We review recent results on dynamical aspects of viscous fingering. The Saffman–Taylor
instability is studied beyond linear stability analysis by means of a weakly nonlinear analysis …

We present a theoretical study of a variant of the classical viscous fingering instability, which
occurs when a high viscosity fluid is displaced by a low viscosity fluid in a Hele-Shaw cell. In …

We propose a continuum model of two-phase flow in a Hele-Shaw cell. The model describes
the multiphase three-dimensional flow in the cell gap using gap-averaged quantities such as …

When two fluids of different densities move in a rotating Hele-Shaw cell, the interface
between them becomes centrifugally unstable and deforms. Depending on the viscosity …

A ferrofluid droplet confined in a Hele-Shaw cell can be deformed into a stably spinning
“gear,” using crossed magnetic fields. Previously, fully nonlinear simulation revealed that the …

The different finger morphologies that arise at the interface separating two immiscible fluids
in a rotating Hele-Shaw cell are studied numerically. The whole range of viscosity contrast is …

We examine the formation of interfacial patterns when a magnetic liquid droplet (ferrofluid, or
a magnetorheological fluid), surrounded by a nonmagnetic fluid, is subjected to a radial …

Two-dimensional free surface flows in Hele-Shaw configurations are a fertile ground for
exploring nonlinear physics. Since Saffman and Taylor's work on linear instability of fluid …

Using air to displace a viscous fluid contained in a Hele-Shaw cell can create a fingering
pattern at the interface between the fluids if the capillary number exceeds a critical value …

The experimental evidence reveals that sessile drops on a dielectric horizontal substrate
subjected to sub-critical in-plane electric field acquire steady-state configurations where a …