Viscous and Viscoelastic Fingering Instabilities

The growth of interfacial instabilities gives rise to many complex patterns observed in nature and our daily life. Viscous fingering, created at the fluid-fluid interface when a higher viscosity fluid is displaced by another less viscous fluid, provides a quintessential example of such instabilities and model system for investigating coating instabilities. The instabilities and pattern formation associated with fingering are most well-studied for pairs of Newtonian fluids, where a single parameter, the ratio of viscosity of inner to outer fluid, plays the role of control parameter. However, characterizing fingering instabilities for complex fluids, including polymer solutions, remains a challenge because most complex fluids display flow kinematics and instabilities that are distinct from Newtonian fluids influenced by conjunctional combination of rate-dependent viscosity and elasticity. To decouple these effects, David Boger formulated ‘purely elastic’ fluids by dissolving low amounts of high molecular weight polymer in a relatively high viscosity solvent. As Boger fluids that exhibit rate-independent viscosity, are usually formulated to allow elasticity measurements on torsional rheometer, such fluids are typically too viscous for fingering experiments and emulating coating flows and instabilities. In this dissertation, we used aqueous PEO/PEG and PEO/glycerin Boger fluids as low viscosity, elastic fluids. We characterize distinct influence on fingering onset and growth even though characterizing elasticity using state-of-the-art torsional rheometry is challenging due to elasticity being too low to be measurable, or as it drives elastic instabilities that cause non-viscometric flows. We observe that the PEO-based Boger fluids increase the number of fingers or formed, and influence both onset and growth of instabilities. Here we utilize Dripping-onto-Substrate (DoS) rheometry protocols which rely on the characterization of capillarity-driven pinching dynamics for measurement of relaxation time (elasticity) and extensional viscosity. Thus, we probe and investigate the effects Boger fluids elasticity on fingering instabilities without relying on torsional rheometry for quantifying elastic response evaluation, and also consider effect of extensional rheology response, as streamwise velocity gradients can arise near deforming interface. While the majority of studies using complex fluids focused on the analysis of the critical wavelength or finger width, which describes the pattern selection at the onset, a variety of growth features and length scales that emerge after sufficient time of fingering propagation are usually neglected. Here we carry out a systematic comparison of fingering with viscoelastic and Newtonian fluids as a function of viscosity ratio at the onset and late stages of the instability and characterize the effects of elasticity on the large-scale patterns. We show that dimensionless numbers based on viscoelastic measures obtained using DoS rheometry help in capturing and comparing the influence of viscoelasticity in Hele-Shaw cell flows.