Numerical Simulation of Viscoelastic Start-up Flow between Parallel Plates Using Stochastic Calculation

The start-up flow of polymeric liquids between parallel plates was numerically simulated using a stochastic approach. The extra stress was calculated by solving the stochastic equation of a reptation model instead of using a constitutive equation. The numerical results showed that the present numerical simulation was capable to describe typical macroscopic behaviors of polymeric liquids such as the change in velocity profile with time, the growth in shear stress, and overshoot phenomena of velocity and wall shear stress. Moreover, the stochastic approach can predict microscopic behaviors such as the time development of polymer orientation. It is advantage of the present method that information related to the behavior of microscopic polymer structures in a flow can be obtained. In addition, the comparison with the numerical prediction using an approximated constitutive model showed that a closure approximation used led to a remarkable error just after the onset of the flow.