Rheological Behavior of FENE Dumbbell Suspension under Elongational Flow

This Demonstration plots the transient behavior of the elongational viscosity (usually expressed in cpoise). It also displays an estimation of the value of this elongational viscosity. The determination of the rheological properties is based on finitely extensible nonlinear elastic (FENE) dumbbells simulations called Brownian dynamics.

Two beads are attached by a spring and are subject to opposite forces:

,

where is the distance between bead centers, is the spring constant, and is the maximum extension length of the dumbbell. The force becomes infinite as values of approach . Beads are also subject to Brownian motion and to an elongational flow characterized by its elongational rate (usually expressed in ).

For an elongational flow, the velocity gradient tensor has the form

, where is the elongation rate.

One can observe that the values of the elongational viscosity are lower as the elongational rates decrease. Similar computations using FORTRAN 77 were performed by H. Binous and R. Phillips at the University of California, Davis in 1997 (for references see the details).

H. Binous and R. J. Phillips, "Dynamic Simulation of One and Two Particles Sedimenting in Viscoelastic Suspensions of FENE Dumbbells," Journal of Non-Newtonian Fluid Mechanics, 83, 1999 pp. 93–130.