Numerical simulations of miscible fluids on a rotating Hele-Shaw cell with effects of Coriolis forces

2005 ◽  
Vol 48 (8) ◽  
pp. 853-867 ◽  
Author(s):  
Ching-Yao Chen ◽  
Yu-Chia Liu
Keyword(s):  
Numerical Simulations ◽  
Miscible Fluids ◽  
Coriolis Forces ◽  
Hele Shaw Cell

Magnetic instability between miscible fluids in a Hele--Shaw cell

2008 ◽  
Vol 44 (2) ◽  
pp. 135-142 ◽  
Author(s):  
C. Derec ◽  
P. Boltenhagen ◽  
S. Neveu ◽  
J.-C. Bacri
Keyword(s):  
Miscible Fluids ◽  
Magnetic Instability ◽  
Hele Shaw Cell

Density-driven unstable flows of miscible fluids in a Hele-Shaw cell

2002 ◽  
Vol 451 ◽  
pp. 239-260 ◽  
Author(s):  
J. FERNANDEZ ◽  
P. KUROWSKI ◽  
P. PETITJEANS ◽  
E. MEIBURG
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Brinkman Equation ◽  
Length Scale ◽  
Dominant Wavelength ◽  
Miscible Fluids ◽  
Nonlinear Simulations ◽  
Instability Growth ◽  
Gap Width ◽  
Hele Shaw Cell

Density-driven instabilities between miscible fluids in a vertical Hele-Shaw cell are investigated by means of experimental measurements, as well as two- and three-dimensional numerical simulations. The experiments focus on the early stages of the instability growth, and they provide detailed information regarding the growth rates and most amplified wavenumbers as a function of the governing Rayleigh number Ra. They identify two clearly distinct parameter regimes: a low-Ra, ‘Hele-Shaw’ regime in which the dominant wavelength scales as Ra−1, and a high-Ra ‘gap’ regime in which the length scale of the instability is 5±1 times the gap width. The experiments are compared to a recent linear stability analysis based on the Brinkman equation. The analytical dispersion relationship for a step-like density profile reproduces the experimentally observed trend across the entire Ra range. Nonlinear simulations based on the two- and three-dimensional Stokes equations indicate that the high-Ra regime is characterized by an instability across the gap, wheras in the low-Ra regime a spanwise Hele-Shaw mode dominates.

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

Numerical simulations of a viscous-fingering instability in a fluid with a temperature-dependent viscosity

2006 ◽  
Vol 84 (4) ◽  
pp. 273-287 ◽  
Author(s):  
Kristi E Holloway ◽  
John R Bruyn
Keyword(s):  
Growth Rate ◽  
Numerical Simulations ◽  
Viscosity Ratio ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Cell Width ◽  
Inlet Velocity ◽  
Fingering Instability ◽  
Dependent Viscosity ◽  
Hele Shaw Cell

We have performed numerical simulations of the flow of hot glycerine as it displaces colder, more viscous glycerine in a radial Hele–Shaw cell. We find that fingering occurs for sufficiently high inlet velocities and viscosity ratios. The wavelength of the instability is independent of inlet velocity and viscosity ratio, but depends weakly on cell width. The growth rate of the fingers is found to increase with inlet velocity and decrease with the cell width. We compare our results with those from experiments.PACS No.: 47.54.–r

Numerical simulations of sink flow in the Hele-Shaw cell with small surface tension

1997 ◽  
Vol 8 (6) ◽  
pp. 533-550 ◽  
Author(s):  
E. D. KELLY ◽  
E. J. HINCH
Keyword(s):  
Surface Tension ◽  
Integral Equation ◽  
Viscous Fluid ◽  
Numerical Simulations ◽  
Boundary Integral Equation ◽  
Numerical Algorithm ◽  
Boundary Integral ◽  
Inviscid Fluid ◽  
Small Surface ◽  
Hele Shaw Cell

The motion of an initially circular drop of viscous fluid surrounded by inviscid fluid in a Hele-Shaw cell withdrawn from an eccentric point sink is considered. Using a numerical algorithm based on a boundary integral equation, the solution for small, finite surface tension is observed. It is found that the zero-surface-tension formation of a cusp is avoided, and instead a narrow finger of inviscid fluid forms, which then rapidly propagates towards the sink. The scaling of the finger in the sink vicinity is determined.

Sign in / Sign up

Export Citation Format

Share Document