Laminar-flow-based sound absorption with a single Hilbert curve surpassing the Rozanov bound

Abstract

Advances in metamaterials, additive manufacturing, and computational design have enabled significant progress in airborne sound absorption. However, most absorbers still rely on two conventional mechanisms, i.e., friction-induced viscous loss and pressure-fluctuation-induced thermal loss, leaving their thickness constrained by the Rozanov bound. Here, we investigate an acoustic metamaterial based on a single three-dimensional Hilbert curve, designed to achieve sound absorption beyond this theoretical limit. The Hilbert curve forms continuous, tightly spaced winding channels whose geometry enables laminar flow-like shear dissipation. Experimental, numerical, and theoretical results demonstrate that with an optimal slit width close to the viscous boundary layer thickness, the actual thickness can be approximately 86% of the calculated Rozanov bound. This finding suggests a dissipation mechanism distinct from classical porous and resonator-based absorbers, opening different avenues for ultra-thin broadband sound absorbers.