The Role of Substrate Roughness in Superfluid Film Flow Velocity

TL;DR

This study investigates how substrate surface roughness and morphology significantly enhance superfluid helium film flow rates, with findings suggesting that increased effective perimeter due to roughness boosts flow without changing critical velocity.

Contribution

It provides a detailed experimental analysis linking substrate roughness to superfluid flow enhancement and models the effect using surface morphology and vortex depinning theory.

Findings

Flow rate increases over two orders of magnitude with rough surfaces.

Effective perimeter increase explains flow enhancement.

Critical velocity remains largely unchanged.

Abstract

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.