Cross-diffusion-driven gravitational instability in a Hele-Shaw cell saturated with a ternary solution

2016 ◽  
Vol 28 (8) ◽  
pp. 084103 ◽  
Author(s):  
Min Chan Kim ◽  
Kwang Ho Song
Keyword(s):  
Gravitational Instability ◽  
Ternary Solution ◽  
Cross Diffusion ◽  
Hele Shaw Cell

Gravitational instability of miscible fluids in a Hele-Shaw cell and chemical reaction

2001 ◽  
Vol 11 (PR6) ◽  
pp. Pr6-99-Pr6-106
Author(s):  
J. Martin ◽  
N. Rakotomalala ◽  
D. Salin ◽  
M. Böckmann ◽  
S. Müller
Keyword(s):  
Chemical Reaction ◽  
Gravitational Instability ◽  
Miscible Fluids ◽  
Hele Shaw Cell

Gravitational instability due to the dissolution of carbon dioxide in a Hele-Shaw cell

2016 ◽  
Vol 1 (6) ◽  
Author(s):  
A. Vreme ◽  
F. Nadal ◽  
B. Pouligny ◽  
P. Jeandet ◽  
G. Liger-Belair ◽  
...  
Keyword(s):  
Carbon Dioxide ◽  
Gravitational Instability ◽  
Hele Shaw Cell

Gravitational instability of miscible fluids in a Hele-Shaw cell

2002 ◽  
Vol 14 (2) ◽  
pp. 902-905 ◽  
Author(s):  
J. Martin ◽  
N. Rakotomalala ◽  
D. Salin
Keyword(s):  
Gravitational Instability ◽  
Miscible Fluids ◽  
Hele Shaw Cell

A flow-front instability in viscous gravity currents

1998 ◽  
Vol 369 ◽  
pp. 1-21 ◽  
Author(s):  
DON SNYDER ◽  
STEPHEN TAIT
Keyword(s):  
Gravitational Instability ◽  
Gravity Current ◽  
High Viscosity ◽  
Gravity Currents ◽  
Ambient Fluid ◽  
Cell Width ◽  
Dense Fluid ◽  
Unstable Layer ◽  
Gravitational Mechanism ◽  
Hele Shaw Cell

We describe an instability that appears at the front of laminar gravity currents as they intrude into a viscous, miscible ambient fluid. The instability causes a current to segment into fingers aligned with its direction of flow. In the case of currents flowing along a rigid floor into a less dense fluid, the case of primary interest here, two mechanisms can produce this instability. The first is gravitational and arises because the nose of the gravity current is elevated above the floor and overrides a buoyantly unstable layer of ambient liquid. The second is a form of viscous fingering analogous to a Saffman–Taylor instability in a Hele-Shaw cell. Whereas the ambient fluid must be more viscous than the current in order for the latter instability to occur, the gravitational instability can occur even if the ambient fluid is less viscous, as long as it is viscous enough to elevate the nose of the current and trap a layer of ambient fluid. For the gravitational mechanism, which is most important when the current and ambient fluids have comparable viscosities, the wavelength when the instability first appears is proportional to a length scale constructed with the viscosity, the flux and the buoyancy. The Saffman–Taylor-type mechanism is most important when the ambient liquid is much more viscous than the current. We have carried out experiments with miscible fluids in a Hele-Shaw cell that show that, at the onset of instability, the ratio of the finger wavelength to the cell width is a constant approximately equal to 2. This result is explained by using the principle that the flow tends to minimize the dissipation associated with the finger perturbation. For the gravity currents with high viscosity ratios, the ratio of the wavelength to the current thickness is also a constant of about 2, apparently consistent with the same mechanism. But, further analysis of this instability mechanism is required in order to assess its role in wavelength selection for gravity currents.

scholarly journals Phase Separation of an Evaporating Ternary Solution in a Hele-Shaw Cell

Langmuir ◽  
2021 ◽  
Vol 37 (35) ◽  
pp. 10450-10460
Author(s):  
Ricardo Arturo Lopez de la Cruz ◽  
Noor Schilder ◽  
Xuehua Zhang ◽  
Detlef Lohse
Keyword(s):  
Phase Separation ◽  
Ternary Solution ◽  
Hele Shaw Cell

Saturation mechanism and generated viscosity in gravito-turbulent accretion disks

2020 ◽  
Vol 640 ◽  
pp. A53
Author(s):  
L. Löhnert ◽  
S. Krätschmer ◽  
A. G. Peeters
Keyword(s):  
Growth Rate ◽  
Numerical Simulations ◽  
Accretion Disks ◽  
Gravitational Instability ◽  
Turbulent Viscosity ◽  
Radial Distance ◽  
Maximum Growth ◽  
Wave Number ◽  
Radiative Cooling ◽  
Mixing Length

Here, we address the turbulent dynamics of the gravitational instability in accretion disks, retaining both radiative cooling and irradiation. Due to radiative cooling, the disk is unstable for all values of the Toomre parameter, and an accurate estimate of the maximum growth rate is derived analytically. A detailed study of the turbulent spectra shows a rapid decay with an azimuthal wave number stronger than ky−3, whereas the spectrum is more broad in the radial direction and shows a scaling in the range kx−3 to kx−2. The radial component of the radial velocity profile consists of a superposition of shocks of different heights, and is similar to that found in Burgers’ turbulence. Assuming saturation occurs through nonlinear wave steepening leading to shock formation, we developed a mixing-length model in which the typical length scale is related to the average radial distance between shocks. Furthermore, since the numerical simulations show that linear drive is necessary in order to sustain turbulence, we used the growth rate of the most unstable mode to estimate the typical timescale. The mixing-length model that was obtained agrees well with numerical simulations. The model gives an analytic expression for the turbulent viscosity as a function of the Toomre parameter and cooling time. It predicts that relevant values of α = 10−3 can be obtained in disks that have a Toomre parameter as high as Q ≈ 10.

Sign in / Sign up

Export Citation Format

Share Document