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Shape oscillations of particle-coated bubbles and directional particle expulsion † † Electronic supplementary information (ESI) available. See DOI: 10.1039/c6sm01603k Click here for additional data file. Click here for additional data file.

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ABSTRACT

112: Bubbles stabilised by colloidal particles can find applications in advanced materials, catalysis and drug delivery. For applications in controlled release, it is desirable to remove the particles from the interface in a programmable fashion. We have previously shown that ultrasound waves excite volumetric oscillations of particle-coated bubbles, resulting in precisely timed particle expulsion due to interface compression on a ultrafast timescale [Poulichet et al., Proc. Natl. Acad. Sci. U. S. A., 2015, , 5932]. We also observed shape oscillations, which were found to drive directional particle expulsion from the antinodes of the non-spherical deformation. In this paper we investigate the mechanisms leading to directional particle expulsion during shape oscillations of particle-coated bubbles driven by ultrasound at 40 kHz. We perform high-speed visualisation of the interface shape and of the particle distribution during ultrafast deformation at a rate of up to 104 s–1. The mode of shape oscillations is found to not depend on the bubble size, in contrast with what has been reported for uncoated bubbles. A decomposition of the non-spherical shape in spatial Fourier modes reveals that the interplay of different modes determines the locations of particle expulsion. The n-fold symmetry of the dominant mode does not always lead to desorption from all 2n antinodes, but only those where there is favourable alignment with the sub-dominant modes. Desorption from the antinodes of the shape oscillations is due to different, concurrent mechanisms. The radial acceleration of the interface at the antinodes can be up to 105–106 ms–2, hence there is a contribution from the inertia of the particles localised at the antinodes. In addition, we found that particles migrate to the antinodes of the shape oscillation, thereby enhancing the contribution from the surface pressure in the monolayer.

No MeSH data available.


Mode decomposition of shape oscillations. (a) Image analysis gives the bubble contour and centre of mass, from which the radial amplitude R(θ,t) is obtained (left). The mean radius R(t) is computed from eqn (2) (right). Scale bar: 80 μm. (b) Deviation from spherical shape, δR(θ) = R(θ) – R, for the frame shown. (c) Fourier decomposition of δR(θ), where δRn(θ) is the contribution of mode n, for the first 8 modes. (d) Deviation from spherical shape reconstructed from the sum of the first 8 modes only. (e) Maximum amplitude of the first 10 modes, showing that the three dominant modes are n = 5, 6, 7. (f) Time evolution of the mean radius R(t). The mean radius oscillates with period T = 1/f. (g) Time evolution of the amplitude of modes n = 5, 6, 7. Every second peak corresponds to the same bubble shape, consistent with subharmonic behaviour with period 2T (frequency f/2).
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fig2: Mode decomposition of shape oscillations. (a) Image analysis gives the bubble contour and centre of mass, from which the radial amplitude R(θ,t) is obtained (left). The mean radius R(t) is computed from eqn (2) (right). Scale bar: 80 μm. (b) Deviation from spherical shape, δR(θ) = R(θ) – R, for the frame shown. (c) Fourier decomposition of δR(θ), where δRn(θ) is the contribution of mode n, for the first 8 modes. (d) Deviation from spherical shape reconstructed from the sum of the first 8 modes only. (e) Maximum amplitude of the first 10 modes, showing that the three dominant modes are n = 5, 6, 7. (f) Time evolution of the mean radius R(t). The mean radius oscillates with period T = 1/f. (g) Time evolution of the amplitude of modes n = 5, 6, 7. Every second peak corresponds to the same bubble shape, consistent with subharmonic behaviour with period 2T (frequency f/2).

Mentions: Fig. 2a shows a bubble undergoing shape oscillations with a dominant n = 6 mode. The bubble's contour obtained from image analysis, overlaid on the image in Fig. 2a, gives the radial amplitude as a function of the angular coordinate, R(θ). The mean radius for the same representative frame, R, is also shown. The corresponding radial deviation from spherical shape, δR(θ) = R(θ) – R, is plotted in Fig. 2b. The Fourier transform of δR(θ) reveals the contribution of different spatial modes. The amplitudes of the first 8 modes, δRn(θ) with n = 2–8, are shown in Fig. 2c. While n = 6 is clearly the dominant mode, the amplitudes of other modes are non-negligible, particularly n = 5 and 7. Fig. 2d shows the reconstructed radial deviation, δRsum, obtained by taking the sum of the first 8 modes. The reconstructed signal satisfactorily reproduces the experimental data, indicating that modes of higher order can be safely neglected. The Fourier analysis is performed on the entire image sequence to obtain the time-dependent amplitude of each mode, δRn(θ,t). The maximum amplitude in time for each mode, An,max = max[An(t)], with An(t) defined in eqn (4), is shown in Fig. 2e. We focus on the three modes with the largest amplitudes, n = 5, 6, and 7, for the analysis of the time-dependent behaviour. Fig. 2f shows the time evolution of the mean radius, R(t). The mean radius oscillates in time as the bubble undergoes volumetric oscillations driven by the ultrasound wave. The oscillations are at the frequency of the acoustic driving, f = 40 kHz, which corresponds to a period T = 1/f = 25 μs. The observation that the oscillations are not around a constant value of the mean radius is likely due to an experimental artefact: since the bubble is not surrounded by an unbounded fluid, but is in contact with the solid wall of the sample cell, during oscillations it flattens against the wall. As a consequence, the projection of the shape in the observation plane is no longer representative of the bubble volume. Fig. 2g shows the time evolution of the mode amplitude, An, for n = 5, 6, and 7. The three modes develop at t ≈ 0.3 ms. All the modes exhibit subharmonic behaviour, as they oscillate with a period 2T, as expected.


Shape oscillations of particle-coated bubbles and directional particle expulsion † † Electronic supplementary information (ESI) available. See DOI: 10.1039/c6sm01603k Click here for additional data file. Click here for additional data file.
Mode decomposition of shape oscillations. (a) Image analysis gives the bubble contour and centre of mass, from which the radial amplitude R(θ,t) is obtained (left). The mean radius R(t) is computed from eqn (2) (right). Scale bar: 80 μm. (b) Deviation from spherical shape, δR(θ) = R(θ) – R, for the frame shown. (c) Fourier decomposition of δR(θ), where δRn(θ) is the contribution of mode n, for the first 8 modes. (d) Deviation from spherical shape reconstructed from the sum of the first 8 modes only. (e) Maximum amplitude of the first 10 modes, showing that the three dominant modes are n = 5, 6, 7. (f) Time evolution of the mean radius R(t). The mean radius oscillates with period T = 1/f. (g) Time evolution of the amplitude of modes n = 5, 6, 7. Every second peak corresponds to the same bubble shape, consistent with subharmonic behaviour with period 2T (frequency f/2).
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Related In: Results  -  Collection

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fig2: Mode decomposition of shape oscillations. (a) Image analysis gives the bubble contour and centre of mass, from which the radial amplitude R(θ,t) is obtained (left). The mean radius R(t) is computed from eqn (2) (right). Scale bar: 80 μm. (b) Deviation from spherical shape, δR(θ) = R(θ) – R, for the frame shown. (c) Fourier decomposition of δR(θ), where δRn(θ) is the contribution of mode n, for the first 8 modes. (d) Deviation from spherical shape reconstructed from the sum of the first 8 modes only. (e) Maximum amplitude of the first 10 modes, showing that the three dominant modes are n = 5, 6, 7. (f) Time evolution of the mean radius R(t). The mean radius oscillates with period T = 1/f. (g) Time evolution of the amplitude of modes n = 5, 6, 7. Every second peak corresponds to the same bubble shape, consistent with subharmonic behaviour with period 2T (frequency f/2).
Mentions: Fig. 2a shows a bubble undergoing shape oscillations with a dominant n = 6 mode. The bubble's contour obtained from image analysis, overlaid on the image in Fig. 2a, gives the radial amplitude as a function of the angular coordinate, R(θ). The mean radius for the same representative frame, R, is also shown. The corresponding radial deviation from spherical shape, δR(θ) = R(θ) – R, is plotted in Fig. 2b. The Fourier transform of δR(θ) reveals the contribution of different spatial modes. The amplitudes of the first 8 modes, δRn(θ) with n = 2–8, are shown in Fig. 2c. While n = 6 is clearly the dominant mode, the amplitudes of other modes are non-negligible, particularly n = 5 and 7. Fig. 2d shows the reconstructed radial deviation, δRsum, obtained by taking the sum of the first 8 modes. The reconstructed signal satisfactorily reproduces the experimental data, indicating that modes of higher order can be safely neglected. The Fourier analysis is performed on the entire image sequence to obtain the time-dependent amplitude of each mode, δRn(θ,t). The maximum amplitude in time for each mode, An,max = max[An(t)], with An(t) defined in eqn (4), is shown in Fig. 2e. We focus on the three modes with the largest amplitudes, n = 5, 6, and 7, for the analysis of the time-dependent behaviour. Fig. 2f shows the time evolution of the mean radius, R(t). The mean radius oscillates in time as the bubble undergoes volumetric oscillations driven by the ultrasound wave. The oscillations are at the frequency of the acoustic driving, f = 40 kHz, which corresponds to a period T = 1/f = 25 μs. The observation that the oscillations are not around a constant value of the mean radius is likely due to an experimental artefact: since the bubble is not surrounded by an unbounded fluid, but is in contact with the solid wall of the sample cell, during oscillations it flattens against the wall. As a consequence, the projection of the shape in the observation plane is no longer representative of the bubble volume. Fig. 2g shows the time evolution of the mode amplitude, An, for n = 5, 6, and 7. The three modes develop at t ≈ 0.3 ms. All the modes exhibit subharmonic behaviour, as they oscillate with a period 2T, as expected.

View Article: PubMed Central - PubMed

ABSTRACT

112: Bubbles stabilised by colloidal particles can find applications in advanced materials, catalysis and drug delivery. For applications in controlled release, it is desirable to remove the particles from the interface in a programmable fashion. We have previously shown that ultrasound waves excite volumetric oscillations of particle-coated bubbles, resulting in precisely timed particle expulsion due to interface compression on a ultrafast timescale [Poulichet et al., Proc. Natl. Acad. Sci. U. S. A., 2015, , 5932]. We also observed shape oscillations, which were found to drive directional particle expulsion from the antinodes of the non-spherical deformation. In this paper we investigate the mechanisms leading to directional particle expulsion during shape oscillations of particle-coated bubbles driven by ultrasound at 40 kHz. We perform high-speed visualisation of the interface shape and of the particle distribution during ultrafast deformation at a rate of up to 104 s–1. The mode of shape oscillations is found to not depend on the bubble size, in contrast with what has been reported for uncoated bubbles. A decomposition of the non-spherical shape in spatial Fourier modes reveals that the interplay of different modes determines the locations of particle expulsion. The n-fold symmetry of the dominant mode does not always lead to desorption from all 2n antinodes, but only those where there is favourable alignment with the sub-dominant modes. Desorption from the antinodes of the shape oscillations is due to different, concurrent mechanisms. The radial acceleration of the interface at the antinodes can be up to 105–106 ms–2, hence there is a contribution from the inertia of the particles localised at the antinodes. In addition, we found that particles migrate to the antinodes of the shape oscillation, thereby enhancing the contribution from the surface pressure in the monolayer.

No MeSH data available.