Abstract
We present a nonlinear unsteady Darcy's equation which includes inertial effects for flows in a porous medium or Hele-Shaw cell and discuss the conditions under which it reduces to the classical Darcy's law. In the absence of surface tension we derive a generalized Polubarinova-Galin equation in a circular geometry, using the method of conformal mapping. The linear stability of the base-flow state is examined by perturbing the corresponding conformal map. We show that inertia always has a tendency to stabilize the interface, regardless of whether a less viscous fluid is displacing a more viscous fluid or vice versa.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 436-445 |
| Number of pages | 10 |
| Journal | Journal of Fluid Mechanics |
| Volume | 668 |
| DOIs | |
| State | Published - Feb 10 2011 |
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All Science Journal Classification (ASJC) codes
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
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Inertial effects on viscous fingering in the complex plane. / He, Andong; Belmonte, Andrew.
In: Journal of Fluid Mechanics, Vol. 668, 10.02.2011, p. 436-445.Research output: Contribution to journal › Article
TY - JOUR
T1 - Inertial effects on viscous fingering in the complex plane
AU - He, Andong
AU - Belmonte, Andrew
PY - 2011/2/10
Y1 - 2011/2/10
N2 - We present a nonlinear unsteady Darcy's equation which includes inertial effects for flows in a porous medium or Hele-Shaw cell and discuss the conditions under which it reduces to the classical Darcy's law. In the absence of surface tension we derive a generalized Polubarinova-Galin equation in a circular geometry, using the method of conformal mapping. The linear stability of the base-flow state is examined by perturbing the corresponding conformal map. We show that inertia always has a tendency to stabilize the interface, regardless of whether a less viscous fluid is displacing a more viscous fluid or vice versa.
AB - We present a nonlinear unsteady Darcy's equation which includes inertial effects for flows in a porous medium or Hele-Shaw cell and discuss the conditions under which it reduces to the classical Darcy's law. In the absence of surface tension we derive a generalized Polubarinova-Galin equation in a circular geometry, using the method of conformal mapping. The linear stability of the base-flow state is examined by perturbing the corresponding conformal map. We show that inertia always has a tendency to stabilize the interface, regardless of whether a less viscous fluid is displacing a more viscous fluid or vice versa.
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U2 - 10.1017/S0022112010005859
DO - 10.1017/S0022112010005859
M3 - Article
VL - 668
SP - 436
EP - 445
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
SN - 0022-1120
ER -