Abstract
Inertial lift is a fluid phenomena exploited in microfluidic devices to separate particles/cells based on their size. Whilst it has been studied extensively for spherical particles suspended in flow through straight ducts, typically of rectangular shape, many applications involve ducts that are curved. This paper explores the estimation of focusing behaviour in curved ducts by simply adding inertial lift forces computed for a straight duct (having the same cross-section) to the drag forces within the cross-sectional plane which are generated by the secondary motion of the fluid flow through the curved duct. We examine the specific case of a curved rectangular duct with height `, width 2` and bend radius R in which a neutrally buoyant particle with radius a is suspended. The simple force model is appropriate when R is large and the flow rate is low such that the Dean number is small. The magnitude of the secondary flow drag relative to the inertial lift force scales with κ = ` 4 /(a 3 R) and the dominant focusing behaviour is found to approximately collapse onto
a single curve when plotted against κ, particularly when κ ≤ 30.
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