Viscoelastic control of acoustic particle migration and trapping in microchannels

This study demonstrates that fluid viscoelasticity fundamentally alters acoustic particle migration and trapping in microchannels by shifting equilibrium locations and significantly reducing the critical particle size required for manipulation, thereby overcoming key limitations of conventional acoustofluidics in Newtonian fluids.

The Gist

Imagine you are trying to sort a bag of mixed marbles and dust motes inside a long, narrow glass tube. You want to use sound waves (ultrasound) to push the marbles to specific spots. In a normal liquid like water, this is a bit of a tug-of-war.

The Two Competing Forces
Think of the sound waves as creating two invisible hands trying to move the particles:

1. The "Radiation Hand" (Acoustic Radiation Force): This is a strong, direct push. It wants to shove larger particles straight toward a specific "safe zone" (a pressure node) in the middle of the tube. It's like a magnet pulling a heavy iron ball.
2. The "Streaming Hand" (Acoustic Streaming Drag): When sound waves move through a fluid, they create tiny, steady currents or whirlpools, much like wind blowing through a canyon. This creates a drag force that pushes particles along with the flow. For very small particles (like dust or bacteria), this "wind" is often stronger than the "magnet," carrying them away from the safe zone and into swirling eddies.

In normal water, this tug-of-war is hard to control. If you want to catch a tiny particle, the "wind" usually wins, blowing it away. If you want to catch a big one, the "magnet" wins, but you can't easily change where the magnet pulls.

The Secret Ingredient: Jiggly Jelly
The researchers in this paper asked: What if we change the liquid itself? Instead of water, they used a "viscoelastic" fluid. Think of this not as water, but as a mixture of water and a little bit of jelly or slime (like a polymer solution). This fluid has "memory"—it's stretchy and bouncy, not just squishy.

They discovered that by tweaking how "jiggly" or elastic this fluid is, they could completely rewrite the rules of the tug-of-war.

The Magic Switch: The "Jiggly" Dial
The team found two main knobs they could turn to control the outcome:

• The "Stretchiness" Knob (Deborah Number): This measures how much the fluid acts like a rubber band versus a liquid.
• The "Thickness" Knob (Viscous Diffusion Number): This measures the balance between the water part and the jelly part of the fluid.

By turning these knobs, they could make the "Streaming Hand" (the wind) do things it never did before:

• Stop the Wind: They could make the swirling currents disappear, letting the "Radiation Hand" (the magnet) take over and trap even tiny particles.
• Reverse the Wind: They could make the wind blow in the opposite direction, pushing particles from the center back toward the walls, or from the walls toward the center.
• Change the Destination: In normal water, particles usually get stuck in one specific line. In this "jiggly jelly," the researchers could make particles get trapped at the walls, in the exact center of the tube, or in the middle of the fluid, just by changing the fluid's recipe.

The "Size Limit" Breakthrough
Usually, there is a "cutoff size." Particles smaller than this size are too light to be caught by the sound waves; they just get blown away by the streaming currents. The paper shows that by using this special fluid, they can lower this cutoff size significantly. It's like turning a heavy door that only opens for adults into a door that even a child can push open. This means they can now catch and hold onto particles that are smaller than a human hair (submicron particles), which was very difficult to do before.

The Journey Matters
The researchers also noticed that the path a particle takes matters. A particle might rush to the center quickly at first, but then get swept away to the wall later. It's like a runner who sprints to the finish line but then gets caught in a side current that drags them to the bleachers. By understanding both the "early sprint" and the "late drift," they can predict exactly where a particle will end up.

In Summary
This paper demonstrates that by adding a little bit of "jelly" to the fluid, scientists can act like a conductor, directing sound waves to push and pull particles to almost any location they want. They can switch between catching big things and tiny things, and move them to the walls, the center, or specific lines, simply by adjusting the fluid's stretchiness. This gives them a powerful new way to sort and trap microscopic objects without needing to build complex new machines.

Technical Summary

Technical Summary: Viscoelastic Control of Acoustic Particle Migration and Trapping in Microchannels

Problem Statement
Acoustofluidics utilizes acoustic radiation forces (ARF) and acoustic streaming-induced drag to manipulate suspended particles. In Newtonian fluids, the relative dominance of these mechanisms is primarily governed by particle size: ARF (scaling with volume) drives larger particles, while streaming drag (scaling linearly with size) dominates smaller particles. This competition creates a "crossover size" (e.g., $\approx 2 \mu m$ in water at 2 MHz), below which effective trapping is difficult due to streaming dominance. Furthermore, in radiation-dominated regimes, particles with identical acoustic contrast factors often migrate to the same equilibrium locations, limiting size-selective control. While previous studies have examined viscoelastic effects on ARF and streaming independently, the coupled influence of fluid viscoelasticity on particle migration and trapping dynamics within realistic microchannel geometries remains largely unexplored. This work addresses the central question: Can fluid viscoelasticity be exploited to modulate the force balance between ARF and streaming drag, thereby enabling continuous control over particle trajectories and trapping locations without altering device geometry?

Methodology
The study employs a unified theoretical and experimental framework to investigate particle transport in a viscoelastic fluid subjected to ultrasonic excitation in a rectangular microchannel.

• Theoretical Model: The suspending fluid is modeled as an Oldroyd-B fluid, capturing solvent viscosity, polymer elasticity, and fluid relaxation. The governing equations (continuity, momentum, and constitutive) are solved using a perturbation framework to derive the oscillatory acoustic field and the resulting steady streaming flows in both the bulk and near-wall boundary layers.

  • Key Parameters: The dynamics are characterized by the Deborah number ($De = \tau/t_{ac}$), comparing fluid relaxation time to the acoustic timescale, and the viscous diffusion number ($Dv = t_{d,s}/t_{d,p}$), comparing solvent and polymer viscous diffusion timescales.
  • Force Balance: Acoustic radiation forces are incorporated via a semi-analytical model for viscoelastic fluids, while streaming-induced drag is derived from the second-order streaming velocity field. The particle velocity is determined by balancing these forces.
  • Critical Size: A critical particle radius ($a_c$) is derived to define the transition between streaming-dominated and radiation-dominated regimes as a function of $De$ and $Dv$.

• Experimental Validation: Experiments were conducted using a glass-silicon-glass microfluidic device with a 2.0 MHz standing acoustic wave. Spherical fluorescent polystyrene particles (1 $\mu$m and 5 $\mu$m) were suspended in viscoelastic solutions of Polyethylene Oxide (PEO) and Methyl Cellulose (MC). Particle migration and trapping were visualized using high-speed cameras and confocal fluorescence microscopy to resolve three-dimensional distributions across the channel depth.

Key Results
The study reveals that fluid viscoelasticity fundamentally alters the competition between ARF and streaming drag, leading to distinct migration regimes and tunable trapping locations.

1. Emergence of Six Trapping Regimes: Depending on $De$ and $Dv$, particle trajectories transition through six distinct regimes:

   • AS-BP: Acoustic streaming-dominated bulk-point trapping (particles trapped in vortex centers).
   • PNL-WP: Migration from the pressure nodal line (PNL) to wall points (WP).
   • PNL: Stable trapping at the pressure nodal line.
   • PNL-CP: Migration from the PNL to the channel center (CP).
   • CP: Direct trapping at the channel center (a regime absent in Newtonian fluids).
   • USL-CP: Migration from the ultrasound symmetry line (USL) to the center.
   • The transitions between these regimes are non-monotonic with respect to $De$, particularly at high $Dv$, where regimes can recur as elasticity increases.

2. Force Balance and Flow Reversal: Theoretical analysis shows that increasing $De$ initially enhances streaming-induced drag, but at higher $De$, the streaming flow can weaken or even reverse direction. This reversal of the streaming-induced drag force is the primary mechanism driving particles from the PNL toward the channel center or symmetry line, creating trapping locations not accessible in Newtonian fluids.

3. Critical Particle Size Reduction: The study determines that the critical particle size ($a_c$) governing the transition between regimes can become significantly smaller than that in a Newtonian fluid for specific combinations of $De$ and $Dv$. This reduction implies that viscoelasticity enables the effective manipulation of submicron particles, which are typically difficult to trap in conventional acoustofluidic systems due to streaming dominance.

4. Dynamic Evolution: Both early-time and late-time analyses are necessary to fully characterize trapping. Particles may initially migrate toward a PNL (early time) but subsequently drift toward walls or the center (late time) as the force balance evolves, highlighting the dynamic nature of the trapping process.

Significance and Claims
The paper claims to establish a unified framework linking force competition, fluid rheology, and particle size to controllable migration and trapping under ultrasound. The primary significance lies in demonstrating that fluid viscoelasticity acts as an independent control parameter that can:

• Continuously tune particle trajectories and final equilibrium locations without modifying channel geometry or acoustic actuation.
• Overcome the limitation of conventional acoustofluidics regarding the manipulation of submicron particles by reducing the critical size required for radiation-dominated transport.
• Enable the differentiation of particles with the same acoustic contrast factor by exploiting rheological differences, a capability not readily achievable in Newtonian systems.

These findings provide a mechanism for tunable particle migration and trapping in complex fluids, with potential relevance for lab-on-a-chip applications involving biological samples (e.g., blood, plasma) where fluid rheology is intrinsic.