Mathematical characteristics of the pom-pom model |
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Authors: | Jae Wook Lee Dukjoon Kim Youngdon Kwon |
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Institution: | (1) School of Applied Chemistry and Chemical Engineering, Sungkyunkwan University, Suwon, Kyunggi-do 440-746, Korea e-mail: ydkwon@yurim.skku.ac.kr, KR |
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Abstract: | Recently, in order to describe the complex rheological behavior of polymer melts with long side branches like low density
polyethylene, new constitutive equations called the pom-pom equations have been derived in the integral/differential form
and also in the simplified differential type by McLeish and Larson on the basis of the reptation dynamics with simplified
branch structure taken into account. In this study, mathematical stability analysis under short and high frequency wave disturbances
has been performed for these constitutive equations. It is proved that the differential model is globally Hadamard stable,
as long as the orientation tensor remains positive definite or the smooth strain history in the flow is previously given.
However both versions of the model are Hadamard unstable if we neglect the arm withdrawal in the case of maximum backbone
stretch. It is also dissipatively unstable, since the steady shear flow curves exhibit non-monotonic dependence on shear rate.
Additionally, in the flow regime of creep shear flow where the applied constant shear stress exceeds the maximum achievable
value in the steady flow curves, the constitutive equations exhibit severe instability that the solution possesses strong
discontinuity at the moment of change of chain dynamics mechanisms.
Received: 14 August 2001 Accepted: 18 October 2001 |
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Keywords: | Pom-pom model Hadamard stability Creep shear flow Dissipative stability |
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