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Elastic Waves in Helium Saturated Porous Media


Elastic Waves in a Superfluid Helium-Saturated Porous Media

Tech Area / Field

  • PHY-SSP/Solid State Physics/Physics

3 Approved without Funding

Registration date

Leading Institute
Institute of Cybernetics, Georgia, Tbilisi

Supporting institutes

  • Tbilisi State University / Institute of Physics (Ge), Georgia, Tbilisi

Project summary

Flow phenomena in porous media are important to a wide variety of problems and have been studied theoretically and experimentally for a long time. Such problems as oil extraction from underground reservoirs, drainage and imbibition in soil, mercury porosimetry in a porous catalyst for determining its pore-size distribution and other processes connected with environment are all in this class of phenomena. Actuality of study of processes, which occur in the porous media, is enhanced because of special properties of superfluid helium that fills porous media. Two types of motion are known to exist in superfluid helium, corresponding to the normal and superfluid components. The existence of these two motions (superfluid and normal) produces distinctive wave processes in liquid HeII. The propagation of two undamped sound waves is possible in an unbounded volume filled with liquid HeII. The first wave, which is called first sound, is characterized by the fact that its normal and superfluid components oscillate in phase. In the propagation of the second wave, or second sound the superfluid and normal fluid components oscillate oppositely to one another. Moreover, transverse waves exist in connection with motion of only the normal component and are called viscous waves. They occur at the walls of a vessel filled with HeII and are of the same nature as viscous waves in an ordinary fluid. However, because of the special properties of superfluid helium, wave processes can take place not only in large vessels, but also in very narrow channels, whose width is much smaller than the viscous-wave penetration depth. In this case fourth sound propagates through the superfluid component and the experimental observation of the second sound (thermal wave) in plane-parallel geometry formed by two glass plates under this conditions has been reported.

Usually the propagation of waves has been studied under no-slip conditions for the normal component and diffuse scattering of the excitations. However, instead of totally “sticking” to the surface (no-slip), the quasi-particles maintain a certain finite, albeit small velocity relative to the surface. In future we shall investigate the propagation of waves in porous media filled with superfluid helium, when the interaction of the normal component with the walls is taken into account by the slip boundary condition for the velocity of normal motion.

In a series of papers, Biot proposed a simple phenomenological theory of elastic and viscous behavior in porous, macroscopically homogeneous, and isotropic, elastic media saturated with a compressible viscous fluid. Because the motion of the solid and fluid parts are followed separately and on equal footing, this theory represents the most general theory possible for two-component porous solid/fluid systems. The theory takes into account the motion of the fluid in the interconnected voids of a porous solid and predicts the existence of two types of bulk compressional waves and a single shear wave. One bulk compressional wave is the standard classical compressional wave whose phase velocity is almost independent of frequency at low frequencies. The other bulk compressional wave is slow and it propagates in the manner of a diffusion wave at low frequency. The phase velocity of latter wave approaches zero at the zero-frequency limit, and it is highly dispersive and attenuated at low frequencies. As the frequency increases, the slow compressional wave takes on the character of a propagating wave. Our aim is to generalize Biot's results in case the porous media is saturated with liquid HeII. So our project will study the theory for three-component pore solid-superfluid systems.

Early investigations were carried out in conditions of restricted geometry or in a porous media to study properties of superfluid helium. We propose to turn this situation around and use the superfluid as a probe of the transport properties of porous media as much number of different types of waves can propagate in the superfluid helium. This approach is justified, as rich and valuable information on the properties of superfluid-saturation porous media can be obtained from the analysis of oscillations propagating in it.

According to the above mentioned the purpose and objective of the project include: The development of the theory of propagation of stress waves in a porous elastic solid containing superfluid helium and estimation of effective permeability and tortuosity and their connection with structure of porous media; also utilization ultrasonic and low frequency acoustic techniques for studying the interactions of sound waves with superfluid-filled porous media and for understanding the effects of pore structure and eventually to use such measurement to predict properties such as permeability which are important in many applications.

The majority of scientists involved in the project are the highly qualified specialists in the fields of solid state physics, low and ultralow temperature physics.

The realization of the project will make it possible to support financially the continuation of basic researches in the field of solid state and low temperatures physics, which have been traditionally carrying out on a high level in the Institute of Cybernetics and in the Institute of Physics. Five scientists earlier involved in the weapon activity will participate in the project.

The foreign scientists involving in the project as collaborators are foreseen. It will promote the international scientific contacts. The exchange by information with the collaborators about the course of project fulfillment, joint discussions of the obtained results and a joint use of the unique installations is foreseen. Foreign Scientists will present comments on the reports being sent to ISTC.


The International Science and Technology Center (ISTC) is an intergovernmental organization connecting scientists from Kazakhstan, Armenia, Tajikistan, Kyrgyzstan, and Georgia with their peers and research organizations in the EU, Japan, Republic of Korea, Norway and the United States.


ISTC facilitates international science projects and assists the global scientific and business community to source and engage with CIS and Georgian institutes that develop or possess an excellence of scientific know-how.

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