Canopy elastic turbulence: Insights and analogies to canopy inertial turbulence

Canopy flows occur when a moving fluid encounters a matrix of free-standing obstacles and are found in diverse systems, from forests and marine ecology to urban landscapes and biology (e.g. cilia arrays). In large-scale systems, involving Newtonian fluids (like water or air), canopy flows typically exhibit inertial turbulence due to high Reynolds numbers (Re). However, in small-scale systems like cilia, where Re is low, but the fluid can be viscoelastic (like mucus), the relevant control parameter is the Weissenberg number (Wi), quantifying elastic stresses in the flow. Here, we investigate the flow of a viscoelastic polymer solution over a microscopic canopy within a microfluidic device. As the Weissenberg number increases, the flow undergoes distinct transitions, eventually becoming unstable beyond a critical Wi. At high Wi, we observe the emergence of elastic turbulence (ET), a chaotic flow regime that, despite differing underlying mechanisms, exhibits striking similarities to large-scale canopy inertial turbulence. Similar to canopy inertial turbulence, ET within the canopy can be spatially divided into distinct regions: a porous layer within the canopy, a mixing layer at the canopy tips, a transitional region just above the canopy, and a Poiseuille-like flow further up. The separation of the flow into different regions reveals a new analogy between inertial turbulence and ET, providing a fresh insight into ET flows and expanding their potential for innovative microfluidic designs and real-world applications.