Curvature-driven passive mixing in three-dimensional conical helix micromixers

Passive microfluidic mixing is fundamentally constrained by the dominance of laminar flow, a limitation commonly addressed using embedded obstacles or surface modifications, often at the cost of increased fabrication complexity and hydraulic resistance. Here, we introduce a conical helix micromixer (CHM) that combines circular and helical microchannel topologies into a monolithic geometry capable of passively generating progressively intensified Dean vortices through continuously varying curvature. This curvature-driven mechanism induces strong transverse transport and achieves  a mixing index (MI) > 95% in the first turn of the CHM across varying flow rates (1-2500 µL min^-1) without requiring any internal roughness structures or external energy inputs, as validated by field-based mixing simulations. A central methodological contribution is a reduced-order planar representation of the full three-dimensional (3D) CHM geometry for flow-field analysis and optimization. Direct geometrical validation against the original 3D conical-helix centreline demonstrated projection-induced deviations below 2% across all investigated configurations, with most cases remaining below 1%, confirming that the planar representation preserves the dominant geometric characteristics of the true 3D flow path with negligible loss of fidelity. This reduced-order strategy lowered computational costs by approximately an order of magnitude, while preserving a strong correlation with full 3D field-based calculations across the investigated ranges of Reynolds numbers. Geometric and flow parameters were systematically explored using a Taguchi framework, while gradient-boosted machine-learning models were employed as mechanistic analytical tools to quantify parameter sensitivity. Both analyses consistently identified the inlet curvature radius as the dominant design variable governing Dean vortex onset and mixing-length compression, with tighter curvature significantly accelerating the development of transverse mixing. The results prove that controlled curvature modulation alone can function as an efficient passive mixing engine, providing a compact, fabrication-ready platform for microreactor synthesis, point-of-care diagnostics, and scalable lab-on-a-chip applications.