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The Feasibility of Acoustophoresis Multimodal Control

Guilherme Perticarari, Dongjun Wu, Thierry Baasch

TL;DR

The paper tackles the challenge of scaling acoustophoretic control to many particles by linking manipulation success $S$ to a geometry-derived local controllability ratio $R$ computed from the pressure field. It combines a physics-based multimodal model with a reduced state-space and a PILOT optimization approach, augmented by Monte Carlo analysis and Wendel's geometric probability theorem to predict controllability in ideal and noisy 1D/2D settings. Key findings show $S$ tracks $R$ closely (about $0.97$ correlation); in ideal 1D systems $S \approx 1 - P/M$, and Wendel's theorem describes behavior under randomness with a near-linear $M$–$P$ relationship, enabling control of up to $P=60$ particles with $M=600$ modes. The results provide a computationally efficient design guideline for ACP device optimization and scalable multimodal control, with potential to rival optical methods in flexibility and cost.

Abstract

Actuating the acoustic resonance modes of a microfluidic device containing suspended particles (e.g., cells) allows for the manipulation of their individual positions. In this work, we investigate how the number of resonance modes $M$ chosen for actuation and the number of particles $P$ affect the probability of success $S$ of manipulation tasks, denoted Acoustophoretic Control Problems (ACPs). Using simulations, we show that the ratio of locally controllable volume to the state-space volume correlates strongly with $S$. This ratio can be efficiently computed from the pressure field geometry as it does not involve solving a control problem, thus opening possibilities for experimental and numerical device optimization routines. Further, we show numerically that in noise-free 1D systems $S \approx 1 - P/M$, and that in noisy 1D and 2D systems $S$ is accurately predicted by Wendel's Theorem. We also show that the relationship between $M$ and $P$ for a given $S$ is approximately linear, suggesting that as long as $P/M$ is constant, $S$ will remain unchanged. We validate this finding by successfully simulating the control of systems with up to $60$ particles with up to $600$ modes.

The Feasibility of Acoustophoresis Multimodal Control

TL;DR

The paper tackles the challenge of scaling acoustophoretic control to many particles by linking manipulation success to a geometry-derived local controllability ratio computed from the pressure field. It combines a physics-based multimodal model with a reduced state-space and a PILOT optimization approach, augmented by Monte Carlo analysis and Wendel's geometric probability theorem to predict controllability in ideal and noisy 1D/2D settings. Key findings show tracks closely (about correlation); in ideal 1D systems , and Wendel's theorem describes behavior under randomness with a near-linear – relationship, enabling control of up to particles with modes. The results provide a computationally efficient design guideline for ACP device optimization and scalable multimodal control, with potential to rival optical methods in flexibility and cost.

Abstract

Actuating the acoustic resonance modes of a microfluidic device containing suspended particles (e.g., cells) allows for the manipulation of their individual positions. In this work, we investigate how the number of resonance modes chosen for actuation and the number of particles affect the probability of success of manipulation tasks, denoted Acoustophoretic Control Problems (ACPs). Using simulations, we show that the ratio of locally controllable volume to the state-space volume correlates strongly with . This ratio can be efficiently computed from the pressure field geometry as it does not involve solving a control problem, thus opening possibilities for experimental and numerical device optimization routines. Further, we show numerically that in noise-free 1D systems , and that in noisy 1D and 2D systems is accurately predicted by Wendel's Theorem. We also show that the relationship between and for a given is approximately linear, suggesting that as long as is constant, will remain unchanged. We validate this finding by successfully simulating the control of systems with up to particles with up to modes.

Paper Structure

This paper contains 19 sections, 1 theorem, 22 equations, 9 figures.

Table of Contents

  1. Introduction
  2. System Dynamics
  3. The Physics of Acoustophoresis
  4. State-Space and Mode-Mixing
  5. Numerical Simulation
  6. Acoustophoretic Control Problem (ACP)
  7. Random Experiments
  8. Local Controllability Ratio
  9. $R$ Is a Proxy for $S$
  10. Results
  11. Ideal 1D Problem
  12. Unstructured Dynamics: Wendel's Theorem
  13. Non-ideal 1D Problem
  14. Non-Ideal 2D Problem
  15. Numerical Verification: Pick and Place
  16. ...and 4 more sections

Key Result

Theorem 1

Let $M$ points be scattered at random on the surface of the unit sphere in an $D$-dimensional space. The probability that all points lie on some hemisphere is given by

Figures (9)

  • Figure 1: (a) Three particles are introduced into the rectangular device with width $W$ and heigh $H$ at positions $\bm{x}_1=(x_1,y_1)$, $\bm{x}_2=(x_2,y_2)$, and $\bm{x}_3=(x_3,y_3)$. (b) Actuating the mode $(m_x, m_y)$ induces the acoustic radiation force $\boldsymbol{F}_a$, which is balanced by the Stokes drag force $\bm{F}_d$. The effect results in particles moving with velocity $\dot{\boldsymbol{x}}$ in the direction of $\bm{F}_a$.
  • Figure 2: The aim of the Acoustophoretic Control Problem (ACP) is to bring the system from its initial state $\bm{q}_s = \bm{x}_1 \oplus \bm{x}_2$ into its target state $\bm{q}_r = \bm{r}_1 \oplus \bm{r}_2$ using a series of control inputs.
  • Figure 3: (Left) State $\boldsymbol{q}$ is not locally controllable under $\bm{F}_3(\boldsymbol{q})$ since there are blindspots around it. (Right) State $\boldsymbol{q}$ is locally controllable under $\bm{F}_4(\boldsymbol{q})$.
  • Figure 4: To estimate the local controllability ratio $R$, we sample $N$ states i.i.d. from $\mathcal{S}^P$, verify which are locally controllable (green) and take $R$ as the ratio of locally controllable states to $N$.
  • Figure 5: The Local Controllability Ratio, $R$, and the success rate of a random experiment, $S$, are estimated for ACPs with varying number of particles and modes. The data shows a 0.97 correlation between both metrics.
  • ...and 4 more figures

Theorems & Definitions (1)

  • Theorem 1: Wendel's Theorem