arXiv subjects

Radha Ramachandran

Publications and source records attributed to Radha Ramachandran.

3 recordsLinked to original sources

arXiv2017

Stability and onset of two-dimensional viscous fingering in immiscible fluids

Viscous flows in a quasi-two-dimensional Hele-Shaw geometry can lead to an interfacial instability when one fluid, of viscosity $η_{in}$ displaces another of higher viscosity, $η_{out}$. Recent studies have shown that there is a delay in the onset of fingering in miscible fluids as the viscosity ratio, $η_{in}/η_{out}$, increases and approaches unity; the interface can remain stable even though the displacing liquid is less viscous. This paper shows that a delayed onset and stable pattern can occur in immiscible fluids as well. However, there are two significant differences between the two cases. First, in miscible fluids, stable patterns are obtained whenever $η_{in}/η_{out} > 0.33$ while in immiscible fluids, the radius at which the onset of fingering starts, $R_{onset}$, increases steadily until $η_{in}/η_{out}=1$. A stable pattern is obtained only when the total size of the plate used is smaller than $R_{onset}$. Second, once the delayed fingering starts in immiscible fluids, the fingers grow faster than the central circular region. In miscible fluids, there is a regime in which the fingers and the central region grow in proportion to each other. These differences between miscible and immiscible fingering are maintained even when we compare immiscible fluids that have very low interfacial tension with miscible fluids that have negligible diffusion.

cond-mat.soft↗

arXiv2015

An island of stability in a sea of fingers: emergent large-scale features of the viscous flow instability

The displacement of a more viscous fluid by a less viscous one in a quasi-two dimensional geometry leads to the formation of complex fingering patterns. This fingering has been characterized by a most unstable wavelength, $λ_c$, which depends on the viscosity difference between the two immiscible fluids and sets the characteristic width of the fingers. How the finger length grows after the instability occurs is an equally important, but previously overlooked, aspect that characterizes the global features of the patterns. As the lower viscosity fluid is injected, we show that there is a stable inner region where the outer fluid is completely displaced. The ratio of the finger length to the radius of this stable region depends only on the viscosity ratio of the fluids and is decoupled from $λ_c$.

physics.flu-dyn↗

arXiv2014

Fingering versus stability in the limit of zero interfacial tension

The invasion of one fluid into another of higher viscosity in a quasi-two dimensional geometry typically produces complex fingering patterns. Because interfacial tension suppresses short-wavelength fluctuations, its elimination by using pairs of miscible fluids would suggest an instability producing highly ramified singular structures. Previous studies focused on wavelength selection at the instability onset and overlooked the striking features appearing more globally. Here we investigate the non-linear growth that occurs after the instability has been fully established. We find a rich variety of patterns that are characterized by the viscosity ratio between the inner and the outer fluid, $η_{in}$/$η_{out}$, as distinct from the most-unstable wavelength, which determines the onset of the instability. As $η_{in}$/$η_{out}$ increases, a regime dominated by long highly-branched fractal fingers gives way to one dominated by blunt stable structures characteristic of proportionate growth. Simultaneously, a central region of complete outer-fluid displacement grows until it encompasses the entire pattern at $η_{in}$/$η_{out}$$\approx$0.3.

physics.flu-dyn↗