arXiv subjects

Gelu Paşa

Publications and source records attributed to Gelu Paşa.

5 recordsLinked to original sources

arXiv2022

Unbounded eigenfunctions in the stability problem for a three-layer flow in porous media

We study the linear stability of the displacement of three Stokes fluids with constant viscosity in a porous medium when the middle fluid is contained in a bounded region. We use the Hele-Shaw model. The eigenfunctions of the stability system are the amplitudes of the linear perturbations. These amplitudes must be small. We get unbounded eigenfunctions. So the stability problem has no physical sense.

math.AP↗

arXiv2021

A non-existence result due to small perturbations in an eigenvalue problem

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 intervals and approximate the function $m$ by a simple (step) function $m_S$, constant on each small interval. The eigenfunctions corresponding to $m_S$ do not exist.

math.GM↗

arXiv2019

On the strong instability of the multi-layer Hele-Shaw flows

We study the effects of some injection policies used in oil recovery process. The Saffman-Taylor instability occurs when a less viscous fluid is displacing a more viscous one, in a rectangular Hele-Shaw cell. The injection of $N$ successive intermediate phases with constant viscosities (the multi-layer Hele-Shaw model) was studied in some recent papers, where a minimization of the Saffman-Taylor instability was obtained for large enough $N$. However, in this paper we get a particular eigenfunction of the linear stability system which leads to eigenvalues which become infinite for large wave numbers. We obtain a strong instability of the multi-layer Hele-Shaw displacement, even if $N$ is very large.

physics.flu-dyn↗

arXiv2019

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

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 maximum value of growth constants can not decrease under a certain value, not depending on the surface tensions on the interfaces. This contradiction with the Saffman-Taylor result makes us have some doubts concerning the correctness of multi-layer model.

physics.flu-dyn↗

arXiv2018

A paradox in Hele-Shaw displacements

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 numbers of perturbations. The same amount of intermediate liquid is used in both cases.

physics.flu-dyn↗