Abstract
| Original language | English |
|---|---|
| Pages (from-to) | 564-577 |
| Number of pages | 14 |
| Journal | European Journal of Mechanics - B/Fluids |
| Volume | 28 |
| Issue number | 4 |
| Early online date | 5 Feb 2009 |
| DOIs | |
| Publication status | Published - Aug 2009 |
Fingerprint
Keywords
- viscous fingering
- instability
- viscosity
- Hele-Shaw cell
Cite this
}
The linear stability of double-diffusive miscible rectilinear displacements in a Hele-Shaw cell. / Pritchard, D.
In: European Journal of Mechanics - B/Fluids, Vol. 28, No. 4, 08.2009, p. 564-577.Research output: Contribution to journal › Article
TY - JOUR
T1 - The linear stability of double-diffusive miscible rectilinear displacements in a Hele-Shaw cell
AU - Pritchard, D.
PY - 2009/8
Y1 - 2009/8
N2 - We investigate the viscous instability of a miscible displacement process in a recti-linear geometry, when the viscosity contrast is controlled by two quantities whichdiuse at dierent rates. The analysis is applicable to displacement in a porousmedium with two dissolved species, or to displacement in a Hele-Shaw cell with twodissolved species or with one dissolved species and a thermal contrast. We carry outasymptotic analyses of the linear stability behaviour in two regimes: that of smallwavenumbers at intermediate times, and that of large times.An interesting feature of the large-time results is the existence of regimes in whichthe favoured wavenumber scales with t−1/4, as opposed to the t−3/8 scaling foundin other regimes including that of single-species ngering. We also show that theregion of parameter space in which the displacement is unstable grows with time,and that although overdamped growing perturbations are possible, these are neverthe fastest-growing perturbations so are unlikely to be observed. We also interpretour results physically in terms of the stabilising and destabilising mechanisms actingon an incipient nger.
AB - We investigate the viscous instability of a miscible displacement process in a recti-linear geometry, when the viscosity contrast is controlled by two quantities whichdiuse at dierent rates. The analysis is applicable to displacement in a porousmedium with two dissolved species, or to displacement in a Hele-Shaw cell with twodissolved species or with one dissolved species and a thermal contrast. We carry outasymptotic analyses of the linear stability behaviour in two regimes: that of smallwavenumbers at intermediate times, and that of large times.An interesting feature of the large-time results is the existence of regimes in whichthe favoured wavenumber scales with t−1/4, as opposed to the t−3/8 scaling foundin other regimes including that of single-species ngering. We also show that theregion of parameter space in which the displacement is unstable grows with time,and that although overdamped growing perturbations are possible, these are neverthe fastest-growing perturbations so are unlikely to be observed. We also interpretour results physically in terms of the stabilising and destabilising mechanisms actingon an incipient nger.
KW - viscous fingering
KW - instability
KW - viscosity
KW - Hele-Shaw cell
U2 - 10.1016/j.euromechflu.2009.01.004
DO - 10.1016/j.euromechflu.2009.01.004
M3 - Article
VL - 28
SP - 564
EP - 577
JO - European Journal of Mechanics - B/Fluids
JF - European Journal of Mechanics - B/Fluids
SN - 0997-7546
IS - 4
ER -