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Inertial focusing in curved microfluidic ducts exploits the interaction ofdrag force from the Dean flow with the inertial lift force to separateparticles or cells laterally across the cross-section width according to theirsize. Experimental work has identified that using a trapezoidal cross-section,as opposed to a rectangular one, can enhance the sized based separation ofparticles/cells over a wide range of flow rates. Using our model, derived bycarefully examining the way the Dean drag and inertial lift forces interact atlow flow rates, we calculate the leading order approximation of these forcesfor a range of trapezoidal ducts, both vertically symmetric and non-symmetric,with increasing amount of skew towards the outside wall. We then conduct asystematic study to examine the bifurcations in the particle equilbira thatoccur with respect to a shape parameter characterising the trapezoidalcross-section. We reveal how the dynamics associated with particle migrationare modified by the degree of skew in the cross-section shape, and show theexistence of cusp bifurcations (with the bend radius as a second parameter).Additionally, our investigation suggests an optimal amount of skew for thetrapezoidal cross-section for the purposes of maximising particle separationover a wide range of bend radii.

Inertial focusing dynamics of spherical particles in curved microfluidic ducts with a trapezoidal cross-section