Mesoscopic approach for linear polymers melts and solutions: nonlinear effects in viscometric flows and unidimensional approximation for nonisothermal flows
A. Rybakov , A. Gusev , G. Pyshnograi

Altai State Technical University

Abstract: Rheological equations of state of linear polymer solutions and melts are obtained using methods of statistical mechanics and thermodynamics for the description and interpretation of nonlinear effects. These equations have been formulated on the basis of Brownian dynamics with entered non Markovian anisotropic noise and it has been shown that introduction of a certain kind of non Markovian fluctuations leads to the occurrence at a macrolevel of intermediate scales of length which may be interpreted as the radius of a tube as in theory by De Gennes, or as the length of a chain between entanglements as in the theory by Graessley. For the description of the process of formation of a polymeric film it is necessary to account for the fact that the received film is cooled and exposed to a stretching. As these processes occur simultaneously their mathematical modeling requires the joint solution of the equations for pressure and heat conduction. In this work in order to find the established pressure at a stretching a rheological model has been used in which the parameters are functions of temperature. For the thermal calculation it was assumed that the thickness of a film is small. Also the non-uniform current of a nonlinear viscoelastic liquid between parallel plates under the action of a constant pressure gradient is calculated. A comparison of the results of the calculation of the velocity with experimental data is performed. This allows us to draw the conclusion, that in the considered case of Poiseuille flow, the rheological model does not lead to a parabolic profile of velocity between parallel plates a result that does not contradict experimental data.