MICRO FLUIDICS | ARTICLE
MODELLING INERTIAL FOCUSING IN STRAIGHT AND CURVED MICRO FLUIDIC CHANNELS
Researchers from Massachusetts General Hospital and Veryst are using multiphysics analysis to investigate the micro fluidic process of inertial focusing.
Joseph Martel and Mehmet Toner | BioMEMS Resource Center, Massachusetts General Hospital, and Nagi Elabbasi, David Quinn, and Jorgen Bergstrom | Veryst Engineering
<<Figure 1: Basic forces acting on a particle in a micro channel. >>
I
n many medical procedures and tests it is necessary to isolate cells of interest for further analysis. Micro fluidics has revolutioniSed the way in which these tests are conducted. One
of the most promising micro fluidic techniques to separate and concentrate cells of interest is called inertial focusing. Originally discovered in 1960s, the phenomenon of inertial focusing found new utility in micro fluidics, and in particular biomedical device design, recently playing a key role in a device enabling the ability to detect cancer from a blood sample. The phenomenon is characterised by suspended particles in a flow spontaneously migrating across streamlines to equilibrium positions within a channel cross-section, where they continue to flow in an ordered formation. By changing the geometry of the channel it is possible to control the equilibrium positions of particles of different sizes.
This phenomenon occurs when the particle Reynolds number, ReP, is approximately equal to 1 and is due to the balance of two
forces; a shear gradient lift force directed towards the walls of the channel and a wall-interaction force directed away from each wall. The balance of these two forces determines the equilibrium position (see figure 1). In a straight channel with a rectangular cross section this leads to a pair of equilibria centred on the long faces of the channel as shown in figure 2A. The addition of curvature to the channel changes the resulting force on the particles thus altering the equilibrium positions. A secondary transverse flow occurs across the channel due to the momentum of the faster moving fluid in the centre of the channel, which induces a drag force on the particles and thus adjusts their equilibrium positions, as depicted in figure 2B. The strength of this secondary flow depends on the curvature of the channel and is characterised by the non-dimensional Dean number, De. The equilibrium positions for a particle in curved channel flows are consequently a function of the channel dimensions, particle size, particle and channel Reynolds numbers, and Dean number.
32 | commercial micro manufacturing international Vol 7 No.1
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