Size Control of Sessile Microbubbles for Reproducibly Driven Acoustic Streaming

Acoustically actuated bubbles are receiving growing interest in microfluidic applications, as they induce a streaming field that can be used for particle sorting and fluid mixing. An essential but often unspoken challenge in such applications is to maintain a constant bubble size to achieve reproducible conditions. We present an automatized system for the size control of a cylindrical bubble that is formed at a blind side pit of a polydimethylsiloxane microchannel. Using a pressure control system, we adapt the protrusion depth of the bubble into the microchannel to a precision of approximately $0.5\mu \mathrm{m}$ on a timescale of seconds. By comparing the streaming field generated by bubbles of width $80\mu \mathrm{m}$ with a protrusion depth between $-12$ and $60\mu \mathrm{m}$, we find that the mean velocity of the induced streaming fields varies by more than a factor of 4. We also find a qualitative change of the topology of the streaming field. Both observations confirm the importance of the bubble size control system in order to achieve reproducible and reliable bubble-driven streaming experiments.

Figure 1

(a) System for automatized bubble control. A PDMS microchannel of width $W$, height $H$, and length $L$ is filled with liquid (PDMS in green, liquid in blue). A side pit, of width $w$ and length $l$, contains air forming a cylindrical bubble. A camera observes the bubble interface through a microscope (yellow square). The bubble protrusion depth $d$ [see (b)] is detected from the recorded images. A PID algorithm compares $d$ with the target protrusion depth $d_t$ and adapts the bubble by adjusting the pressure in the channel with a pressure controller. (b) Sketch of the cylindrical bubble with protrusion depth $d$, radius $R$, and half-width $a=w/2$ of the side pit. (c) Typical streaming pattern of an acoustically actuated cylindrical bubble (2D projection; streamlines deduced from experimental results). Depending on the actuation frequency, different modes of bubble oscillations can be induced (here, the dominant first mode in red).

Figure 2

Measured protrusion depth $d$ of the bubble and target protrusion depth $d_t$ as a function of time $t$. $d_t$ is changed discretely to observe the response of $d$ when being controlled by the PID algorithm. Within a typical time of approximately 10 s, which is limited by the response time of the system, the bubble adapts to the target value with a standard deviation of approximately $0.01a$, corresponding to submicrometer precision. The images on top of the figures represent the shape of the bubble in the five time domains after stabilizing. (a) Automatized size control of a bubble in the stable regime (see Sec. 3). The inset shows an enlarged view of the stabilized bubble at $d=0.5a$. Using Gaussian fitting, the bubble is detected with a resolution of $0.002a$. (b) Automatized size control of a bubble in the unstable regime.

Figure 3

Young-Laplace pressure $p_{\mathrm{surf}}$ as a function of the protrusion depth $d$ of a cylindrical bubble in a PDMS channel that is filled with water. For $d\le d_1$, the liquid-gas interface is pinned to the leading edges of the side pit, and the bubble pressure follows Eq. (3). For $d\ge d_1$, the bubble is growing while keeping its shape, and the bubble pressure can be expressed with Eq. (4). The inset shows the measured receding contact angle ${\theta }_r\approx 85°$ and advancing contact angle ${\theta }_a\approx 102°$ at a straight wall of the used PDMS channel using an aqueous glycerol solution (23.8% w/w glycerol).

Figure 4

Measured streaming flows of cylindrical microbubbles at an actuation frequency $f=21.8\mathrm{kHz}$. Pink lines indicate the bubble interfaces. Measurements are performed using particle-tracking velocimetry [20]. (a) Small protrusion depth $d=0.21a$ of a bubble into the main channel. The streaming pattern shows two counterrotating vortices. The maximum streaming velocity is approximately $3\mathrm{mm}/\mathrm{s}$. (b) Intermediate protrusion depth $d=0.67a$ of a bubble into the main channel. The streaming pattern shows two counterrotating vortices. The streaming velocity is slightly higher than for a small protrusion depth. (c) Large protrusion depth $d=1.36a$ of a bubble into the main channel. The streaming velocity is lower than for other investigated flows. Besides the two main vortices, two additional vortices appear at $x=0$.

Figure 5

Average velocity $v_{\mathrm{avg}}$ of particles in the field of view as a function of the protrusion depth of the bubble $d$. The nonmonotonic behavior of $v_{\mathrm{avg}}$ can be divided into three different regimes. In regime $\mathrm{I}$ ($d<0a$), the bubble is within the side pit. The average particle velocity is low, and several small vortical structures are observed. In regime II ($0a<d<0.9a$), two strong and large counterrotating vortices are observed, and the average particle velocity is increasing up to its highest value at $d_p\approx 0.4a$. Regime III ($d>0.9a$) can be characterized by two main flow vortices at high absolute $x$ values. Additionally, two small vortices appear in the center at small absolute values of $x$ (see also Fig. 4).

Figure 6

Flow velocity measured with tracer particles of diameter $2.24\mu \mathrm{m}$ as a function of the distance from the vortex center $r_v$. (a) Sketch of lines along which the velocity profile is measured. Starting from the vortex center ($r_v=0$), the flow velocity is measured radially outwards along lines orthogonal to streamlines. Profiles are determined by taking the mean of the two symmetric measurements. (b) Flow velocity profiles for different protrusion depths $d$ of the bubble. A similar exponential decay is observed for all investigated bubble sizes with a power-law exponent of $-0.016$. In agreement with Fig. 5, the highest flow velocities are found for protrusion depths in the range $0.2a-0.6a$.