# Heterogeneous Acoustofluidic Distributions Induced by Different Radiation Surface Arrangements in Various Pseudo-Sierpiński-Carpet-Shaped Chambers

## TL;DR

This paper explores how fractal-shaped chambers can create complex acoustofluidic patterns for manipulating micro-particles in new ways.

## Contribution

The study introduces fractal structures to generate diverse acoustofluidic distributions without complex parameter adjustments.

## Key findings

- Pseudo-Sierpiński-carpet-shaped chambers produce unique acoustofluidic patterns at different recursion levels.
- Adjusting radiation surface arrangements allows controllable spatial partitioning and intensity modulation.
- Fractal elements like Sierpiński carpets and Koch snowflakes expand the application of acoustofluidic effects.

## Abstract

In this research, an innovative scheme to generate heterogeneous acoustofluidic distributions in various pseudo-Sierpiński-carpet-shaped chambers with different filling fractions and cross-sectional configurations has been proposed and calculated for topographical manipulation of large-scale micro-particles. All of the structural components positioned in the pseudo-fractal chambers are symmetrically distributed in space, and all ultrasonic radiation surfaces hold the unified settings of input frequency point, oscillation amplitude, and initial phase distribution along their respective normal directions. A large number of fascinating acoustofluidic patterns can be generated in the originally-static pseudo-Sierpiński-carpet-shaped chambers at different recursion levels without complicated vibration parameter modulation. The simulation results of acoustofluidic distributions and particle motion trajectories under different radiation surface arrangements further demonstrate the manipulation performance of these specially designed devices, and indicate that controllable spatial partitioning and intensity modulation of the acoustofluidic field can be achieved by adjusting the hierarchical order, cross-sectional configuration and combination mode of the radiation surfaces. Unlike the existing device construction method of miniaturized microfluidic systems, the artificial introduction of fractal elements like Sierpiński carpet/triangle, Koch snowflake, Mandelbrot set, Pythagoras tree, etc., can provide extraordinary perspectives and expand the application range of the acoustofluidic effect, which also makes ultrasonic micro/nano-scale manipulation technology more abundant and diversified. This exploratory research indicates the potential possibility of applying fractal structures as alternative component parts to purposefully customize acoustofluidic distributions for the further research of patterned manipulation of bio-organisms and navigation of micro-robot swarms in brand new ways that cannot be achieved through traditional methods.