# A paradox in Hele-Shaw displacements

@article{Pacsa2020API, title={A paradox in Hele-Shaw displacements}, author={Gelu Pacsa}, journal={ANNALI DELL'UNIVERSITA' DI FERRARA}, year={2020} }

We study the Hele-Shaw immiscible displacements when all surfaces tensions on the interfaces are zero. The Saffman-Taylor instability occurs when a less viscous fluid is displacing a more viscous one, in a rectangular Hele-Shaw cell. We prove that an intermediate liquid with a variable viscosity can almost suppress this instability. On the contrary, a large number of constant viscosity liquid-layers inserted between the initial fluids gives us boundless growth rates with respect to the wave…

## 4 Citations

### THREE-LAYER HELE-SHAW DISPLACEMENT WITH AN INTERMEDIATE NON-NEWTONIAN FLUID

- PhysicsInternational Journal of Apllied Mathematics
- 2021

: We study the displacement of two Stokes immiscible ﬂuids in a porous medium, approximated by the Hele-Shaw horizontal model. An intermediate non-Newtonian polymer-solute, whose viscosity is…

### An ill-posed problem in hydrodynamic stability of multi-layer Hele-Shaw flow

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- 2020

An useful approximation for the displacement of two immiscible fluids in a porous medium is the Hele-Shaw model. We consider several liquids with different constant viscosities, inserted between the…

### On the Linear Stability Problem for a Three-Layer Displacement in a Porous Media

- MathematicsInternational Journal of Petroleum Technology
- 2022

In this paper, we study the secondary oil recovery process. The oil from a porous reservoir at low pressure is pushed by a forerunner, less viscous fluid (a polymer solute). Then the well-known…

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We consider a well-posed eigenvalue problem on (a, 0), depending on a continuous function m. The boundary conditions in the points a, 0 are depending on the eigenvalues. We divide (a, 0) into small…

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