Evaluation of dynamical-billiard-shaped chambers as divergent elements of passive micromixers

Efficient mixing of fluid streams in microfluidic devices remains a critical challenge due to the dominance of laminar flow, where mixing relies solely on diffusion. To overcome this limitation, various microfluidic mixers have been developed to transition from laminar to non-laminar regimes, enabling faster mixing rates. Passive micromixers utilize geometric channel designs instead of external energy sources, making them advantageous due to their simplicity. Among these, convergent-divergent micromixers employ alternating narrow and wide channels to stretch and fold fluid streams, enhancing the mixing process. This study explores a novel series of microfluidic mixers based on dynamical-billiard-shaped chambers. Each microfluidic mixer comprises twenty consecutive nanoliter billiard-shaped chambers connected by relatively narrow channels of equal or variable lengths. Six chamber designs were analyzed: three chaotic billiard shapes (Bunimovich-stadium, diamond-shape, and Sinai-billiard) and their respective non-chaotic counterparts (ellipse, triangle, and ring). Two spatial arrangements—out-of-axis and on-axis chambers—were tested to evaluate their impact on mixing efficiency. Key findings reveal that an out-of-axis chamber configuration significantly enhances mixing, as does connectors with varying lengths. Orientation of the initial chamber at a 36° angle further improves performance. However, chaotic chambers did not consistently outperform non-chaotic ones, likely due to limitations in flow rates. Comparisons with a previously reported baffled structure, considered an excellent micromixer, showed improved mixing efficiency using both chaotic and non-chaotic chambers. These results provide valuable insights into passive mixing mechanisms, contributing to the design of more efficient microfluidic mixers adaptable to specific experimental conditions.