Comparative study of the dynamics of laser and acoustically generated bubbles in viscoelastic media

Experimental observations of the growth and collapse of acoustically and laser-nucleated single bubbles in water and agarose gels of varying stiffness are presented. The maximum radii of generated bubbles decreased as the stiffness of the media increased for both nucleation modalities, but the maximum radii of laser-nucleated bubbles decreased more rapidly than acoustically nucleated bubbles as the gel stiffness increased. For water and low stiffness gels, the collapse times were well predicted by a Rayleigh cavity, but bubbles collapsed faster than predicted in the higher stiffness gels. The growth and collapse phases occurred symmetrically (in time) about the maximum radius in water but not in gels, where the duration of the growth phase decreased more than the collapse phase as gel stiffness increased. Numerical simulations of the bubble dynamics in viscoelastic media showed varying degrees of success in accurately predicting the observations.

Figure 1

Schematic drawing of the experimental setup, top-down view. Gel samples were lowered into the transducer from above (into the page).

Figure 2

Visualization of the multiflash imaging technique with timing diagrams of the variable flash sequences used during each phase of the bubble's evolution with example images.

Figure 3

Example images showing single bubbles generated using laser and acoustic nucleation mechanisms in: (a) water, (b) 0.3% agarose gel $\left(E=1.13\mathrm{kPa}\right)$, and (c) 2.5% agarose gel $\left(E=242\mathrm{kPa}\right)$. Asterisks mark frames outside of the bubbles primary lifetime which were not included in the analysis of the data. Crosses mark frames containing multiple flashes from the light source. The horizontal stripes observed in images are camera artifacts.

Figure 4

Mean and standard deviations of bubble maximum radii vs. gel stiffness. The horizontal gray bars show the standard deviations of the maximum radii of the bubbles nucleated in water. The number of samples associated with each data point are shown in Fig. 5.

Figure 5

Normalized $R\left(t\right)$ curves of single bubbles nucleated in water and agarose gels via laser and acoustic mechanisms. The measured values of $R_m$ were used to individually normalize the experimental $R\left(t\right)$ curves. $t_c$ is the cavity collapse time in a fluid, given by $t_c=0.9148R_m\sqrt{\rho /P_{\infty }}$. The experimentally measured $R\left(t\right)$ curves were temporally aligned with respect to their collapses. All adjustments were bounded to within the temporal resolution error of the image containing $R_m$. The unlabeled gray “x”s in the plots show the measured $R\left(t\right)$ curves from the plots in the opposite column, i.e., in the “Laser-Nucleated” column the “x”s show the data from the plots in the “Acoustically Nucleated” column and vice versa. The value, $N$, in each plot corresponds to the number of cavitation events in each sample set that were measured to meet the inclusion criteria for this study. Note also that all radii captured in the image frame associated with collapse were included as data points in these plots. As such, the rising “tails” observed at later times, though made up of points captured in the frame associated with collapse, may represent the earliest portion of the first rebound.

Figure 6

Initial radii of bubbles returned from simulations and the previously reported pore sizes of agarose as a function of agarose gel concentration. Simulation results show the initial radii in simulations which produced the best agreement with the measured values ${\overline{R}}_m\pm \mathrm{std}\left(R_m\right)$ at each gel concentration. The data points and scaling relationship curve from Ref. [57] show the pore sizes of agarose gels in that study which were prepared following procedures in closest agreement with those in the present study. The shaded region shows the bounds of the scaling relationship in Ref. [57] for gels which were allowed to solidify at temperatures from ${15}^{\circ }\mathrm{C}$ to ${35}^{\circ }\mathrm{C}$.