FENE model

In polymer physics, the finite extensible nonlinear elastic (FENE) model, also called the FENE dumbbell model, represents the dynamics of a long-chained polymer. It simplifies the chain of monomers by connecting a sequence of beads with nonlinear springs. Its direct extension the FENE-P model, is more commonly used in computational fluid dynamics to simulate turbulent flow. The P stands for the last name of physicist Anton Peterlin, who developed an important approximation of the model in 1966. The FENE-P model was introduced by Robert Byron Bird et al. in the 1980s. In 1991 the FENE-MP model (PM for modified Peterlin) was introduced and in 1988 the FENE-CR was introduced by M.D. Chilcott and J.M. Rallison.

In polymer physics, the finite extensible nonlinear elastic (FENE) model, also called the FENE dumbbell model, represents the dynamics of a long-chained polymer. It simplifies the chain of monomers by connecting a sequence of beads with nonlinear springs. Its direct extension the FENE-P model, is more commonly used in computational fluid dynamics to simulate turbulent flow. The P stands for the last name of physicist Anton Peterlin, who developed an important approximation of the model in 1966. The FENE-P model was introduced by Robert Byron Bird et al. in the 1980s. In 1991 the FENE-MP model (PM for modified Peterlin) was introduced and in 1988 the FENE-CR was introduced by M.D. Chilcott and J.M. Rallison. \textbf{F}_i=k\frac{\textbf{R}_i}{1-(R_i/L_{\rm max})^2} , where R_i = |\textbf{R}_i| , k is the spring constant and Lmax the upper limit for the length extension. Total stretching force on i-th bead can be written as \textbf{F}_i - \textbf{F}_{i-1} . The Werner's spring force approximate the inverse Langevin function found in other models. \textbf{F}_i=k\frac{\textbf{R}_i}{1-\lang R^2_i/L_{\rm max}^2\rang} , where the \lang\cdots\rang indicates the statistical average.

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