The purpose of this project was to determine the first normal stress difference of an elastic polymer flowing through with a hyperbolic contraction, which has been known to characterize the elasticity of complex fluids. Although the normal stress difference is difficult to measure in reality, we can take advantage of virtual tools and solve for the normal stress difference using a computer aided model. The geometry used consisted of a quarter circle contraction taken out of a rectangle and is shown below. The solution was obtained by solving for the Maxwell and Phan-Thien-Tanner models using COMSOL Multiphysics 3.3. The figure below shows a result obtained using the Maxwell model for a Weissenberg number of 0.06. The colored plot indicates the pressure concentration and and the red streamlines indicate the velocity in the x-direction. |