Extensional deformation of non-Newtonian liquid bridges

A numerical method for simulating the extensional dynamics of elongating filaments of non-Newtonian fluids in a filament stretching rheometer is presented. The boundary element method, in conjunction with either the Oldroyd-B or the generalized multimode Upper-Convected Maxwell constitutive model, is used to calculate the transient evolution of the liquid interface, the applied force on the stationary end plate and the polymeric stresses. The numerical results are compared to experimental results and are in excellent agreement at low Hencky strains (Newtonian response) but provide less accurate modeling of the stress growth observed in experiments at higher strains. A comparison of different methods for measuring the apparent extensional viscosity from global measurements of the net force and the mid-point radius of the filament is presented. At large strains calculations show that the fluid motion in these devices closely approximates ideal uniaxial elongation.