Three-Dimensional Phenomena in Microbubble Acoustic Streaming

Ultrasound-driven oscillating microbubbles are used as active actuators in microfluidic devices to perform manifold tasks such as mixing, sorting, and manipulation of microparticles. A common configuration consists of side bubbles created by trapping air pockets in blind channels perpendicular to the main channel direction. This configuration consists of acoustically excited bubbles with a semicylindrical shape that generate significant streaming flow. Because of the geometry of the channels, such flows are generally considered as quasi-two-dimensional. Similar assumptions are often made in many other microfluidic systems based on flat microchannels. However, in this Letter we show that microparticle trajectories actually present a much richer behavior, with particularly strong out-of-plane dynamics in regions close to the microbubble interface. Using astigmatism particle-tracking velocimetry, we reveal that the apparent planar streamlines are actually projections of a stream surface with a pseudotoroidal shape. We, therefore, show that acoustic streaming cannot generally be assumed as a two-dimensional phenomenon in confined systems. The results have crucial consequences for most of the applications involving acoustic streaming such as particle trapping, sorting, and mixing.

Figure 1

Typical experimental setup. Left: The PDMS channel and the piezoelectric actuator are bonded to a glass slide. Right: Top view of the semicylindrical bubble in the microchannel and visualization of the acoustic streaming flow through different experimental particle trajectories.

Figure 2

Trajectories of four different particles. Top left: Projection of particles’ trajectories in the $XY$ plane. Top right: Orthographic projection of the particle trajectories. Bottom: Projection of particles’ trajectories in the $XZ$ plane. The symmetry planes (midplane or transverse plane at $z=0$ and sagittal plane at $x=0$) are clearly visible in the figure. A third plane of symmetry (coronal plane at $y=0$) should appear for perfectly cylindrical bubbles. Instead, our system allocates the channel wall at that position, altering the global symmetry of the system.

Figure 3

Detail of a typical particle trajectory. The green and blue paths depict, respectively, the inner and outer particle loops, in which the particle travels, respectively, away from and towards the midplane $z=0$. Left: Projection of the particle in the $ZX$ plane (top) and in the $XY$ plane (bottom). Top right: Particle vertical distance from the system’s midplane $z=0$; notice the jumps that the particle performs when closely approaching the bubble’s surface. The red discontinuous line shows the results from simulations. Bottom right: Radial distance $r=\sqrt{x^2+y^2}$ from the bubble’s symmetry axis in time.

Figure 4

Particle velocity distributions. Top: Off-plane velocity component $V_z$; note that they only become significant in the vicinity of the bubble’s surface. The arcs drawn in the top left figure represent the section plotted in the top right plot. Middle: Azimuthal velocity component $V_{\theta }$. Bottom: Radial velocity $V_r$ with maximum values at the sagittal plane and at approximately $\theta =30°$ (bottom right plots).