Optimal counter-current exchange networks

TL;DR

This paper analyzes the efficiency of counter-current exchange networks, revealing that optimal designs involve densely packed, possibly fractal, structures that significantly outperform regular flat exchangers, especially in biological contexts.

Contribution

It introduces a general framework linking exchange device efficiency to geometry, proposing fractal and crumpled structures as optimal configurations for exchange surfaces.

Findings

Optimal exchangers can be fractal or crumpled surfaces.

Densely packed pipe networks enhance efficiency.

Significant efficiency gains over flat exchangers in biological systems.

Abstract

We present a general analysis of exchange devices linking their efficiency to the geometry of the exchange surface and supply network. For certain parameter ranges, we show that the optimal exchanger consists of densely packed pipes which can span a thin sheet of large area (an `active layer'), which may be crumpled into a fractal surface and supplied with a fractal network of pipes. We derive the efficiencies of such exchangers, showing the potential for significant gains compared to regular exchangers (where the active layer is flat), using parameters relevant for biological systems.