New Temperature Dependent Configurational Probability Diffusion Equation for Diluted FENE Polymer Fluids: Existence of Solution Results

The theory for the non-isothermal rheology of polymer fluids proposed in Curtiss and Bird (Adv Polym Sci 125:1–101, 1996) used several approximations including the so-called linear gradient approximations for the temperature field and Brownian forces. While it had the significant advantage of dealin...

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Bibliographic Details
Published in:Journal of dynamics and differential equations 2022-12, Vol.34 (4), p.2913-2935
Main Authors: Ciuperca, Ionel Sorin, Palade, Liviu Iulian
Format: Article
Language:English
Subjects:
Applications of Mathematics
Approximation
Density
Dilution
Fluid flow
Incompressible flow
Linear equations
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Polymers
Rheological properties
Rheology
Temperature dependence
Temperature distribution
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Summary:The theory for the non-isothermal rheology of polymer fluids proposed in Curtiss and Bird (Adv Polym Sci 125:1–101, 1996) used several approximations including the so-called linear gradient approximations for the temperature field and Brownian forces. While it had the significant advantage of dealing with linear equations, the approximations involved may have led to several non-physical predictions. This work is a continuation of Curtiss and Bird (1996) in that it obtains the corresponding non-linear configurational probability density equation in dimensionless form without the linear gradient approximations for the temperature field and Brownian forces. It does so for incompressible diluted polymer solutions with polymer molecules being modeled as FENE ( F initely E xtensible N onlinear E lastic) chains. Next we prove the existence of temperature dependent, positive variational solutions for the probability density equation of the FENE model.
ISSN:1040-7294
1572-9222
DOI:10.1007/s10884-021-09948-6