Numerical Modeling of Micro Fluidics of Polymer Melts

A new Galerkin finite element scheme for the numerical simulation of three-dimensional time-dependent flow of K-BKZ fluids has been developed. The scheme was used to model the polymer melt flow in nano imprint lithography (NIL). In NIL a sub micrometer pattern is hot pressed onto a thin polymer film on a hard substrate.

The numerical method is based on a Lagrangian kinematics description of the fluid, where the (Cartesian) coordinate system attached to the particles is discretized by ten-node quadratic tetrahedral elements. The time integral in the K-BKZ model is discretized by a quadratic interpolation ensuring third order convergence in time.

The method has been benchmarked on the free surface problem of a filament stretched between two plates.