Sreeram K. Kalpathy | Searcharxiv

arXiv2020

Side branched patterns, coalescence and stable interfaces during radial displacement of a viscoelastic fluid

We explore the interfacial instability that results when a Newtonian fluid (a glycerol-water mixture, inner fluid) displaces a viscoelastic fluid (a dense cornstarch suspension, outer fluid) in a radial Hele-Shaw cell. As the ratio of viscosities of the inner and outer fluids is increased, side branched interfacial patterns are replaced by more stable interfaces that display proportionate growth and finger coalescence. We correlate the average finger spacing with the most dominant wavelength of interfacial instability, computed using a mathematical model that accounts for viscous fingering in miscible Hele-Shaw displacements. The model predictions on the role of viscosity ratio on finger spacing are in close agreement with the experimental observations. Our study lends insight into the significant contribution of the viscoelasticity of the outer fluid on the morphology and growth of interfacial patterns.

cond-mat.soft↗

arXiv2019

On the role of variable surface viscosity in free viscous films

The stability of a thin liquid film bounded by two free surfaces is examined in the presence of insoluble surface active agents. The surface active agents not only cause gradients in surface tension, but could also render surface viscosity to be significant, and variable, as a function of their concentration. A set of three coupled nonlinear evolution equations are derived for the film height, concentration of surface active agents, and the horizontal liquid velocity which governs the dynamics of the free film. Suitable phenomenological models for variation of surface tension and surface viscosity with the concentration of surface active agents are incorporated in the interfacial stress boundary condition. Linear stability analysis reveals the effect of various non-dimensional parameters, specifically the retarding nature of surface viscosity and Marangoni effects on film rupture. An analysis of the `jamming' limit of surfactant concentration reveals that $Γ_0^{(nl)}<3 \mathbb{D}/M$ is a sufficient criteria for instability of the system, where $Γ_0^{(nl)}$ is a normalized initial surface particle concentration, $\mathbb{D}$ is the disjoining pressure number and $\textit{M}$ is the Marangoni number. Nonlinear simulations suggest film profiles at rupture are also qualitatively different from those reported in earlier studies, revealing that free films in the jamming limit are remarkably stable and their free surfaces behave like immobile interfaces. Furthermore, self-similar exponents extracted from our nonlinear simulations are used to explain topological differences between zero and constant surface viscosity in the vicinity of rupture.

physics.flu-dyn↗