One-step creation of hierarchical fractal structures

Relatively recently, we advanced a route to create, in a controlled fashion, combined horizontal and vertical stratified structures by simple and energy-efficient processing operations employing static mixing elements. While in state-of-the-art static mixing the focus is on layer multiplication, here the aim is to create hierarchical fractal structures. Therefore, the main question addressed in this article is how structures, rather than layers, can be multiplied. The key aspect is the addition of layers on the sides or in the midplane of the flow during the process; every addition step increases the hierarchy by one level. This article derives the general formalism for forming fractal structures with controlled hierarchy, and we develop the language required to design and construct the dies. The main part of the article addresses this main topic and is based on the splitting serpentine static mixer geometry that can be easily made on the parting surfaces of a mold on both the micro- and the macroscale. The second part of the article addresses the strategy to minimize the number of mirroring steps, eventually avoiding mirroring completely, and is based on the rotation-free multiflux static mixer geometry. With the design language derived, complex hierarchical fractal structures can be generated simply by changing the number and sequence of operators within extrusion dies or molds, providing a one-step solution to produce material structures for potential use in diverse applications ranging from advanced mechanical systems to photovoltaic devices, where controlled assembly of dissimilar materials, and the realization of huge interfaces and genuine cocontinuity throughout the cross section, is critical.