Feedback control of inertial microfluidics using axial control forces

Abstract

Inertial microfluidics is a promising tool for many lab-on-a-chip applications. Particles in channel flows with Reynolds numbers above one undergo cross-streamline migration to a discrete set of equilibrium positions in square and rectangular channel cross sections. This effect has been used extensively for particle sorting and the analysis of particle properties. Using the lattice Boltzmann method, we determine equilibrium positions in square and rectangular cross sections and classify their types of stability for different Reynolds numbers, particle sizes, and channel aspect ratios. Our findings thereby help to design microfluidic channels for particle sorting. Furthermore, we demonstrate how an axial control force, which slows down the particles, shifts the stable equilibrium position towards the channel center. Ultimately, the particles then stay on the centerline for forces exceeding a threshold value. This effect is sensitive to particle size and channel Reynolds number and therefore suggests an efficient method for particle separation. In combination with a hysteretic feedback scheme, we can even increase particle throughput.

Direct measurement of particle inertial migration in rectangular microchannels

“…Lateral migration velocities along the manifold quantitatively agree with the asymptotic theory in equation (7). We filtered the measured velocities to select particles that were within a distance 2.25µm of the slow manifold.…”

“…Though there are many theories for the magnitudes of inertial focusing forces, direct experimental measurement of these forces remains an unmet challenge. Indeed existing theory [2][3][4][5], numerical simulations [6][7][8], and indirect experimental measurements [9] have produced contradictory scalings for the dependence of forces on particle size and velocity. In this paper, we directly measure inertial migration velocities by tracking the motion of particles in a rectangular channel over Reynolds numbers ranging from 30 to 180, and find that their measured migration velocities agree well with existing asymptotic theory [5].…”

Optimal control of particle separation in inertial microfluidics

“…External fields not only act directly on the particles. By slowing the particles down or enhancing their velocities along the channel axis, also the lift force profiles are modified [52,53]. Furthermore, so far we looked at dilute suspensions where hydrodynamic interactions between the particles are negligible.…”

Controlling inertial focussing using rotational motion

“…Here, more stable and unstable fixpoints occur [31] and it will be interesting to check how they are modified under controlled rotation. Furthermore, at low Reynolds number dense suspensions of colloids subject to a constant torque show very interesting collective behavior [23].…”

“…Here numerical simulation studies are important. Previous investigations used the finite-element method [28,29], lattice-Boltzmann simulations [30,31], and the method of multi-particle collision dynamics [32].…”