Sound conversion phenomena at the free surface of liquid helium. I. Calculation of the coefficients of reflection, transmission, and transformation of sound waves incident on the liquid-vapor interface of helium

Abstract

On the basis of a set of boundary conditions describing quite generally mass and energy transport processes across the free surface of helium II, the acoustic coefficients of reflection, transmission, and transformation of first sound, second sound, and the sound wave propagating in the vapor are calculated in the case of perpendicular incidence of sound waves against the liquid-vapor phase boundary. Considering rigorously the influences of the Onsager surface coefficients, the isobaric thermal expansion coefficients, and the thermal conductivities of the liquid and the ,Japor, we derive sets of equations from which the acoustic coefficients are determined numerically. For estimations, simple explicit formulas of the acoustic coefficients are given. It is shown that the evaporation and energy transport processes occurring at the free surface of helium H due to the incidence of sound waves may be connected with appreciable energy dissipation. The surface absorption coefficients of first, second, and gas sound waves are deduced.

A possible explanation of sound conversion at the free surface of superfluid helium near Tλ

“…A few years ago, an interesting experimental study of the free surface of superfluid helium was performed by Wiechert and Buchholz (WB) [l] who measured the reflection, transmission and conversion coefficients of sound waves at the surface. While their data outside the critical region agree quantitatively with their own theory [2], there appeared a pronounced deviation of the data from the theory near the &point, TA. This phenomenon suggested that the Onsager coefficients describing the transport across the fluid-gas interface have a critical anomaly at TA.…”

“…[l]. The broken curve shows the results of the theory of WB [2], and the full curve shows the numerical results of equation (5.9).…”

“…We assume here that the thermal wave travelling back into the vapour is very weak for the reason that the thermal conductivity of He I1 is divergent at TA. With these assumptions we can regenerate the acoustic coefficients from ( 47 The parameters n', L , Z 2 , uG, pGo and heo are defined in [2] and references therein. The discussion given above suggests that (5.12) (5.13) where al, b,, a2 and b2 are factors that cannot be determined from the theory due to the fact that the model that we used is a phenomenological model.…”

“…The discussion given above suggests that (5.12) (5.13) where al, b,, a2 and b2 are factors that cannot be determined from the theory due to the fact that the model that we used is a phenomenological model. However, we can determine them by considering that when I t I 3 10-1 the WB theory [2] is correct and when I z 1 < lo-' the theory should be modified as far as possible. We find that if we take the K1 and K2 to be…”

“…The conversion coefficient TG2 versus the logarithm of TA -T. The crosses and the circles are the experimental data of W B[l]. The broken curve shows the results of the theory of WB[2], and the full curve shows the numerical results of equation (5.9).…”