Introduction

Beyond its decorative value in jewelry and intrinsic economic reliability throughout human history, gold is important in many industries including electronics, aerospace and biomedicine. By current estimates, 64 kt of gold remains in mineable natural reserves1. Based on the average annual output of 3.6 kt over the past decade2, the known mineable gold reserves are expected to run out within the next 20 years. In addition to mining, 1.2 kt of gold is sourced from recycled products each year, of which e-waste constitutes less than 5%3. In 2022, from the documented 62 000 kt of produced e-waste, less than 25% was collected and recycled4. While printed circuit boards constitute only a fraction of e-waste, they are appealing for recycling due to their high content of rare and precious metals (RPMs). Compared to mined ore, the concentration of gold in PCBs is 400–800 times higher3. Although gold accounts for merely 0.02% of the weight of PCBs, it constitutes 50% of the raw materials cost, as reported in a 2020 study5. Gold in PCBs is predominantly used on the surface of edge connectors due to its corrosion resistance and high electrical conductivity.

PCB recycling is mostly done with traditional methods, comprising a combination of mechanical, pyro-, and hydrometallurgical processes. PCBs typically first undergo manual disassembly and crushing/shredding, followed by the removal of non-metallic substances by incineration (pyrometallurgy), and finally the remaining metals are separated through multiple phases of chemical leaching (hydrometallurgy)6. While effective for RPM recovery, these traditional methods are energy intensive and taxing to the environment, involving harmful emissions and toxic byproducts7,8,9,10. Alternative greener methods are being developed, including bioleaching, electrochemical technology, ionic liquid technology, supercritical fluid technology, and mechanochemical technology11. Currently these emerging technologies remain limited in either RPM recovery rates or economic viability.

This paper expands on a recently reported novel green technology for gold recovery from intact PCBs12. The method employs high-intensity focused ultrasound (HIFU) in water to mechanically remove gold from the surface of edge connectors. The gold removal relies on imploding cavitation bubbles formed at the focus of a high-intensity acoustic field. By employing MHz-range HIFU, cavitation can be spatially confined to a small focal volume whose width is comparable with gold-plated connector pads. Because the method selectively targets the surface gold on connector pads, it can be directly applied to intact PCBs. Here the gold removal efficiency is significantly improved, contributing to the ongoing progress towards industrial viability. The approach towards efficiency improvement is guided by existing literature in the medical field, where HIFU applications are well-documented.

Eroding surfaces with HIFU-induced cavitation is an established technology in the medical field, where it is used for noninvasive comminution of kidney stones (lithotripsy) and ablation of tissue (histotripsy)13. Beyond the medical field, applications of HIFU-induced cavitation have been little explored. One reported application involves using HIFU to break down biological samples in water for DNA extraction14,15. Two distinct HIFU applications were also demonstrated in previous work: controlled surface machining of aluminum16 and a non-contact surface sampling technique17. While the dynamics of single-bubble cavitation is understood, HIFU involves the formation and subsequent collapse of bubble clusters (cloud cavitation) within the focal volume of the acoustic field. Over the past decade, experiments and simulations have unveiled complex phenomena related to cloud cavitation-induced erosion, including e.g., high-pressure secondary rebound shockwaves, the deviation of cloud resonant frequency from its natural frequency, and the interplay between acoustic pressure, frequency, cloud and bubble size, gas volume fraction and stand-off distance of the initial bubble cloud18. Despite impressive progress, the interplay of the complex dynamics associated with cloud cavitation-induced erosion remains to be fully resolved. For instance, there is ambiguity in whether cloud collapse propagates inward in an amplifying manner, or if outer bubbles shield inner ones from the incident pressure waves that induce collapse – the dynamics of which depend on the acoustic field and initial conditions of the cloud and its constituent bubbles.

For single bubbles, the pressure threshold for onsetting cavitation decreases with frequency19. Qualitatively this can be understood as lower frequencies imparting a longer bubble growth time during the rarefaction phase, resulting in a larger maximum bubble radius and a more energetic collapse20. In focused acoustic fields, higher frequencies (shorter wavelengths) undergo less diffraction, resulting in more confined focal beams, i.e., higher focusing gains. Cloud-cavitation HIFU experiments have shown that bubble density increases and bubble size decreases with increasing frequency21, which agrees with the aforementioned observations on single-bubble dynamics and focused fields. While high frequencies increase focusing gain and low frequencies reduce the cavitation threshold, the collapse energy of a cavitation bubble ultimately depends on its maximum size. It is therefore expected that lower frequencies are preferable for HIFU-induced cavitation erosion due to both a lower cavitation threshold, and a prolonged bubble expansion phase.

In HIFU applications, nonlinear acoustics plays an important role. As waves propagate towards the focus and the acoustic intensity increases, the propagating waveform becomes distorted through harmonic generation22. In experiments the focal acoustic field should be characterized, since it drives cavitation cloud formation and dynamics – and by extension the ensuing cavitation erosion. The focal pressure field cannot be directly measured since cavitation bubbles impede the incident pressure waves from reaching the sensing element (hydrophone). Instead, the focal pressure field can be resolved by nonlinear transient acoustic holography, which involves measuring the pressure waveforms across a plane between the transducer and its focus, and numerically propagating the waveforms to the focus, taking into account cumulative nonlinearity arising from the increasing acoustic intensity23,24.

In this paper the gold removal efficiency of a novel green e-waste recycling method is improved, indicating progress towards industrial relevance. Improvement is achieved by experiments, whereby the effect of acoustic frequency on the removal efficiency of gold from PCB edge connectors is investigated. Three custom-built transducers, with identical geometries and different resonant frequencies, 4.2 MHz, 7.3 MHz, and 11.8 MHz, were used to first image the PCB at low power to locate the gold, then driven at high power to remove it. A schematic illustration of the experimental concept is provided in Fig. 1, showing the focused ultrasound exposure and the resulting cavitation activity at the sample surface. Because the target PCB used here differs from that in our previous study, direct quantitative comparison of the two works is problematic. As such, the present work focuses solely on frequency-dependent trends observed within this study. Within the tested frequency range, gold removal efficiency increased as the excitation frequency decreased. Finally, the acoustic field of each transducer is resolved using nonlinear transient acoustic holography to better understand their erosion capabilities.

Fig. 1
figure 1

Conceptual schematic of experimental method. A focused ultrasound transducer irradiates the PCB surface, where a cavitation cloud develops within the focal region and drives localized gold removal.

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Methods

Experimental setup

A schematic of the experimental setup is shown in Fig. 2. A PCB sample with gold-plated edge connectors was submerged in de-ionized water (RiOs Essential Water Purification Systems, Milli-Q, Germany). The water was degassed for 1 h prior to HIFU experiments to maintain comparable gas concentrations between experiments, which could otherwise introduce uncontrolled differences in cavitation inception and behaviour between sonications. A custom-built HIFU transducer was mounted to a 3-axis motorized linear stage. Three transducers with different resonant frequencies were used, each comprising an epoxy-backed bowl-shaped piezo (Type Pz26, \(\:{f}_{c}\) = [4.2, 7.3, 11.8] MHz, Ø = 19 mm, \(\:R\) = 15 mm, CTS Ferroperm, Denmark) in a 3D-printed housing, and electrically matched to 50 Ω with LC matching circuits. Excitation signals were produced with a signal generator and amplified with a Class A RF amplifier (500A100A, Amplifier Research, USA). The excitation signal and received echoes were monitored with a digital oscilloscope.

Fig. 2
figure 2

Schematic of the experimental setup.

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A photo of the target PCB is shown in Fig. 3a. The thickness of the edge connector layers (1.6 μm gold on 1.9 μm nickel) was characterized by Rutheford backscattering spectroscopy using a 3 MeV proton beam. To locate the gold pads, the sample was imaged with each transducer using Gaussian amplitude-modulated linear chirps (relative bandwidth 24%). Example amplitude maps are shown in Fig. 3b. High-amplitude echoes from the connectors are distinguishable from the low-amplitude echoes from the epoxy-fiberglass substrate for all transducers.

Fig. 3
figure 3

(a) Photo of the target PCB, (b) Amplitude maps of the PCB sample produced with different transducers, showing high amplitude from gold and low amplitude from epoxy-fiberglass substrate.

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Characterizing removed gold

The removed gold volume was quantified from optical microscope images. The resolution of the images was calibrated to (1.4 × 1.4) µm2/pixel with a calibration target (1951 USAF Resolution Test Targets, Ø = 1”, Thorlabs, USA). The erosion areas were extracted from the images using an automated segmentation script written in MATLAB. The algorithm identifies gold-depleted regions based on local colour variations and converts them into binary masks, from which areas were computed. All detected contours were visually inspected for each image to ensure correct segmentation of the eroded regions. The calculated areas were then converted to volumes by multiplication with the measured gold thickness. Uncertainty in the removed gold volume thus arises from the repeat-to-repeat variability in the erosion area, pixel-resolution and boundary discretization effects in the binary masks, and the measured thickness of the gold layer. The standard deviation of the three repeated measurements, caused by the stochasticity of cavitation, is the dominant uncertainty source, with minor contributions from random errors from segmentation noise and pixel-level discretization. The pixel resolution and typical erosion-spot dimensions imply a discretization uncertainty in the order of a few percent in area, which is small compared to the observed repeat variability. The gold layer thickness contributes a systematic uncertainty, comprising a relative error of approximately 2.5%.

Gold removal

Two sets of gold removal experiments were conducted. The optimal transducer-sample distance for each transducer was first identified with a sequence of sonications. At the optimal distance for each transducer, a sequence of sonications with a varying number of bursts was then performed to evaluate gold removal efficiency. Control sonications with 5 × 106 bursts were also performed at excitation voltages that did not exceed the cavitation threshold, as verified from monitored echoes. No measurable erosion was observed under these conditions.

Transducer-sample distance optimization

Based on preliminary experiments, an appropriate range and increment of transducer-sample distances, and sonication parameters were selected. For each transducer the focus, from which the largest amplitude echo was received, served as the reference zero-position. Positive (negative) distances imply retracting (approaching) the transducer away from (towards) the PCB surface. The range of distances and steps for each transducer were: ±1400 μm at 200 μm steps for 4.2 MHz, (­−600 to +2200) µm at 200 μm steps for 7.3 MHz, and (­−500 to +900) µm at 100 μm steps for 11.8 MHz. The transducers were driven with a peak-to-peak excitation voltage of Upp = 430 V, and the resultant pressure fields were determined using acoustic nonlinear transient holography. Other sonication parameters were the same for all frequencies: 0.5 × 106 bursts, 50 cycles, and 500 Hz pulse-repetition-frequency (PRF).

Removal efficiency optimization

To compare the removal efficiency, sets of sonications were performed with different burst counts. Based on the transducer-sample distance optimization experiments, sonications for each transducer were conducted at the transducer-sample distance yielding the largest gold removal volume. Sonication parameters were kept constant between transducers: Upp = 430 V, 50 cycles, 500 Hz PRF, and burst counts ranging from (0.1–1.9) × 106 at steps of 0.2 × 106. These sonications were repeated three times, randomizing the order of burst count values to prevent systematic drift in either temperature or gas content from influencing the results.

Acoustic field characterization

Direct pressure measurements in the focal volume are obscured by the presence of cavitation bubbles. Therefore, a transient nonlinear acoustic holography numerical method, adapted from Jing et al.23, was implemented in MATLAB. For each transducer, pressure waveforms were measured in the nearfield across a plane perpendicular to the acoustic axis. The measured waveforms were then numerically propagated with a stepping algorithm, derived from the Westervelt equation:

$$\:\begin{array}{*{20}c} {P\left( {z + \Delta z} \right) = P\left( z \right){\text{exp}}\left( {iK\Delta z} \right) + \frac{{\beta \omega ^{2} }}{{2i\rho _{0} c_{0}^{4} K}}P\left( z \right){\text{exp}}\left( {K\Delta z} \right) \otimes P\left( z \right)exp\left( {K\Delta z} \right)\Delta z} \\ \end{array}$$
(1)

Where \(\:P\) is the 3D Fourier transform of pressure, \(\:{\Delta\:}z\) the propagation step, \(\:K\) the dispersion relation (\(\:K={\omega\:}^{2}/{c}_{0}^{2}-{k}_{x}^{2}-{k}_{y}^{2}-i\delta\:{\omega\:}^{3}/{c}_{0}^{4}\), where \(\:{k}_{x}\) and \(\:{k}_{y}\) are the wave vector components, and \(\:\delta\:\) the sound diffusivity), \(\:\beta\:\) the nonlinearity parameter (\(\:\beta\:=1+B/2A\), where \(\:A\) and \(\:B\) are the coefficients of the linear and quadratic terms in the Taylor expansion of pressure as a function of density), \(\:\omega\:\) the angular frequency, \(\:{\rho\:}_{0}\) the ambient density, \(\:{c}_{0}\) the speed of sound, and \(\otimes\) is the convolution operator (with respect to \(\:{k}_{x},{k}_{y},\omega\:\)). In place of physical sound diffusivity22, a small artificial diffusivity (larger than the physical sound diffusivity) was needed to reduce the Gibbs effect, serving as a low-pass filter to counter the accumulation of high-frequency noise and maintain stability of the numerical simulation24,25. For each frequency, the diffusivity was incrementally increased until stable results were obtained. The diffusivities used were 8∙10­4 m2/s for 4.2 MHz, 3∙10­4 m2/s for 7.3 MHz and 2∙10­4 m2/s for 11.8 MHz. Pressure measurements were conducted 5 mm above the transducer focus with a fiberoptic hydrophone (HFO-690 [Ø = 100 μm], ONDA, USA), across a (10 × 10) mm2 plane with a step size of 25 μm. Recorded voltage signals were deconvolved with the hydrophone sensitivity using a custom MATLAB script.

Results

Acoustic field characterization

The average focal radial-pressure-amplitude profiles for the three transducers, obtained by nonlinear acoustic holography, are presented in Fig. 4. Relevant geometric dimensions of the profiles are indicated in the figure: the positive (FWHM+) and negative (FWHM−) full-width half-maxima and the distance between the first side-lobe maxima (DSLM). As expected, all these dimensions decrease with increasing frequency; high frequencies undergo less diffraction than low frequencies, leading to a narrower focal beam width. While the focal maximum pressure increases from 4.2 MHz (152 MPa) to 11.8 MHz (187 MPa), it is smallest for 7.3 MHz (107 MPa). An increase in maximum pressure would be expected for higher frequencies due to tighter focusing and higher harmonic generation. The same discrepancy for 7 MHz is observed for the focal minimum pressures: ­40 MPa for 4 MHz, ­25 MPa for 7 MHz and ­35 MPa for 12 MHz. The ratio of focal maximum to side-lobe maximum gives an indication of the degree of focusing, a higher value indicating that a larger fraction of acoustic energy resides in the focal beam. These ratios for 4.2 MHz, 7.3 MHz, and 11.8 MHz were 9.8, 3.9 and 16.4, respectively. For 7.3 MHz more energy is deposited in the sidelobes, which accounts for the lower magnitude of the focal maximum and minimum values.

Fig. 4
figure 4

Average focal radial positive (red) and negative (blue) pressure amplitude profiles for the three transducers, obtained by nonlinear transient acoustic holography. The positive (FWHM+) and negative (FWHM−) full-width half-maxima, and the distance between the first side-lobe maxima (DSLM) are shown. FWHM+, FWHM−, and DSLM decrease with increasing frequency due to reduced diffraction at higher frequencies. The maximum pressure, and the ratio between the maximum pressure and side-lobe maxima, is highest for 11.8 MHz, indicating a higher focusing gain.

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Transducer-sample distance optimization

Optical microscope images and the calculated removed gold volumes for different defocusing distances are presented in Figs. 5 and 6. The defocus is defined as the offset from the transducer-sample distance at which a maximal echo amplitude is observed. Both figures show that gold removal increases progressively to a maximum near the focus (the distance at which recorded echo is maximized), after which the removal tapers off. Two calculated erosion volumes are shown in Fig. 6: the largest volume is calculated from the largest individual erosion area at each position (top), and the total volume is calculated from the sum of the largest erosion area and any smaller peripheral removal areas (bottom). For all frequencies most gold was removed at a slight positive defocus. This result is in agreement with previous work, where it was shown that most effective stone comminution with HIFU was obtained at a slight positive defocus, corresponding to a region where the (ellipsoidal) acoustic beam at the stone surface is widest26. Optimal defocuses for removal were selected as: +200 μm, + 500 μm and + 200 μm for 4.2 MHz, 7.3 MHz and 11.8 MHz, respectively.

Fig. 5
figure 5

Optical microscope images of removed gold at different transducer-sample distances for the three transducers. Colours represent the true appearance of the sample: the intact gold layer appears gold and gold-depleted regions appear silver due to exposed nickel. The focus of each transducer, defined as the position at which the recorded echo is maximized, is indicated with red borders. No values are given for the defocus distances due to differing step sizes between frequencies (200 μm for 4.2 MHz and 7.3 MHz, and 100 μm for 11.8 MHz). Removal increases with transducer-sample distance up to a maximum (indicated with blue borders), after which removal tapers off. For all frequencies maximal removal is observed slightly beyond the focus (Fig. 6).

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Fig. 6
figure 6

Removed gold volume as function of defocus. The largest volume (top) is calculated from the single largest continuous removed gold area, and the total volume (bottom) from the sum of all removed gold areas. For all frequencies, the volumes are normalized to their respective maximum. For all frequencies maximum removal is observed above the focus, around which removal tapers off. For 4.2 MHz significant removal in total volume is observed also at negative defocuses, owing to dispersed small removal spots. Asterisks (*) denote the selected optimal defocuses: +200 μm for 4.2 MHz and 11.8 MHz, and + 500 μm for 7.3 MHz. Lines are shown to guide the eye.

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Removal efficiency characterization

In this study, removal efficiency is defined as the removed gold volume normalized by the input electrical energy. Optical microscope images of gold removal with an increasing number of burst counts are shown in Fig. 7. Geometric features of the focal pressure fields (Fig. 4) are overlayed on select images. The removal patterns are similar for 7.3 MHz and 11.8 MHz. Removal is mostly confined to a small focal area which grows with increasing bursts. A dark peripheral ring appears at 0.7 × 106 bursts, which for 7.3 MHz develops into sporadic gold removal with higher burst numbers. For 4.2 MHz scattered gold removal is observed already at 0.3 × 106 bursts, which expands in area with increasing bursts. For 4.2 MHz, particularly at higher burst counts, a broader erosion area was accompanied by deep pitting at the center of the sonicated region, locally exposing the underlying copper layer. For all frequencies, at low burst counts the removal area corresponds to the FWHM+, and the largest removal area at high burst counts to the FWHM−. For 7.2 MHz and 11.8 MHz, the peripheral ring corresponds to the DSLM.

Fig. 7
figure 7

Optical microscope images of gold removal using different burst counts for the three transducers. Colours represent the true appearance of the sample: the intact gold layer appears gold, gold-depleted regions appear silver due to exposed nickel, and deep erosion exposing the copper substrate appears dark brown. Geometric features of the focal pressure fields (from Fig. 4) are shown as overlayed circles: positive amplitude full-width half-maximum (FWHM+, first column), negative amplitude full-width half-maximum (FWHM-, second last column), and distance between positive side-lobe maxima (DSLM, last column). For all frequencies these features correlate with gold removal progression; at low bursts (0.3 × 106) removal is confined within the FWHM+, at high burst counts (1.5 × 106) the maximum central removal area correlates with the FWHM-. For 7.3 MHz and 11.8 MHz at high burst counts (1.9 × 106), the peripheral removal ring correlates with the DSLM. For all frequencies removal increases with burst count.

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The calculated removed gold volumes as a function of sonication burst counts are shown in Fig. 8. For all frequencies increasing the burst counts removes more gold. The removed volume increases with decreasing frequency, although there is only a marginal increase from 11.8 MHz to 7.3 MHz. Only for 7.3 MHz, there is a clear difference in the trends between the largest and total removed volumes. Due to significant gold removal in the side-lobe region, commencing at 1.5 × 106 bursts, the total volume increases more aggressively at high burst counts.

Fig. 8
figure 8

Removed gold volume as a function of burst count. The data is the average of three experiments ± 1 SD. Largest volume (left) is calculated from the largest individual removed gold area, and total volume (right) from the sum of all removed gold areas. Lines are shown to guide the eye. The removed gold volume increases with decreasing frequency.

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For the three transducers, the electrical excitation signal amplitude and the number of cycles per burst were kept constant. Hence the input electrical energy was not constant at each burst count value; lower frequencies have a longer temporal period, which implies that for the same number of cycles per burst, the energy content will be higher for lower frequencies. It should also be noted that all three transducers were electrically matched to 50 Ω and built with piezos of the same material with the same electromechanical coupling coefficients. To compare gold removal efficiency, the burst sweep data (Fig. 8) was normalized with the total input electrical energy, calculated from burst duration and peak-to-peak voltage (Upp = 430 V). The removed gold volumes per input electrical energy as a function of burst count is shown in Fig. 9.

Fig. 9
figure 9

Removed gold volume normalized by the input electrical energy, as function of burst count. The data is the average of three experiments ± 1 SD. Largest volume (left) is calculated from the largest individual removed gold area, and total volume (right) from the sum of all removed gold areas. A maximum in largest volume removal efficiency is observed for all frequencies, after which removal rate diminishes. For 7.3 MHz the total volume removal rate does not reach a maximum, owing to significant removal within the sidelobe. Lines are shown to guide the eye.

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For the largest gold volumes (Fig. 9, left) all frequencies undergo a rapid increase in gold removal efficiency upto a maximum, followed by a gradual decline. The efficiency maxima indicate that the main lobe has become void of gold, after which subsequent bursts remove gold at a diminished rate. While the rate diminishes, it does not halt entirely; cavitation is evidently most prominent within the high-amplitude main lobe, but less frequent cavitation events are expected to occur in the side-lobes and in the region between the main lobe and the side lobes (pressure amplitude does not drop to zero between the main and side lobes, as seen in Fig. 4). For 7.3 MHz, the total gold volume removal efficiency (Fig. 9, right) does not seem to saturate to a maximum. This can be attributed to the onset of significant gold removal within the sidelobes (Fig. 7), the prominence of which can be attributed to the relatively large side-lobe pressure amplitude (Fig. 4). Comparing the ratio of efficiency maxima for each transducer, 4.2 MHz (at 1.1 × 106 bursts) is 4.6 times more efficient than 11.8 MHz (at 0.3 × 106 bursts) and 3.8 times more efficient than 7.3 MHz (at 1.9 × 106 bursts).

Discussion

Recovering gold from e-waste is in principle a sustainable solution to the scarcity of mineable gold. However, established recycling methods are harmful to the environment, producing toxic fumes, using caustic substances and generating large volumes of wastewater7,8,9,10. Environmentally friendly alternatives have emerged over the past decade, but they remain limited in either recovery efficiency, economic viability, or only target one step in traditional methods. This paper builds upon a green, chemical-free HIFU-based method for removing gold from intact PCBs recovered from e-waste using only HIFU in water12. Reducing sonication frequency is expected to increase the erosion potential of acoustic cavitation21. Due to the complexity of bubble-bubble and shockwave-bubble interactions, the prominence of different erosion mechanisms in cloud cavitation have not been fully resolved.

Here, the effect of frequency on gold removal efficiency was investigated using three custom-built transducers operating at different frequencies (4.2 MHz, 7.3 MHz, 11.8 MHz). The transducers featured identical geometry, were built from the same materials including the piezo element, and were all electrically matched to 50 Ω. In sonication experiments, the transducers were driven with identical parameters (amplitude, cycles per burst, burst count, PRF). For each transducer, the focal pressure field was resolved with nonlinear transient acoustic holography. Direct comparison of erosion marks to the resolved focal pressure fields provides qualitative insight into the cloud dynamics and resulting erosion mechanisms.

Frequency effects

The results demonstrated that lower frequencies were more efficient at removing gold; 4.2 MHz was 4.6 and 3.8 times more efficient than 11.8 MHz and 7.3 MHz, respectively. Interestingly, erosion marks with the 4.2 MHz transducer differed from the other two frequencies. At high burst counts, the higher frequencies showed distinct gold removal areas corresponding to the main lobe (FWHM−, Fig. 7) and the first side-lobe (DSLM, Fig. 7). Removal with 4.2 MHz was confined within the main lobe, although removal at the edges was highly dispersed. Also, with 4.2 MHz, deep pitting occurred at the center of the removal area, revealing copper underneath the exposed nickel. These discrepancies hint at a difference in cloud dynamics.

As discussed in the Introduction, low drive frequencies promote the growth of larger cavitation bubbles, which subsequently collapse with high energy20. Following the initial collapse of a cavitation bubble, a toroidal ring of small microbubbles typically forms27. The size of this toroid increases with the maximum radius of the initial bubble28, which would imply that rebound microbubbles will be more dispersed at low frequencies than at high frequencies. In the context of this study, over the course of repeated bursts these microbubbles serve as cavitation-facilitating nucleation sites, and would be expected to eventually disperse beyond the focal volume. Particularly at the edges of the cavitating region, the more intense dynamics could explain the less defined and more dispersed erosion area observed at 4.2 MHz. A similar effect of cloud spreading due to remnant microbubbles was recently observed in a study on HIFU ablation of a tissue-mimicking phantom, where the effect of PRF on cloud geometry and lesion formation was investigated29.

The deep center pitting for 4.2 MHz was mainly confined within the dimension of the positive amplitude main lobe (FWHM+, Fig. 7). Based on literature, lower frequencies are expected to reduce bubble density within the cavitation cloud21. A lower bubble density would imply less bubble shielding, effectively allowing the incident pressure waves to penetrate deeper into the cavitating volume. While the negative pressure drives bubble formation, the subsequent positive peak can reflect off the bubble surface. Due to the low impedance of gas compared to liquid water, the incident high-amplitude positive peak can be reflected off and inverted by the bubble, amplifying both bubble growth and the subsequent collapse intensity30. This back-scattering amplification, together with a reduced bubble density, could explain the deep central pitting observed with 4.2 MHz. For 7.3 MHz and 11.8 MHz, at low (0.3 × 106) bursts where gold removal was first observed, the removal spots corresponded to the width of the positive amplitude main lobe (FWHM+, Fig. 7), which could also be explained by back-scattering. Once the bubble cloud grows over subsequent acoustic cycles, however, due to a higher bubble density, bubble shielding likely reduces the amplification effect.

Practical considerations

A decision had to be made on how to best compare frequencies in a fair manner. In the context of the technological application, energy efficiency was of primary interest. The three transducers featured identical geometries and piezo elements of the same material, and all were matched electrically to 50 Ω. The input electrical parameters were kept constant: amplitude, cycles, PRF. Other viable approaches would have been to vary the amplitude or number of cycles to keep the electrical power constant. A constant number of cycles was selected so that bubbles would be exposed to the same number of acoustic cycles regardless of frequency, allowing observed erosion effects to be attributed more directly to frequency-specific dynamics rather than sonication time.

The excitation amplitude was selected based on the equipment available, being the maximum output amplitude of the commercial amplifier, which was observed to be sufficient for gold removal at all three frequencies. While the focal acoustic pressures varied between the transducers, as seen in the post hoc nonlinear acoustic holography results (Fig. 4), a constant electrical amplitude was used during experiments. This approach, which was adopted prior to detailed pressure field characterization, ensured consistent input conditions across transducers and simplified interpretation of frequency-dependent erosion trends.

The focal pressure of the 7.3 MHz transducer was lower than expected from simple frequency scaling. The acoustic field characterization also showed that at 7.3 MHz a larger fraction of the acoustic power was distributed in the side lobes. Electrical impedance matching was verified, and no anomalies were observed in the S11 response. Although the exact cause could not be determined, differences in beam quality arising from manufacturing tolerances or internal piezoelectric layer variations might contribute to the observed discrepancy. A replacement element with identical specifications was not available. Nonetheless, the maximum removal efficiencies for each transducer followed a consistent trend, with the lowest frequency yielding the highest efficiency and the highest frequency the lowest.

Already previously, it was estimated that the removed gold value exceeded the cost of electricity used even at low gold yields12. For the highest removal efficiency achieved here (1.1 × 106 bursts with 4 MHz), energy consumption per gram of removed gold was 186 kWh/g. While the gold removal efficiency was much improved in this study, the method remains slow; the highest gold removal efficiency was obtained with 1.1 × 106 bursts using the 4.2 MHz transducer, which required 37 min sonication at a PRF of 500 Hz. Presently the PRF was limited by the thermal stability of the piezos used; higher PRFs caused excessive heating, leading to fractures in the piezo. Adding passive or active cooling to the transducer would increase heat dissipation from the piezo, which might allow for higher PRFs.

Further reducing the excitation frequency could improve efficiency, however, a lower frequency generates a larger main lobe and thus a larger cavitation region. The observed approx. 500 μm diameter gold removal spot size for 4.2 MHz is already suitable for PCB edge connectors, which have typical widths of hundreds of micrometers. A larger spot size would both waste energy by initiating cavitation on areas where there is no gold and lead to the removal of adjacent materials (e.g. epoxy). Furthermore, the deep pitting (exposing copper, Fig. 7) would likely increase with lower frequencies.

The purpose of this study was to improve gold removal efficiency; however, no effort was made to collect the removed gold. Recovering and separating the removed metals (gold, nickel, copper), could be carried out with established methods. Recovery should be straightforward with traditional methods e.g. filtration, evaporation, centrifugation. Since nickel is ferromagnetic (unlike gold and copper), it is separable with magnetic separation techniques31, while copper could be separated e.g. using environmentally friendly electrochemical methods32.

This study was conducted on a single representative PCB sample as part of a lab-scale investigation. Future work will include repeat tests across a broad set of PCB samples to assess the effect of material variability on erosion behaviour. Furthermore, in practical e-waste streams, samples often have irregular geometries and height variations. In principle, the approach used here could be extended to such materials by first imaging the sample at low power to obtain acoustic impedance and surface topography maps, then selected regions could be targeted by dynamically adjusting the focal position. Developing automated scanning and adaptive focusing to handle irregularly shaped or partially fragmented waste will be an important direction for future work.

Conclusion

Building on the proof-of-concept demonstrated in previous work12, this study focused on improving the efficiency of a novel green e-waste recycling technology. Three ultrasound transducers operating at different frequencies were used to remove gold from PCB edge connectors via HIFU-induced cavitation. Comparison of the erosion profiles to focal pressure fields, resolved by nonlinear acoustic holography, hints at the complexity of the dynamics at play in cloud cavitation. The lowest frequency (4.2 MHz) showed 3.8 and 4.6 times more efficient gold removal than 7.3 MHz and 11.8 MHz, respectively.