Abstract
Curved and spiral microfluidic channels are widely used in particle and cell sorting applications. However, the average Dean velocity of secondary vortices which is an important design parameter in these devices cannot be estimated precisely with the current knowledge in the field. In this paper, we used co-flows of dyed liquids in curved microchannels with different radii of curvatures and monitored the lateral displacement of fluids using optical microscopy. A quantitative Switching Index parameter was then introduced to calculate the average Dean velocity in these channels. Additionally, we developed a validated numerical model to expand our investigations to elucidating the effects of channel hydraulic diameter, width, and height as well as fluid kinematic viscosity on Dean velocity. Accordingly, a non-dimensional comprehensive correlation was developed based on our numerical model and validated against experimental results. The proposed correlation can be used extensively for the design of curved microchannels for manipulation of fluids, particles, and biological substances in spiral microfluidic devices.
Highlights
Understanding the causes and effects of Dean flow in curved channels is of paramount importance to design of microfluidic devices
Dean velcosity (VDe). (a) Water streams dyed with methylene blue and red food dye were introduced from the two inlets and their radial displacement was imaged
Two additional properties studied were fluid axial velocity (Vx) and kinematic viscosity as fully discussed
Summary
Understanding the causes and effects of Dean flow in curved channels is of paramount importance to design of microfluidic devices. Martel and Toner[29] reported the necessity of existence of an accurate formula to predict the velocity at which particle focusing occurs in a spiral channel They took two different approaches to investigate the inertial focusing, one by ignoring and the other by including the Dean velocity (VDe). Norouzi and Biglari[33] used curvature ratio as the perturbation parameter to solve the secondary flow problem in curved ducts Their solution showed acceptable agreement with experimental results but associated errors were remarkably high for sharp curvatures that are prevalent in microfluidic devices. Ookawara et al.[30] numerically studied Dean flows in a rectangular curved microchannel and proposed two correlations, both in the form of power functions, for estimation of average (Eq 3) and maximum Dean flow velocities
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