Nikoloz Chkhaidze

A theory of the propagation of acoustic waves in a porous medium filled with superfluid helium is developed. The elastic coefficients in the system of equations are expressed in terms of physically measurable quantities. The equations obtained describe all volume modes which propagate in a porous medium saturated with superfluid helium. The propagation velocities of longitudinal and transverse waves are calculated in the limit of high and low oscillation frequencies of the thermodynamic quantities.

A theory of the propagation of acoustic waves in a porous medium filled with superfluid 3He–4He solution is developed. The elastic coefficients in the system of equations are expressed in terms of physically measurable quantities. The equations obtained describe all volume modes that can propagate in a porous medium saturated with superfluid 3He–4He solution. Finally, derived equations are applied to the most important particular cases when the normal fluid component is locked inside a highly porous medium (aerogel) by viscous forces. The velocities of two longitudinal sound and transverse modes are calculated.

The dynamical equations are obtained for a system comprising a porous material and a 3He– 4He superfluid mixture. The elastic coefficients that appear in the equations are expressed in terms of physically measurable quantities. The equations obtained describe all of the bulk modes that propagate in a porous medium filled with a 3He– 4He superfluid mixture. The propagation of acoustic modes is investigated for an aerogel filled with a 3He– 4He superfluid mixture. The velocities of the longitudinal modes propagating in that system are calculated, and the relations between oscillatory quantities are established.

The dynamical equations for superfluid 3He–A filled aerogel in finite magnetic fields are determined. The speeds of propagating longitudinal modes in the A1 and A phases of this system are found. It is shown that sound phenomena in the case of 3He–A1 superfluid are modified from those for He II superfluid.

The velocity of fast and slow collective modes of 90, 94, and 98% porosity aerogels filled with superfluid helium are measured by a low-frequency resonant technique at temperatures 0.5–2.5 K. The temperature dependences of the velocities of the two modes are compared with the hydrodynamic theory modified to take into account the mobility of the aerogel matrix, porosity of the media, and tortuosity of the acoustic path. It is found that the fast and slow modes in an aerogel are coupled much more strongly than the first and second sounds in bulk He II.

The velocities of fast and slow collective modes of superfluid He II in 90%, 94% and 98% porosity aerogels were measured by means of low-frequency resonant technique using piezoelectric transducers. The measured temperature dependences of velocities of both modes are compared with the theory based on approach of Biot (J. Acoust. Soc. Am. 28:168, 1956; J. Acoust. Soc. Am. 28:179, 1956) for porous medium filled with superfluid helium with taking into account of tortuosity of an acoustic way and porosity (Kekutia and Chkhaidze in Fiz. Nizk. Temp. 28:1115, 2002). The coefficients of tortuosity are obtained for the aerogel samples studied. Evolution of the fast and slow modes with the temperature and porosity variation is established.