Dynamics of Small Particle Inertial Migration in Curved Square Ducts

Microchannels are well known in microfluidic applications for the control and separation of microdroplets cells. Often objects flow experience inertial effects, resulting dynamics that is a departure from underlying channel dynamics. This paper considers small neutrally buoyant spherical particles suspended through curved duct having square cross-section. The particle experiences combination lift force induced by disturbance primary along duct, drag secondary vortices cross-section, which drive migration within We construct simplified model preserves core topology field yet depends on single parameter $\kappa$, quantifying relative strength two forces. show $\kappa$ bifurcation dynamical system describes motion cross-section duct. At large values there exists an attracting limit cycle each upper lower halves we find migrate to one four stable foci. Between these extremes, intermediate range all focus. Noting positions cycles foci vary with value this behavior indicates that, suitable mixture, bend radius might be chosen segregate size. evaluate time axial distance required focus near unique node, determines length segregation.