Wave-Mode Modification in Liquid Helium with Partially Clamped Normal Fluid

Abstract

When the equations of first and second sound are modified to correspond to wave propagation in the presence of viscous forces on the normal fluid, two wave modes result. In the limit of large viscous forces, second sound becomes an overdamped thermal mode with zero velocity, and first sound becomes an undamped (acoustic) mode with wave velocity $v$ given to first order by ${v}^{2}={(\frac{{\ensuremath{\rho}}_{s}}{\ensuremath{\rho}})}^{2}{{c}_{1}}^{2}+{(\frac{{\ensuremath{\rho}}_{n}}{\ensuremath{\rho}})}^{2}{{c}_{2}}^{2}$ in terms of usual symbols. In this investigation, the onset of wave-mode modification has been examined as degradation of pure second-sound pulses and standing waves in the presence of barriers. Normal fluid was partially clamped in the interstices of emery powder or rouge, with viscous drag controlled by employing several packing densities. The velocity of thermal signals sent through chambers filled with these small particles decreases, and the damping increases with smaller interstices. The theoretical wave velocities of the thermal and acoustic modes are obtained, as functions of temperature and a viscosity coefficient, from the modified wave equations. For suitably chosen constant values of the viscosity coefficient, the theoretical velocity of thermal waves is in approximate quantitative agreement with the observed pulse velocities, and the observations are interpreted in this way. Qualitatively observed attenuation is shown to be in agreement with the same theory. The effect of capacitive thermal losses to the barrier particles, and consequent possible degradation of incipient wave modes to thermal diffusion, is also analyzed.