New insights into the physics of inertial microfluidics in curved microchannels. II. Adding an additive rule to understand complex cross-sections.

Curved microchannels allow controllable microparticle focusing, but a full understanding of particle behavior has been limited-even for simple rectangular and trapezoidal shapes. At present, most microfluidic particle separation literature is dedicated to adding "internal" complexity (via sheath flow or obstructions) to relatively simple cross-sectional channel shapes. We propose that, with sufficient understanding of particle behavior, an equally viable pathway for microparticle focusing could utilize complex "external" cross-sectional shapes. By investigating three novel, complex spiral microchannels, we have found that it is possible to passively focus (6, 10, and 13 μm) microparticles in the middle of a convex channel. Also, we found that in concave and jagged channel designs, it is possible to create multiple, tight focusing bands. In addition to these performance benefits, we report an "additive rule" herein, which states that complex channels can be considered as multiple, independent, simple cross-sectional shapes. We show with experimental and numerical analysis that this new additive rule can accurately predict particle behavior in complex cross-sectional shaped channels and that it can help to extract general inertial focusing tendencies for suspended particles in curved channels. Overall, this work provides simple, yet reliable, guidelines for the design of advanced curved microchannel cross sections.