Abstract:
Phase separation is important in biology, biochemistry, industry, and other areas and is divided into two
types: a spinodal decomposition type and a nucleation and growth type. The spinodal decomposition
type phase separation occurs under the thermodynamically unstable conditions, and the nucleation and
growth type phase separation occurs under thermodynamically metastable conditions. On the other
hand, when a less viscous fluid displaces a more viscous one in porous media, the interface of the two
fluids becomes hydrodynamically unstable and forms a finger-like pattern. The coupling of the
hydrodynamic instability with the thermodynamic instability has been studied. It is reported that the
hydrodynamic instability under thermodynamically unstable conditions, where spinodal decomposition
type phase separation occurs, creates multiple moving droplets with a radius of 3–4 mm because of the
spontaneous convection induced by the Korteweg force, which is driven by a compositional gradient
during phase separation. However, the hydrodynamic instability under metastable conditions, where
the phase separation of nucleation and growth type occurs, is still unrevealed. In this study, we applied
fingering instability (hydrodynamic instability) under the metastable conditions, where the patterns
are changed from fingering or droplets to anomalous patterns such as tip-widening or needle-like (toppointed)
fingering patterns when the initial concentration is metastable, which is considered near
a binodal curve. These patterns are ubiquitous in nature, similar to dendrite crystals (snowflakes) or our
body’s cells. Thus, the patterns created can be controlled through hydrodynamic conditions such as the
injection flow and thermodynamic conditions such as spinodal decomposition (thermodynamically
unstable conditions) and metastable conditions.
