This research involves the development of numerical methods and algorithms for the study of flows of viscoelastic liquids. We use a thin-film approximation to study the formation of nanostructures following the instability and breakup of ultra-thin viscoelastic films on supporting substrates. We also develop discretization schemes and numerical algorithms for the solution of full governing equations coupled with classes of nonlinear partial differential equations for viscoelastic stresses. The numerical methodologies constructed in this research, while focusing on addressing two-phase viscoelastic flows, will be broadly-useful in simulating and investigating a number of different complex flow applications such as polymer processing, biological flows in microfluidic devices, and emulsion flows in polymer blending. In nano/microscale geometries, flows of two immiscible liquids are often dominated by surface tension. Moreover, the interface of two liquids may undergo large deformation rates as it moves in networks of nano/microchannels. The new method for discretizing the viscoelastic constitutive equations allow practical direct simulation of viscoelastic flows with strong elasticity.
We present a computational investigation of thin viscoelastic films and drops on a solid substrate subject to the van der Waals interaction force, in two spatial dimensions. The governing equations are obtained within a long-wave approximation of the Navier–Stokes equations with Jeffreys model for viscoelastic stresses. We investigate the effects of viscoelasticity, Newtonian viscosity, and the substrate slippage on the dynamics of thin viscoelastic films. We also study the effects of viscoelasticity on drops that spread or recede on a prewetted substrate. For dewetting films, the numerical results show the presence of multiple secondary droplets for higher values of elasticity, consistently with experimental findings. For drops, we find that elastic effects lead to deviations from the Cox–Voinov law for partially wetting fluids. In general, elastic effects enhance spreading, and suppress retraction, compared to Newtonian ones.