Abstract
We present the first measurements at millikelvin temperatures of both the real and the imaginary parts of the transverse-acoustic impedance of an oscillating surface in contact with dilute solutions of $^{3}\mathrm{He}$ in $^{4}\mathrm{He}$, as well as with pure $^{3}\mathrm{He}$ with and without a surface boundary layer of $^{4}\mathrm{He}$. Except for pure $^{3}\mathrm{He}$, large departures from hydrodynamic behavior are found which are inconsistent with slip theories incorporating specular scattering at the boundary. The effects of the $^{4}\mathrm{rich}$ surface boundary layer and of surface roughness are discussed.
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