Numerical study on micro-scale extensional viscoelastic flows

Abstract

The capillary thinning dynamics can be considered one of the fingerprints of extensionally-dominated viscoelastic flows. Notably, the rheological behavior of complex fluids in extensional flow has been investigated in different rheometric devices, as for instance in the Capillary Breakup Extensional Rheometer (CaBER), the Dripping-ontoSubstrate (DoS) rheometry, or the Rayleigh Ohnesorge Jetting Extensional Rheometer (ROJER). In recent years, the Computational Rheology community has made a considerable effort to better understand the interplay of viscoelasticity and capillarity effects in such transient rheometric experiments. In this work, we present a numerical study on the dynamics of extensional flows of dilute polymeric solutions at small scales. Our numerical investigation focus primarily on the potential of using small scale two-phase extensional viscoelastic flows as suitable platforms for performing rheometry of weakly viscoelastic polymer solutions. In particular, we have adopted the setup used in the experiments of Sousa et al. [Rheol. Acta 56 (2017) 11-20]. In such set up, the filament stretching is conducted using oil as an outer phase, avoiding sample evaporation, or allowing visualization of the filament interior. In order to handle with the moving interface problem, we have employed a two-phase viscoelastic fluid flow solver, based on a finite differences scheme. In this methodology, the interface between the fluids is approximated by the volume-of-fluid interface reconstruction algorithm, and a second-order operator-split method is used to solve the advection equation. We observed a negligible influence of the use of different types of low viscosity oils as outer fluid on the measurement of the sample relaxation time. We also found that the use of an external low viscosity immiscible oil did not prevent the formation of beads-on-a-string structures.