Employees of the Department of Technical Physics of the Ural Federal University have thoroughly investigated the motion and shape of the boundary between liquids when one displaces the other under pressure. The work of the group of Professor Leonid Martyushev (and co-authors Roman Bando and Evgenia Chervontseva) has not only theoretical, but also important practical significance.
The article titled Instability of the fluid interface at arbitrary perturbation amplitudes. Displacement in the Hele–Shaw cell was published in the international journal Physica A: Statistical Mechanics and its Applications, dedicated to the study of nonequilibrium structures and processes.
“When oil wells are depleted, water is pumped there under pressure to force the residual oil to the surface. If the boundary between water and oil were an even layer, then it would be safe to say that as a result of water injection we recover all the residual oil. But since the interface between the two liquids is a highly distorted section, oil, contrary to expectations, can still remain underground, while water comes out to the surface. This is where our calculations come in handy. In addition, they can be used for environmental safety purposes, to eliminate the spills of hazardous substances, ”explains the professor of the department Leonid Martyushev.
Having carried out extensive numerical hydrodynamic calculations for various geometries and parameters, physicists of the Ural Federal University have constructed diagrams of stable / unstable behavior of the interface between liquids. With their help, you can predict the behavior of fluids in various environments. So, in the calculations, the researchers for the first time found that with close values of the viscosity of the displacing and displaced fluids, a large number of different forms of boundaries can coexist at the same pressure. Determining the motion and shape of the boundary between fluids is a very old and complex hydrodynamic problem. At first, the boundary between the displacing and displaced immiscible liquids is quite simple, but from a certain moment it becomes unstable.
“First, the so-called ‘fingers’ appear, which then, as a result of complex transformations, turn into a branched structure resembling the crown of a tree. Physicists have long been able to calculate the loss of stability of the interface between fluids in the presence of very small perturbations. But until now it was not clear how to make predictions under arbitrary influences. But this is the most important for most practical applications, ”the scientist adds.
The results obtained in this work are very important both for explaining the experimental data on displacement in the Hele–Shaw cell and for the development of a new theoretical method for the analysis of morphological stability based on MEPP. The data obtained are in good agreement with the theoretical predictions that Leonid Martyushev made about 15 years ago. His assumption is based on the principle of maximum entropy production, which states that in any non-equilibrium system, the measure of chaos increases as fast as possible.
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