of approximations. The long and short time behavior of velocity and force correlations for a free Brownian particle is investigated in the general case of a nonequil...

Rheological Properties of Rubber-Carbon Black and Carbon Black-Oil Compounds Including Measurements at Very Low Shear Stresses

Abstract The rheological properties of binary rubber-carbon black compounds at compositions 5, 20, 30, 40 and 50 volume percent carbon black have been investigated as well as ternary compounds with rubber/carbon black/oil compositions of 70/20/10, 60/20/20 and 50/20/30, respectively. The compounds were investigated using (1) a constant stress creep instrument at very low rates of deformation, (2) a rotational rheometer at intermediate shear rates and (3) a capillary extrusion instrument at higher shear rates. In experiment (1), it was found that below a critical yield stress, the strain becomes saturated and finite. Above this stress the strain becomes unbounded and the compound maintained a steady shear flow. This observation was made for all compounds investigated. The values of the yield stresses obtained using the creep instrument were found to be significantly lower than those obtained from common extrapolations from rotational and capillary rheometers. In the ternary compounds it was also observed t...