Optimal control of particle separation in inertial microfluidics

Prohm, Christopher; Tröltzsch, Fredi; Stark, Holger

doi:10.1140/epje/i2013-13118-8

Cited by 16 publications

(25 citation statements)

References 57 publications

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“…(8) over the last 2000 time steps of the simulation. We demonstrated before 15,17 that this procedure does indeed reproduce correct lift-force profiles.…”

Section: Determing Inertial Lift Forcesmentioning

confidence: 68%

Feedback control of inertial microfluidics using axial control forces

Prohm

Stark

2014

Lab Chip

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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.

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“…(8) over the last 2000 time steps of the simulation. We demonstrated before 15,17 that this procedure does indeed reproduce correct lift-force profiles.…”

Section: Determing Inertial Lift Forcesmentioning

confidence: 68%

Feedback control of inertial microfluidics using axial control forces

Prohm

Stark

2014

Lab Chip

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“…3(a) decays like e −κr with κ ∝ L as r → ∞. 4 An interesting aspect of the current system is the reversal of the direction of the radial velocity. Initially, Marangoni flow towards the light spot (v r < 0) acts against the diffusive current of B surfactants, which in active emulsions can cause demixing (see Ref.…”

Section: Single Light Spotmentioning

confidence: 99%

“…For example, advances in digital and inertial microfluidics have resulted in useful biochemical reactors [1] and precise sorting for micron-sized objects [2]. These devices often rely on specific geometries to control fluid flow [3,4,5,6]. But flow can also result from gradients in surface tension through a phenomenon known as the Marangoni effect.…”

Section: Introductionmentioning

confidence: 99%

Feedback control of photoresponsive fluid interfaces

Grawitter

Stark

2018

Soft Matter

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Photoresponsive surfactants provide a unique microfluidic driving mechanism. Since they switch between two molecular shapes under illumination and thereby affect surface tension of fluid interfaces, Marangoni flow along the interface occurs. To describe the dynamics of the surfactant mixture at a planar interface, we formulate diffusion-advection-reaction equations for both surfactant densities. They also include adsorption from and desorption into the neighboring fluids and photoisomerization by light. We then study how the interface responds when illuminated by spots of light. Switching on a single light spot, the density of the switched surfactant spreads in time and assumes an exponentially decaying profile in steady state. Simultaneously, the induced radial Marangoni flow reverses its flow direction from inward to outward. We use this feature to set up specific feedback rules, which couple the advection velocities sensed at the light spots to their intensities. As a result two neighboring spots switch on and off alternately. Extending the feedback rule to light spots arranged on the vertices of regular polygons, we observe periodic switching patterns for even-sided polygons, where two sets of next-nearest neighbors alternate with each other. A triangle and pentagon also show regular oscillations, while heptagon and nonagon exhibit irregular oscillations due to frustration. While our findings are specific to the chosen set of parameters, they show how complex patterns at photoresponsive fluid interfaces emerge from simple feedback coupling.

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“…with e  | | 1 and complex eigenvalues  l Î into equation (7), which gives a transcendental equation for λ,…”

Section: Characteristic Functionmentioning

confidence: 99%

“…From mixing two liquids [1], sorting colloids [2,3], controlling reaction rates [4] and heat transport in microfluidic devices [5], to fluid optics [1] and spiral patterns in liquid crystals [6], soft matter systems often display their most useful or interesting properties under external stresses. Several control and driving schemes have already been applied to these systems, including optimal control [7], hysteresis control [8], and time-delayed feedback [8][9][10]. These methods sense the characteristic response of a material and adapt their control to it.…”

Section: Introductionmentioning

confidence: 99%

Dissipative systems with nonlocal delayed feedback control

et al. 2018

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We present a linear model, which mimics the response of a spatially extended dissipative medium to a distant perturbation, and investigate its dynamics under delayed feedback control. The time a perturbation needs to propagate to a measurement point is captured by an inherent delay time (or latency). A detailed linear stability analysis demonstrates that a nonzero system delay acts to destabilize the otherwise stable fixed point for sufficiently large feedback strengths. The imaginary part of the dominant eigenvalue is bounded by twice the feedback strength. In the relevant parameter space it changes discontinuously along specific lines when switching between eigenvalues. When the feedback control force is bounded by a sigmoid function, a supercritical Hopf bifurcation occurs at the stability-instability transition. Perturbing the fixed point, the frequency and amplitude of the resulting limit cycles respond to parameter changes like the dominant eigenvalue. In particular, they show similar discontinuities along specific lines. These results are largely independent of the exact shape of the sigmoid function. Our findings match well with previously reported results on a feedback-induced instability of vortex diffusion in a rotationally driven Newtonian fluid (Zeitz et al 2015 Eur. Phys. J. E 38 22). Thus, our model captures the essential features of nonlocal delayed feedback control in spatially extended dissipative systems.

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Optimal control of particle separation in inertial microfluidics

Cited by 16 publications

References 57 publications

Feedback control of inertial microfluidics using axial control forces

Feedback control of inertial microfluidics using axial control forces

Feedback control of photoresponsive fluid interfaces

Dissipative systems with nonlocal delayed feedback control

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