Boundary conditions for the microscopic fene models

Chun Liu, Hailiang Liu

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

We consider the microscopic equation of finite extensible nonlinear elasticity (FENE) models for polymeric fluids under a steady flow field. It is shown that for the underlying Fokker-Planck type of equations, anypreassigned distribution on the boundary will become redundant once the nondimensional number Li := Hb/κBT≥2, where H is the elasticity constant, √b is the maximum dumbbell extension, T is the temperature, and κB is the usual Boltzmann constant. Moreover, if the probability density functionis regularenough for its trace to be defined on the sphere |m| = √b, then the trace is necessarily zero when Li > 2. These results are consistent with our numerical simulations as well assome recent well-posedness results by preassuming a zero boundary distribution.

Original languageEnglish (US)
Pages (from-to)1304-1315
Number of pages12
JournalSIAM Journal on Applied Mathematics
Volume68
Issue number5
DOIs
StatePublished - Nov 6 2008

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

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