# A strong contradiction in the multi-layer Hele-Shaw model

@inproceedings{Pacsa2019ASC, title={A strong contradiction in the multi-layer Hele-Shaw model}, author={Gelu Pacsa}, year={2019} }

The Saffman-Taylor instability occurs when a less viscous fluid is displacing a more viscous one in a rectangular Hele-Shaw cell. A surface tension on the interface between the two fluids is improving the stability. The multi-layer Hele Shaw model, consisting of N intermediate fluids with constant viscosities, was studied in some previous papers and very low growth constants were obtained for large N . We prove that this model leads us to a significant instability, even if N is very large. The…

## References

SHOWING 1-10 OF 31 REFERENCES

### Hydrodynamic stability of multi-layer Hele-Shaw flows

- Engineering
- 2008

Upper bound results on the growth rate of unstable multi-layer Hele-Shaw flows are obtained in this paper. The cases treated are constant viscosity layers and variable viscosity layers. As an…

### Evolution of Hele-Shaw interface for small surface tension

- MathematicsPhilosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences
- 1993

We consider the time-evolving displacement of a viscous fluid by another fluid of negligible viscosity in a Hele-Shaw cell, either in a channel or a radial geometry, for idealized boundary conditions…

### Viscous fingering in Hele-Shaw cells

- EngineeringJournal of Fluid Mechanics
- 1986

The phenomenon of interfacial motion between two immiscible viscous fluids in the narrow gap between two parallel plates (Hele-Shaw cell) is considered. This flow is currently of interest because of…

### Universal Stability Properties for Multilayer Hele-Shaw Flows and Application to Instability Control

- MathematicsSIAM J. Appl. Math.
- 2012

Stability results obtained for an arbitrary number of displacing fluids in succession reduce to the Saffman--Taylor case when there is only one displacing fluid, which is likely to improve oil recovery.

### Variable density and viscosity, miscible displacements in horizontal Hele-Shaw cells. Part 1. Linear stability analysis

- PhysicsJournal of Fluid Mechanics
- 2013

Abstract A computational investigation of variable density and viscosity, miscible displacements in horizontal Hele-Shaw cells is presented. As a first step, two-dimensional base states are obtained…

### A simple derivation of an upper bound in the presence of a viscosity gradient in three-layer Hele-Shaw flows

- Mathematics
- 2006

An upper bound on the growth rate of disturbances in three-layer Hele-Shaw flows with the middle layer having a smooth viscous profile is obtained using a weak formulation of the disturbance…

### A theory for the most stable variable viscosity profile in graded mobility displacement processes

- Mathematics
- 1981

The stability of the displacement of a viscous fluid in a porous medium by a less viscous fluid containing an additive is considered. For the case in which the total amount of injected additive is…

### VISCOUS FINGERING IN POROUS MEDIA

- Physics
- 2002

"Viscous fingering" generally refers to the onset and evolution of insta bilities that occur in the displacement of fluids in porous materials. In most but not all cases, the mechanism of the…

### A Theory of the Optimal Policy of Oil Recovery by Secondary Displacement Processes

- Mathematics
- 1983

We consider the stability of the displacement of a viscous fluid in a porous medium by a less viscous fluid containing a solute. For the case in which the total amount of injected solute is fixed, we…