We investigate the stability of radial viscous fingering (VF) in miscible fluids. We show that the instability is decided by an interplay between advection and diffusion during initial stages of flow. Using linear stability analysis and nonlinear simulations, we demonstrate that this competition is a function of the radius r0 of the circular region initially occupied by the less viscous fluid in the porous medium. For each r0, we further determine the stability in terms of Péclet number (P e) and log-mobility ratio (M ). The P e − M parameter space is divided into stable and unstable zones-the boundary between the two zones is well approximated by M = α(r0)P e −0.55 . In the unstable zone, the instability is reduced (enhanced) with an increase (decrease) in r0. Thus, a natural control measure for miscible radial VF in terms of r0 is established. Finally, the results are validated by performing experiments which provide a good qualitative agreement with our numerical study. Implications for observations in oil recovery and other fingering instabilities are discussed.

The flow through a Hele–Shaw cell is an experimental prototype to study the flow through a porous medium as well as the flow in microfluidic devices. In context with porous medium flows, it is used to visualize and understand hydrodynamic instabilities like viscous fingering (VF). The gap between the plates of the cell is an important parameter affecting the flow dynamics. However, the effect of the gap on the Hele–Shaw cell flows has been minimally explored. We perform experiments to understand the effect of the gap on VF dynamics. It is observed that a minimum gap is required to observe rigorous fingering instability. The onset time of instability, as well as the width of the fingers, increases with an increment in the gap due to a decrease in the convection. The instability increases with an increase in Péclet number, but the effect of gap width on fingering patterns is evident with broader fingers observed for larger b. The results are validated by performing numerical simulations. It is further shown that the gap-averaged three-dimensional simulations using the Stokes law approach and the two-dimensional Darcy’s law result in a small gap Hele–Shaw cell.

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We present an experimental investigation of the rheological aspects of collective motion by the swimming Turbatrix aceti nematodes. We discover that these nematodes can signifi- cantly change the rheological properties of the suspension due to their body oscillations and form synchronized waves, which produce strong fluid flows. The strength of the collective state changes the shape of the interface where they swim in synchronization. We unravel that the effective viscosity of the nematode suspension at higher shear rates shows steady viscous behavior with time, where no significant effect of nematode activity is observed. For the first time, we have reported that at low shear rates, the activity effect is significant enough to generate oscillating viscous effects. In addition, we also measured the influence of nematode concentration on suspension viscosity. This work opens a new way for un- derstanding the rheological aspects of active matter under low and high shear rates. We illustrate these dynamics by showing that the force generated by these nematodes is suf- ficient to change the suspension rheology. The various aspects of nematodes, especially their large size and ease of culturing, make them a good model organism for experimental investigation as active fibers with oscillations. The oscillating behavior regulates the inter- facial phenomenon and produces oscillatory rheological dynamics at low shear rates. The results of our work can be utilized to further study the novel metamaterials with negative viscosity which have applications in healthcare and energy systems.