<abstract xmlns="http://www.w3.org/1999/xhtml"><p> We study the linear stability of the immiscible displacement of some fluids in 2D and 3D Hele-Shaw cell. We give a method for avoiding the singularities phenomenons which appears in previous papers. In the case of a non - Newtonian fluid displaced by air in a 3D Hele-Shaw cell, we give a growth constant σ of perturbations, which contains two new terms compared with the Saffman-Taylor formula. Our σ has a very high growth as a parameter appearing in the constitutive relations approaches a critical value.</p></abstract>

We study the linear stability of the immiscible displacement of some fluids in 2D and 3D Hele-Shaw cell. We give a method for avoiding the singularities phenomenons which appears in previous papers. In the case of a non - Newtonian fluid displaced by air in a 3D Hele-Shaw cell, we give a growth constant σ of perturbations, which contains two new terms compared with the Saffman-Taylor formula. Our σ has a very high growth as a parameter appearing in the constitutive relations approaches a critical value.

Some models for immiscible displacements in Hele-Shaw cells

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Some models for immiscible displacements in Hele-Shaw cells"}

We study the linear stability of the immiscible displacement of some fluids in 2D and 3D Hele-Shaw cell. We give a method for avoiding the singularities...

Some models for immiscible displacements in Hele-Shaw cells

Published Online: Nov 22, 2018

Page range: 193 - 207

Received: Dec 01, 2016

Accepted: Jun 01, 2017

DOI: https://doi.org/10.2478/auom-2018-0025

Keywords
Hele-Shaw displacement, non-Newtonian uids, linear stability, dispersion formula

© 2018 Gelu Paşa, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Some models for immiscible displacements in Hele-Shaw cells

Published Online: Nov 22, 2018

Page range: 193 - 207

Received: Dec 01, 2016

Accepted: Jun 01, 2017

DOI: https://doi.org/10.2478/auom-2018-0025

KeywordsHele-Shaw displacement, non-Newtonian uids, linear stability, dispersion formula

© 2018 Gelu Paşa, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Hele-Shaw displacement, non-Newtonian uids, linear stability, dispersion formula