Fabrication of Multscale Fractal-Like Structures by Controlling Fluid Interface Instability.

Tanveer Ul Islam,Prasanna S Gandhi

doi:10.1038/srep37187

Abstract

Nature, in quest for the best designs has shaped its vital systems into fractal geometries. Effectual way of spontaneous fabrication of scalable, ordered fractal-like structures by controlling Saffman-Taylor instability in a lifted Hele-Shaw cell is deployed here. In lifted Hele-Shaw cell uncontrolled penetration of low-viscosity fluid into its high-viscosity counterpart is known to develop irregular, non-repeatable, normally short-lived, branched patterns. We propose and characterize experimentally anisotropies in a form of spatially distributed pits on the cell plates to control initiation and further penetration of non-splitting fingers. The proposed control over shielding mechanism yields recipes for fabrication of families of ordered fractal-like patterns of multiple generations. As an example, we demonstrate and characterize fabrication of a Cayley tree fractal-like pattern. The patterns, in addition, are retained permanently by employing UV/thermally curable fluids. The proposed technique thus establishes solid foundation for bio-mimicking natural structures spanning multiple-scales for scientific and engineering use.

Highlights

Nature, in quest for the best designs has shaped its vital systems into fractal geometries
Penetration of a low viscosity fluid into high viscosity counterpart generates a morphologically unstable interface known as Saffman-Taylor instability[8], which leads to formation of fingering patterns
A limited number of experiments reported for lifted version of Hele-Shaw cell have dealt with topics such as: permanent fractal-like structures produced in non-Newtonian paints[12,13], competition between the penetrating air fingers[14,15,16], stretching of yield stress fluid in the cell[17,18], and fingering instability in adhesives[19]

Summary

Introduction

In quest for the best designs has shaped its vital systems into fractal geometries. Scalable method of lithography-less fabrication of such multi-scale, ordered fractal-like structures by controlling fluid interface instability in a Hele-Shaw cell is presented here.

Results

Conclusion