Multiscale simulation of a polymer melt flow between two coaxial cylinders under nonisothermal conditions

Yuji Hamada; Takeshi Sato; Takashi Taniguchi; Yuji Hamada; Takeshi Sato; Takashi Taniguchi

doi:10.3934/mine.2021042

Mathematics in Engineering

2021, Volume 3, Issue 6: 1-22. doi: 10.3934/mine.2021042

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Multiscale simulation of a polymer melt flow between two coaxial cylinders under nonisothermal conditions

1.
Department of Chemical Engineering, Kyoto University, Kyoto 615-8510, Japan
2.
Department of Physics, Tohoku University, Sendai, Miyagi 980-8578, Japan

Received: 18 March 2020 Accepted: 28 July 2020 Published: 28 October 2020

We successfully extend a multiscale simulation (MSS) method to nonisothermal well-entangled polymer melt flows between two coaxial cylinders. In the multiscale simulation, the macroscopic flow system is connected to a number of microscopic systems through the velocity gradient tensor, stress tensor and temperature. At the macroscopic level, in addition to the momentum balance equation, we consider the energy balance equation, where heat generation plays an important role not only in the temperature distribution but also in the flow profile. At the microscopic level, a dual slip-link model is employed for well-entangled polymers. To incorporate the temperature effect into the microscopic systems, we used the time-temperature superposition rule for the slip-link model, in which the temperature dependence of the parameters is not known; on the other hand, the way to take into account the temperature effect in the macroscopic equations has been well established. We find that the extended multiscale simulation method is quite effective in revealing the relation between nonisothermal polymeric flows for both steady and transient cases and the microscopic states of polymer chains expressed by primitive paths and slip-links. It is also found that the temperature-dependent reptation-time-based Weissenberg number is a suitable measure for understanding the extent of the polymer chain deformation in the range of the shear rate used in this study.
- multiscale simulation,
- temperature-dependent polymeric flow,
- energy balance equation,
- well-entangled polymer melt,
- slip-link model
Citation: Yuji Hamada, Takeshi Sato, Takashi Taniguchi. Multiscale simulation of a polymer melt flow between two coaxial cylinders under nonisothermal conditions[J]. Mathematics in Engineering, 2021, 3(6): 1-22. doi: 10.3934/mine.2021042

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Abstract

We successfully extend a multiscale simulation (MSS) method to nonisothermal well-entangled polymer melt flows between two coaxial cylinders. In the multiscale simulation, the macroscopic flow system is connected to a number of microscopic systems through the velocity gradient tensor, stress tensor and temperature. At the macroscopic level, in addition to the momentum balance equation, we consider the energy balance equation, where heat generation plays an important role not only in the temperature distribution but also in the flow profile. At the microscopic level, a dual slip-link model is employed for well-entangled polymers. To incorporate the temperature effect into the microscopic systems, we used the time-temperature superposition rule for the slip-link model, in which the temperature dependence of the parameters is not known; on the other hand, the way to take into account the temperature effect in the macroscopic equations has been well established. We find that the extended multiscale simulation method is quite effective in revealing the relation between nonisothermal polymeric flows for both steady and transient cases and the microscopic states of polymer chains expressed by primitive paths and slip-links. It is also found that the temperature-dependent reptation-time-based Weissenberg number is a suitable measure for understanding the extent of the polymer chain deformation in the range of the shear rate used in this study.

References

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