Experimental measurement of interparticle acoustic radiation force in the Rayleigh limit

Acoustophoresis is a form of contact-free particle manipulation in microfluidic devices. The precision of manipulation can be enhanced with better understanding of the acoustic radiation force. In this paper we present the measurements of interparticle radiation force between a pair of polystyrene beads in the Rayleigh limit. The study is conducted for three different sizes of beads and the experimental results are of the same order of magnitude when compared with theoretical predictions. However, the experimental values are larger than the theoretical values. The trend of a decrease in the magnitude of the interparticle radiation force with decreasing particle size and increasing center-to-center distance between the particles is also observed experimentally. The experiments are conducted in the specific scenario where the pair of beads are in close proximity, but not in contact with each other, and the beads are approaching the pressure nodal plane with the center-to-center line aligned perpendicular to the incident wave. This scenario minimizes the presence of the primary radiation force, allowing accurate measurement of the interparticle force. The attractive nature of the interparticle force is observed, consistent with theoretical predictions.

Figure 1

(a) Schematic of the experimental setup: (1) computer, (2) syringe, (3) syringe pump, (4) microscope, (5) CCD, (6) valve, (7) waste flask, (8) signal generator, (9) amplifier, (10) oscilloscope, (11) multimeter, (12) light source, (13) microfluidic device, (14) temperature control unit, and (15) thermistor. (b) Laboratory setup for the acoustophoretic experiment [23].

Figure 2

Schematic of the microspheres at different excitation frequencies inside the channel: (a) 1.875 MHz and (b) 2.475 MHz [23]. The arrows indicate the direction of the radiation force.

Figure 3

Primary radiation force components on particles due to plane standing wave. Here ${\overline{\mathbf{F}}}_y^P$ (red arrow) is the nominal primary radiation force along the incident wave direction of the $y$ axis. The perturbations in primary radiation force (${\tilde{\mathbf{F}}}_{xz}^P$ in the transverse plane $x-z$ and ${\tilde{\mathbf{F}}}_y^P$ along the $y$ axis) due to the nonuniformity of the acoustic energy density are indicated by green arrows [23].

Figure 4

Schematic of the scattered field from a suspended sphere in the fluid [23].

Figure 5

Schematic of induced flow through the Stokeslet and the potential dipole due to a concentrated force acting on a translating sphere in the fluid domain [23].

Figure 6

Free body diagrams of the individual beads approaching the pressure node.

Figure 7

Experimental observations of a pair of $7.81-\mu \text{m}$ polystyrene beads (first observation of pair 4 of $7.81-\mu \text{m}$ beads): (a) snapshots of the bead trajectory during the experiment, (b) trajectories of the two beads coming together on the $x-y$ plane, (c) center-to-center distance, (d) $x$ trajectories, and (e) $y$ trajectories.

Figure 8

Experimental observations of a pair of $9.9-\mu \mathrm{m}$ polystyrene beads (second observation of pair 5 of $9.9-\mu \mathrm{m}$ beads) [23]: (a) snapshots of the bead trajectory during the experiment, (b) trajectories of the two beads coming together on the $x-y$ plane, (c) center-to-center distance, (d) $x$ trajectories, and (e) $y$ trajectories.

Figure 9

Experimental observations of a pair of $12.32-\mu \text{m}$ polystyrene beads (first observation of pair 3 of $12.32-\mu \text{m}$ beads): (a) snapshot of the bead trajectory during the experiment, (b) trajectories of the two beads coming together on the $x-y$ plane, (c) center-to-center distance, (d) $x$ trajectories, and (e) $y$ trajectories.

Figure 10

Normalized interparticle radiation force $F_r^s/E_{\text{ac}}{a}^2$ with respect to the normalized center distance $r/a$ between two equal-size polystyrene beads: (a) a pair of 7.81-$\mu \mathrm{m}$ polystyrene beads, (b) a pair of 9.9-$\mu \mathrm{m}$ polystyrene beads, and (c) a pair of 12.32-$\mu \mathrm{m}$ polystyrene beads. Theoretical-1 and Theoretical-2 refer to an analytical formula by Silva and Bruus [17] and a numerical simulation similar to that of Sepehrirahnama et al. [18], respectively.

Figure 11

Comparison of the interparticle radiation force across three different sizes of beads with the theoretical results. Theoretical-1 and Theoretical-2 refer to an analytical formula by Silva and Bruus [17] and a numerical simulation similar to that of Sepehrirahnama et al. [18], respectively.

Figure 12

Comparison of the interparticle radiation force with ($F_r^s$) and without ($F_r^{s*}$) hydrodynamic interaction for different pairs of beads.