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 sintered silver fine powders (particle size: 0.10 \({\upmu }\)m) and porous glass (pore size: 0.5, 1 \({\upmu }\)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 the container as a continuous stream rather than discrete drips. By modeling the surface morphology, we estimated the effective perimeter of the 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 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 31(9):5782, 1985. https://doi.org/10.1103/PhysRevB.31.5782) with several nm size pinning sites.