The Role of Substrate Roughness in Superfluid Film Flow Velocity

It is known that the apparent film flow rate $j_0$ of superfluid $^4$He increases significantly when the container wall is contaminated by a thin layer of solid air. However, its microscopic mechanism has not yet been clarified enough. We have measured $j_0$ under largely different conditions for the container wall in terms of surface area (0.77-6.15 m$^2$) and surface morphology using silver fine powders (particle size: $0.10$ mu m) and porous glass (pore size: 0.5, 1 mu m). We could increase $j_0$ by more than two orders of magnitude compared to non-treated smooth glass walls, where liquid helium flows down from the bottom of container as a continuous stream rather than discrete drips. By modeling the surface morphology, we estimated the effective perimeter of container $L_{mathrm{eff}}$ and calculated the flow rate $j~(= j_0L_0/L_{mathrm{eff}})$, where $L_0$ is the apparent perimeter without considering the microscopic surface structures. The resultant $j$ values for the various containers are constant each other within a factor of four, suggesting that the enhancement of $L_{mathrm{eff}}$ plays a major role to change $j_0$ to such a huge extent and that the superfluid critical velocity, $v_{mathrm{c}}$, does not change appreciably. The measured temperature dependence of $j$ revealed that $v_{mathrm{c}}$ values in our experiments are determined by the vortex depinning model of Schwarz (Phys. Rev. B $textbf{31}$, 5782 (1986)) with several nm size pinning sites.