Kinetic theory and transport phenomena for a dumbbell model under nonisothermal conditions
作者:
Hans Christian Öttinger,
Fabrizio Petrillo,
期刊:
Journal of Rheology
(AIP Available online 1996)
卷期:
Volume 40,
issue 5
页码: 857-874
ISSN:0148-6055
年代: 1996
DOI:10.1122/1.550765
出版商: The Society of Rheology
关键词: Kinetic theory;Transport phenomena;Nonisothermal flow;Dumbbell model;Heat‐flux vector;POLYMERS;SOLUTIONS;TRANSPORT THEORY;BROWNIAN MOVEMENT;HEAT FLUX;DIFFUSION;KINETIC EQUATIONS
数据来源: AIP
摘要:
A Hookean dumbbell model for polymers in dilute solutions undergoing homogeneous flow is generalized to include arbitrary imposed temperature profiles. In order to obtain the ‘‘nonisothermal diffusion equation’’ for the probability density in polymer configuration space we generalize the approach of Schieber and Öttinger [J. Chem. Phys.89, 6972–6981 (1988)] to Brownian motion out of equilibrium. In addition, we derive the polymer contributions to the mass‐flux vector, stress tensor and heat‐flux vector by means of the kinetic theory approach of Curtiss and Bird [Adv. Polym. Sci.125, 1–101 (1996)] for the case of a slowly varying temperature gradient, and we find coupled constitutive equations for the mass, momentum and energy fluxes. For a simple steady shear flow it is then possible to calculate the heat‐flux vector explicitly, at least for small temperature gradients and shear rates. We compare our approach and results with previous works on this subject, and we finally discuss some extensions.
点击下载:
PDF
(256KB)
返 回