Theory of acoustophoresis in counterpropagating surface acoustic wave fields for particle separation

Acousotophoretic particle separations in counterpropagating surface acoustic wave (SAW) fields, e.g., standing SAWs (SSAWs), phase modulated SSAWs, tilted angle SSAWs, and partial standing SAWs, have proven successful. But there still lacks analytical tools for predicting the particle trajectory and optimizing the device designs. Here, we study the acoustophoresis of spherical Rayleigh particles in counterpropagating SAW fields and find that particle motions can be characterized into two distinct modes, the drift mode and the locked mode. Through theoretical studies, we provide analytical expressions of particle trajectories in different fields and different moving patterns. Based on these, we obtain theory-based protocols for designing such SAW acoustofluidic particle separation chips, which are demonstrated through finite-element simulations. The results here provide theoretical guidelines for designing high throughput and high efficiency particle separation devices.

Figure 1

(a) Schematic of the particle separation chip. (b) The top view and (c) the $Y\text{−}z$ cross section.

Figure 2

Trajectories of different radii PS beads in an SSAW field of $f=13.3$ MHz, $p_1=p_2=100$ kPa and $v_{\mathrm{f}}=1.5$ mm/s. The particles enter the field at $X=0, Y={\lambda }_{\mathrm{S}}/4-{\lambda }_{\mathrm{S}}/40$.

Figure 3

The trajectories in TaSSAW fields for (a) 5-$\mu \mathrm{m}$ PS beads at different tilted angle $\theta$, and (b) particles of different radii at $\theta =9^{\circ }$. The dashed lines in panel (b) are the trajectory boundaries of the 4-$\mu \mathrm{m}$ particles.

Figure 4

Acoustophoresis of PS beads in a PM-SSAW field of $f=13.3$ MHz, $p_1=p_2=100$ kPa, and $v_{\mathrm{f}}=1.5$ mm/s. Trajectories of (a) a 5-$\mu \mathrm{m}$ particle at $\dot{\phi }=3$, 6, 9, 12, and 15 rad/s, ${\phi }_0=0$, and (b) a 2-, 3-, 4-, 5-, and 6-$\mu \mathrm{m}$ particle at $\dot{\phi }=9$ rad/s, ${\phi }_0=0$. (c) Trajectory bands (between dashed boundaries) of 3- and 5-$\mu \mathrm{m}$ particles at $\dot{\phi }=9$ rad/s, ${\phi }_0$ is randomly distributed from $-\pi$ to $\pi$.

Figure 5

Acoustophoresis of PY beads in a pSSAW field of $f=13.3$ MHz, $p_1=1$ MPa, $v_{\mathrm{f}}=1.5$ mm/s. (a) $a=1.5\mu \mathrm{m}, l=1$, 1.05, 1.1, 1.15, and 1.2. (b) $a=1$, 1.5, 2, 2.5, and 3 $\mu \mathrm{m}, l=1.1$. The black dashed lines are the trajectory boundaries for $a=1.5\mu \mathrm{m}, l=1.05$ in (a) and $a=1\mu \mathrm{m}, l=1.1$ in (b).

Figure 6

Particle separation in an SSAW field of $f=13.3$ MHz, $p_1=p_2=100$ kPa. (a) Trajectories of the 6-$\mu \mathrm{m}$ and 2-$\mu \mathrm{m}$ particles and $\mathrm{\Delta }Y$. (b) $\mathrm{\Delta }{Y}_{\mathrm{c}}$ as a function of $y_{\mathrm{c}}$. (c) Trajectories of the 6-$\mu \mathrm{m}$ and 5-$\mu \mathrm{m}$ particles and $\mathrm{\Delta }Y$.

Figure 7

The particle trajectories in a TaSSAW device (solid lines) of $\theta =9^{\circ }, \phi =0$ and a PM-SSAW (dotted lines) device of $\dot{\phi }=9.8$ rad/s and ${\phi }_0=0$.

Figure 8

Comparison between the trajectory slope differences $\mathrm{\Delta }K$ (solid lines) and the final separation distances $\mathrm{\Delta }{Y}_{\mathrm{c}}$ (dotted lines) as functions of (a) $\theta$ in TaSSAW fields and (b) $\dot{\phi }$ in PM-SSAW fields for 3- and 5-$\mu \mathrm{m}$ PS particles. $f=13.3$ MHz, $v_{\mathrm{f}}=1.5$ mm/s, $W_{\mathrm{IDT}}=9$ mm.

Figure 9

(a) Top view of the simulated fluid domain; (b) the generated TaSSAW field of $f=13.3$ MHz, $\theta =9^{\circ }, p_1=p_2=100$ kPa, and $W_{\mathrm{IDT}}=3000\mu \mathrm{m}$; and (c) the flow field with a $Y$-averaged flow velocity ${\overline{v}}_{\mathrm{f}}=1.5$ mm/s.

Figure 10

(a) FE simulated tracking of $a=2$, 3, 4, 5, 6 $\mu \mathrm{m}$ PS particles, the grayscale is the distribution of the TaSSAW field of $f=13.3$ MHz, $\theta =9^{\circ }, p_1=p_2=100$ kPa, $W_{\mathrm{IDT}}=3000\mu \mathrm{m}$, and ${\overline{v}}_{\mathrm{f}}=1.5$ mm/s; (b) comparisons between the simulated (dashed lines) and predicted (solid lines) trajectories; (c) $f, p_1$, and ${\overline{v}}_{\mathrm{f}}$ are changed to 19.97 MHz, 120 kPa, and 2 mm/s.