Numerical Methods For Viscoelastic Flows -
Supported by NSF-DMS-1320037
(Work in progress)
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
Instabilities of thin viscoelastic films
We numerically study thin viscoelastic
films on a solid substrate subject to the van der Waals
interactions. We are interested in the interface instabilities
in wetting/dewetting processes. The governing equations are obtained
as the lubrication approximation of the Navier-Stokes equations,
with a Maxwell or Jeffreys model for viscoelasticity.
V. Barra, S. Afkhami, and L. Kondic "Interfacial dynamics of thin viscoelastic films and drops", Journal of Non-Newtonian Fluid Mechanics, vol. 237, pp. 26-38, 2016.
The following video shows the formation of satellite droplets after the breakup of a viscoelastic film.
A numerically conservative method
for direct solution of two-phase viscoelastic flows
A new formulation that transforms the constitutive equation for viscoelastic stress into a conservative form is proposed. This new formulation is amenable to the use of a state-of-the-art adaptive mesh refinement method on octree finite-volume meshes. The goal of this proposal is to develop discretization and solution algorithms that are designed to not only maintain the higher order accuracy, but also guarantee that the discrete set of algebraic equations possess particular characteristics that are contained in the differential form of the constitutive equations. Different constitutive models for viscoelastic liquids are incorporated into the computational framework, allowing the investigation of the effects of constitutive laws on improved fitting to the experimental measurements, especially in flows which contain stress singularities. Parallelized algorithms combined with adaptive mesh refinement and GPU optimization are expected to significantly improve the efficiency of the direct simulations.
S. Afkhami, Y. Renardy, and M. Renardy, "Numerical methods for the flows of two
immiscible viscoelastic liquids", 2016.