Constitutive equations for weakly entangled linear polymers

Pyshnograi, G. V.; Gusev, Alexander; Pokrovskii, Vladimir N.

doi:10.1016/j.jnnfm.2009.07.003

Cited by 27 publications

(3 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Results of calculations of viscometric flows for this rheological model agree well with experimental data [6], which makes it relevant and useful for calculations of more complex flows. For example, in [7,8], steady motion between parallel planes under a constant pressure gradient is considered, and it is shown that model (1) predicts a nonparabolic shape of the velocity profile and the presence of a nonzero pressure gradient in a direction perpendicular to the flow.…”

supporting

confidence: 73%

Mathematical modeling of polymer film casting under biaxial stretching taking into account heat transfer

Pyshnograi

Tretyakov

Altukhov

2012

J Appl Mech Tech Phy

View full text Add to dashboard Cite

Polymer film casting is studied using a modified Vinogradov-Pokrovskii rheological model with heat transfer taken into account. Dependences of the film temperature, velocity, and width on the distance to the extruder exit was obtained and the effect of model parameters on these dependences was examined.Design and manufacture of products from polymer materials using mathematical modeling has a number of advantages, among which are the possibilities of controlling the quality of polymer products and solving a number of optimization problems. A common method for processing polymer materials is the production of polymer films with the use of an extruder through which a polymer melt is extruded [1][2][3][4]. The resulting film falls on a cooling drum. During motion of the film from the extruder to the drum, it is cooled and its width and thickness change. In this process, the film is stretched unevenly, leading to a neck effect [2, 3] which is manifested in the existence of two regions in the curve of the width of the film versus distance to the extruder exit. In the first region, there is a substantial change in the width of the film due to intense deformation, and in the second region, this change is insignificant and the material moves as a whole unit. Since all of these processes occur simultaneously, in their mathematical modeling, one has to simultaneously solve the equations for velocities, stress, and heat transfer. In this work, steady tensile stresses are obtained using a generalized Vinogradov-Pokrovskii rheological model [5] whose parameters are known functions of temperature:(1)Here σ ik is the stress tensor, p is the hydrostatic pressure, η 0 and τ 0 are the initial shear viscosity and relaxation time, ν ik is the velocity gradient tensor, a ik is the symmetric anisotropy tensor of the second rank, I = a jj is the first invariant of the anisotropy tensor, γ ik = (ν ik + ν ki )/2 is the symmetrized velocity gradient tensor, and κ and β are phenomenological parameters of the model that take into account the size and shape of the molecular coil in the equations of dynamics of the macromolecule. Results of calculations of viscometric flows for this rheological model agree well with experimental data [6], which makes it relevant and useful for calculations of more complex flows. For example, in [7,8], steady motion between parallel planes under a constant pressure gradient is considered, and it is shown that model (1) predicts a nonparabolic shape of the velocity profile and the presence of a nonzero pressure gradient in a direction perpendicular to the flow.

show abstract

supporting

confidence: 73%

Mathematical modeling of polymer film casting under biaxial stretching taking into account heat transfer

Pyshnograi

Tretyakov

Altukhov

2012

J Appl Mech Tech Phy

View full text Add to dashboard Cite

show abstract

“…Besides the Rauz parameters (drag coeffi cient of beads, equilibrium size of the coiled macromolecule), it is necessary to introduce into the model parameters taking into account the presence of entanglements in the polymer system. For such a model, we use in the present work the modifi ed Vinogradov-Pokrovskii model [21][22][23][24][25]. The specifi c feature of this model is that it takes into account the tensor character of the drag coeffi cient of beads connected with the induced anisotropy of the shear fl ow.…”

mentioning

confidence: 99%

Rheological Model for Describing Viscometric Flows of Melts of Branched Polymers

Merzlikina

Pyshnograi

Pivokonskii

et al. 2016

J Eng Phys Thermophy

View full text Add to dashboard Cite

The present paper considers the problem of constructing a rheological constitutive relation for melts of branched polymers with the use of a modifi ed Vinogradov-Pokrovskii rheological model generalized to the case of several noninteracting models, each of which corresponds to the account in the stress tensor of the contribution of a particular polymer fraction and is characterized by its own relaxation time and viscosity. Since the number of model parameters markedly increases thereby, simple dependences of its parameters on the mode number are proposed. On the basis of the obtained model, the nonlinear nonstationary effects at simple shear and uniaxial tensor have been considered.Keywords: rheology, polymer melts, mesoscopic approach, rheological equation of state, viscometric fl ows.Introduction. Experimental investigations of various polymer fl uids point to their linear viscoelastic behavior. To investigate such effects, a large number of models describing the rheological behavior of polymer fl uids at both qualitative and quantitative levels were proposed. It should be noted thereby that two radically different classes of models exist: models of the fi rst class use the phenomenological approach, and in models of the second class the microscopic approach is used. In the phenomenological approach, the dynamics of macroscopic bodies is constructed on the basis of the general laws determined experimentally. This class of models includes the Maxwell, Oldroyd [1], and ProkuninLeonov [2] phenomenological models. The other class of models is based on the mesoscopic approach. In such models, the macromolecular dynamics is described on the basis of model notions and, consequently, takes into account, in some approximation, both the structure of the polymer molecule and the processes of intermolecular interaction. Such models often use the one-molecule approximation in which instead of the whole aggregate of macromolecules, one chosen macromolecule moving in some "effective" medium is considered. In some of the models of this class the macromolecule is represented as a series of beads and springs (elastic force) connecting them. For example, one of the fi rst of such models is the Kargin-Slonimskii-Rauz model. Thus, the mesoscopic approach, as opposed to the phenomenological one, makes it possible to follow the relationship between the micro-and macroscopic characteristics of polymer systems and, consequently, explain various phenomena in polymer melts, for example, the diffusion, viscoelasticity, and other phenomena. However, this approach requires the introduction of additional mesoscopic parameters, which should also be determined experimentally. Among the above models are also the Doi-Edwards [3], De Gennes [4], and Curtiss-Bird [5] models. In these models, each macromolecule is considered as a fl exible chain moving inside some tube formed by other macromolecules; and at short observation times the molecule can move only along the tube. However, the initial Doi-Edwards model did not take into account the elongat...

show abstract

“…(1) which considers only one relaxation process complies so greatly to the experimental data. When describing the non-linear dependence of shift viscosity and normal stresses of the firstorder difference, this model shows only qualitative compliance of calculated dependences and the experimental data [4,8,9].…”

Section: Discussionmentioning

confidence: 88%

Modeling of nonlinear viscoelastic polymeric materials at their large periodic deformation

Cherpakova¹,

Pyshnograi²,

Filip³

et al. 2019

Epitoanyag - JSBCM

View full text Add to dashboard Cite

Analyzing the behavior of flows of polymers solutions and melts in the area of non-linear viscoelasticity allows to estimate more precisely the adequacy of the rheological model and to describe the material structure in more detail. Today a lot of models describe non-linear properties of polymeric materials rather accurately. However, the formulation of a uniform rheological model remains open. Therefore this work considers the modified Vinogradov-Pokrovsky rheological model which formed the basis for numerical calculations for periodic deformation of shear flows of polymeric liquids with a large amplitude. The non-linear viscoelastic properties shown in the course of the research of behavior of polymeric material at large deformations were studied by means of the immediate analysis of time dependence of shear stresses which were calculated at various amplitudes. It was stated that when increasing the amplitude of deformation the response stops being the exact harmonica, and a "step" on the left-hand front appears. It manifests the nonlinear response of a sample. The work compares obtained theoretical dependences and the experimental data for 5% mass solutions of the polyethylene oxide in dimethylsulfoxide which was studied at harmonic deformations with the large amplitude reaching 40 relative units. These dependences were measured at 35°C and the frequency of 0.2 Hz. Despite its simplicity, the modified Vinogradov-Pokrovsky rheological model shows good compliance with the experimental data. The results show that the chosen model adequately describes behavior of polymeric materials at large periodic deformations. Therefore this model may be applied for modeling more complex flows of fluid polymeric environments.

show abstract

Constitutive equations for weakly entangled linear polymers

Cited by 27 publications

References 31 publications

Mathematical modeling of polymer film casting under biaxial stretching taking into account heat transfer

Mathematical modeling of polymer film casting under biaxial stretching taking into account heat transfer

Rheological Model for Describing Viscometric Flows of Melts of Branched Polymers

Modeling of nonlinear viscoelastic polymeric materials at their large periodic deformation

Contact Info

Product

Resources

About