Electrical microparticle acceleration by high-speed membrane deformation

Small-object acceleration is a standard and critical technology in several science research fields, such as crater formation in planetary events,¹ needle-free drugs,² and gene³ delivery in medical/agricultural applications. In engineering, surface-reforming applications accelerate particles with diameters of several micrometers (microparticles) using high-speed gas jets. Accelerated microparticles collide with the target and are plastically deformed by their kinetic energy, as observed using the cold-spray method.⁴ When the kinetic energy is lower than a threshold value, the target material is eroded instead of undergoing particle bonding, as observed in sandblast treatment.⁵ An exploding foil initiator (EFI) also accelerates a small object, which is referred to as a “flyer,” at several kilometers per second to act as a shock switch.⁶ To study material phase changes under pulsed dynamic pressure, the accelerated flyer collides with an explosive for initiation or creates a high-pressure field in the range of 10⁹ Pa. For more fundamental aspects, Lee et al. developed laser-induced micro-projectile impact testing (LIPIT), which accelerated a single microparticle in the range of 10³ m/s using an expanding laser ablation gas⁷ to understand the dynamic mechanical behavior of materials subjected to high-velocity impact.

Although the microparticle acceleration technique is a powerful and attractive technology in various research fields, particle acceleration schemes can only be divided into two types, as reviewed in Ref. 8. The first scheme utilizes an expanding high-pressure gas that injects particles into a flowing gas or expanding vaporized metal. The kinetic energy of the ejected particles is directly dependent on the gas velocity, charged gas pressure, input electrical energy, and irradiating laser energy, which are the control parameters in cold spray/sandblasting, EFI, and LIPIT without an elastomer layer,⁷ respectively. The particle velocity increases with increasing input energy, and there are no physical limitations. The second acceleration scheme utilizes high-velocity membrane deformation. Similar to the first scheme, the driving force of membrane deformation is a high-pressure gas created by a shock tube, explosive media, or short-pulse laser irradiation. However, high-pressure gas is confined between the substrate and membrane instead of undergoing free expansion. Due to the pressure confinement effect,⁹ the membrane experiences high-strain deformation in the range of more than 10⁶ s⁻¹,¹⁰ and the particles deposited onto the membrane surface have an initial ejection velocity that corresponds to the membrane deformation velocity. In contrast to the first scheme, the ejected particle(s) are not exposed to high temperatures or even ionized driver gases. Therefore, the second scheme can maintain the original temperature and/or suppress the deactivation of the chemical properties. In addition, the membrane acts as a shield to protect the target from flowing/expanding gas or fragments produced during device operation. However, the deformation velocity is physically limited by the membrane material properties of impulsive loading to prevent fragmentation. Recently, Kim and Jang reported the minimum threshold energy of the EFI operation required to create a flyer under the given dimensions of the device.¹¹ Their numerical results showed that the membrane was deformed by more than 500 m/s when the input power was lower than the threshold energy required for flyer creation. For the intended purpose of EFI, fragmentation should not be avoided. However, considering that the typical particle velocity driven by a shockwave from the shock tube or blast wave from the explosive media is in the subsonic range⁸ (≤340 m/s), low-power (lower than the threshold energy for fragmentation) EFI operation is not a failure condition but a desired condition for particle acceleration by a membrane deformation.

This study investigated the potential use of low-power EFI operation as an electrical microparticle accelerator. The configuration of the investigated device was identical to that of a conventional EFI device. As the electrical input power was changed, we measured the membrane deformation velocity and estimated the breakdown of the applied impulse. We also demonstrated a microparticle ejection to a “dermic” silicone gel target for possible usage of needle-free drug delivery application.

Figure 1(a) shows a schematic of the particle accelerator assembly. The accelerator contained three layers: (1) a substrate layer (FR-4), (2) a conductive layer (copper), and (3) a cover layer (polyimide). As shown in Fig. 1(b), the conductive layer and the cover layer included a converged square-shaped section (“bridge”). The dimensions and masses of the conductive and covered bridges are listed in Table I. Both bridges had the same lengths l but different thicknesses h: the conductive bridge had a single thickness of 9 µm, whereas that of the cove bridge was valid for 25 and 50 µm. The designed mass of the bridge was calculated as m = ρl²h.

Figure 1(c) shows the experimental setup for measuring the cover layer deformation velocity measurement with its electrical circuit. The accelerator was connected to the capacitor with flexible printed circuits in parallel [see also Fig. 1(b)]. A high-voltage direct-current power supply was used to charge the capacitor. The charged energy (E_c) ranged as 23–84 mJ. After the power supply charged the condenser, the switch was turned on to connect the devices serially for the initiation. The discharge current J and voltage V were measured using a voltage probe (THDP0100, Tektronix, Inc.) and Rogowski coil (CWT UM/30 B/1/80, Power Electronic Measurements Ltd). The cover layer deformation velocity was measured using a commercial modular photonic Doppler velocimetry (PDV¹²) system (VH17, IDIL Fibres Optiques) with a bandpass filter (TBF-1550-1.0-FCAPC, Newport Corporation) having a central wavelength and bandwidth of 1550 and 0.8 nm, respectively. For adjusting the probe center with respect to the bridge center, a PDV probe with an outer diameter and working distance of 3.2 and 20 mm, respectively, was set in the PDV probe holder with two gauge pins. The distance between the probe head and bridge surfaces was 8 mm, which was within the working distance of the probe. To record the discharge current, discharge voltage, and PDV signal, two oscilloscopes (1 and 2) were used. Oscilloscope 1 (MDO4024C, Tektronix, Inc.), with a sampling rate of 1.25 GHz, recorded the discharge current and voltage of the condenser. Oscilloscope 2 (MSO64B, Tektronix, Inc.), with a sampling rate of 50 GHz, recorded the discharge current and the PDV probe signal. In both the recordings, the discharge current was used as the trigger signal. All the experiments were conducted at least twice, and reproducibility was confirmed.

The typical time histories of the consumed power P (=JV) in the bridge, cover layer deformation velocity u, and net force f_net applied to the cover layer are shown in Figs. 2(a)–2(c), respectively. The time origin (t = 0) corresponds to the time at which the switch is turned on. The operation conditions of Fig. 2 are summarized in the figure caption. Due to the parasitic inductance of the electrical circuit, the P value oscillated between 3.0 and −1.3 MW. Here, a negative P value indicates power reflection from the bridge due to the counter-electromotive force. In contrast to the conventional transient phenomenon of condenser discharge, a simple attenuation wave was not observed because the resistance at the bridge section continuously changed as the bridge temperature was changed by Joule heating. Through oscillation, the condenser-charged energy E_c was gradually consumed at the bridge for 0.63 µs.

After releasing condenser energy, the cover layer began to undergo plastic deformation with surface velocity u. In Fig. 2(b), the gray circle represents the experimentally measured u value. Each symbol has an error bar from the short-term Fourier transform (STFT) of the PDV signal analysis.¹³ The time width of the STFT, which corresponds to the effective time resolution u, was set to 10 ns. Under the conditions presented in Fig. 2, the uncertainty in velocity was in the range of 10–15 m/s. As shown in Fig. 2(b), at first, u slightly increased for t ≤ 0.20 µs, and in 0.20 < t ≤ 0.63 µs, u exhibited rapid increment to reach the maximum velocity u_max at t = 0.63 µs, which is identical to the time duration of condenser discharge. For t > 0.63 µs, u began to decrease, and at t = 1.5 µs, the cover layer deformation was completed. To estimate the u_max value, we define the fitting function as the summation of the four Gaussian functions. The fitted curve is shown in Fig. 2(d). Under these experimental conditions, u_max was estimated to be 289 m/s. The strain rate u_max/h_c was calculated as 1.1 × 10⁷ s⁻¹, which is the same order as the laser-induced membrane deformation (10⁶–10⁸ s⁻¹).¹⁰ 

During the deformation process, the cover layer experiences both acceleration and deceleration pressures, which arise from the expanding pressure generated by the vaporized conductive layer and internal stresses, including bending and extension phenomena. To calculate the net force per unit area (f_net), we applied the momentum conservation law and derived it from the time deviation of u, given as f_net = ρ_ch_cdu/dt. Figures 2(c) and 2(e) display the calculated f_net using a central difference scheme based on experimental data and analytical deviation, respectively. Two distinct positive pressure peaks were observed: f_net = 4.4 N/mm² at t = 9.5 × 10⁻² µs and 39 N/mm² at t = 0.47 µs. The net impulse density (i_net), which represents the time integration of the positive f_net values, was determined to be 9.4 Pa s. The second positive pressure was the primary force responsible for extending the cover layer. The duration of this second positive pressure was estimated to be 0.43 µs, which accounts for less than one-third of the total deformation time, indicating that electrical membrane deformation can be treated as an impulsive phenomenon.¹⁴ 

To understand the relationship between P, u, and f_net, we established two time zones: Time-zone 1 (0 ≤ t ≤ 0.12 µs) and Time-zone 2 (0.20 µs ≤ t ≤ 0.63 µs) corresponding to the positive input power ranges marked by gray hatching in Fig. 2. In Time-zone 1, the input energy E₁, calculated by time integration of P, amounted to 22 mJ. Considering the bridge's mass with l_b = 0.4 mm and h_b = 9 µm, E₁ exceeded the heat of fusion for the bridge material by more than eightfold. The melted bridge material exerted pressure on the cover layer, resulting in f_net = 4.4 N/mm², and u increased to 16 m/s. Between Time-zones 1 and 2, f_net decreased to zero due to the reflection of condenser discharge power, which was not absorbed by the bridge section. In Time-zone 2, the discharge power was once again absorbed by the bridge section. For the calculation of E₁, the input energy in Time-zone 2, E₂, amounted to 21 mJ. The total input energy, E₁ + E₂, surpassed the combined values of the heat of fusion and evaporation. The vaporized bridge material rapidly expanded, propelling the cover layer as the applied f_net reached 39 N/mm², ultimately achieving maximum velocity.

Figure 3 shows the time history of deformation velocity u with different specific energies e (≡E_c/m_b) with l = 0.4 mm and h_c = 25 µm. The symbols and solid lines represent experimental data and curve fitting, respectively. Regardless of e values, the time duration for cover layer deformation was identical for 1.3 µs. The u_max was strongly dependent on e such that when e increased 1.3 times (from 7.8 to 10.5 MJ/kg), u_max increased by 8.0 times (from 88 to 702 m/s). The maximum strain rate was 2.8 × 10⁷ s⁻¹ for e = 10.5 MJ/kg. In addition, we confirmed that, when e was lower than 7.8 MJ/kg, the PDV diagnostics detected no signal because the deformation velocity was excessively slow. However, when the e value was higher than 10.5 MJ/kg, the cover layer ruptured, and the fragment flowed at more than 1.0 km/s, which is the desirable operating condition for the exploding foil initiator.

The breakdown of the bending and extending stresses, depicted on the right-hand side of Eq. (6), is shown in Fig. 6 as functions of the normalized specific energy e/e₀. Here, $σ̄t$ is calculated as $σ̄t=σ̄b,n+σ̄b,s+σ̄e,n+σ̄e,s$⁠. Regardless of the e/e₀ value, the extensional shear stresses $σ̄e,s$ was the main component of $σ̄t$⁠. When the specific energy was close to e₀ (e/e₀ = 1.0), stresses, except for $σ̄e,s$⁠, contributed ∼20% for $σ̄t$⁠. As e/e₀ increased, $σ̄b,n$ and $σ̄b,s$ decreased, whereas $σ̄e,n$ increased. At e/e₀ = 1.46, the relative rate of both $σ̄b,n$ and $σ̄b,s$ was less than 5% and that of $σ̄e,n$ and $σ̄e,s$ was 26% and 64%, respectively. Because the sum of the extensional stresses (⁠$σ̄e,n$+ $σ̄e,s$⁠) was 90%, the applied impulsive force onto the cover bridge was consumed to induce extensional stresses.

In this section, we demonstrate microparticle acceleration by high-speed membrane deformation for medical applications such as drug delivery to human skin.² One possible application is a suspension of injections for mammary and prostatic cancers. Commonly, a suspension injection uses biodegradable polymer-made microcapsules (diameter of several tens of micrometers), wherein the chemical components are enclosed. We employed a polylactic acid bead (50-00-304, Corefront Corp., mass density ρ_p = 1.2 × 10³ kg/m³) as a test particle. The particles had a mean radius of 17.5 µm and maximum and minimum radii were controlled for 25 and 10 µm, respectively. The beads had a fluorescent mark to distinguish fragments of the cover bridge. The maximum excitation and emission wavelengths were 552 and 580 nm, respectively. A schematic of the particle acceleration/ejection is shown in Fig. 7. The acceleration procedure involves three steps. First, microparticles were deposited onto a cover bridge (Step 1). Subsequently, the switch was turned on to discharge the stored energy of the condenser, and the cover bridge deformed with velocity u, as described in Sec. III A (Step 2). In addition, the deposited particles moved at velocity u. When the deformation velocity reached the maximum value u = u_max, the deposited particles were dislodged.¹⁷ This is because the resistance and friction forces only affect the cover bridge and the inertial force dominates the particle motion. Subsequently, the ejected particles underwent ballistic flight and finally penetrated the target (Step 3).

Figure 8 shows an image of the deposited particles obtained using a digital microscope (DN-117M-JP, Llutico). A micropipette (00-NPP-10, Nichiryo Co., Ltd.) was used to suck 1.0 µl of the particle suspension (10 mg/ml), which was discharged onto the cover bridge with l_c = 0.4 mm and h_c = 50 µm. After 15 min of air drying, the particles were distributed in a 1.35 × 0.77 mm² area, as shown in the yellow box. Among the deposited particles, only those lying on the cover bridge accelerated. Considering the ratio between the particle deposition area estimated by Image J Fuji and the cover bridge area (=l_c²), the total mass of the ejectable particles was ∼1.0 × 10⁻⁹ kg.

Figure 9 shows a microscopic overlay image of the particles captured using a fluorescence microscope (BZ-X800, Keyence Corp.). Because both the bright-field and fluorescence images showed excellent agreement, the detected objects were microparticles only and there were no fragments of the cover bridge. Figure 9 also shows histograms of the relative positions of each particle along the horizontal and vertical directions, as estimated from image analysis using ImageJ Fuji. The histograms for each axis display data exclusively for that axis and do not incorporate information from the other axis. The ejected particles exhibited a distribution spanning ±1.4 mm along the horizontal axis and ±1.6 mm along the vertical axis. Consequently, the deposited particles were propelled from the cover bridge in all directions, consistent with Ref. 15. The distribution of captured particles depends on two key factors: (i) the initial distribution of deposited particles onto the cover layer and (ii) random collisions during their ballistic flight toward the target. During the drying of particle suspensions, capillary flow plays a role in transporting particles from the droplet’s center to its periphery, resulting in a ring-like deposit.²¹ The extent of deviation in the positions of deposited particles is influenced by concentration, with highly concentrated suspensions inhibiting capillary flow, thereby promoting uniform distribution as the solution dries. Shimobayashi et al. have suggested that adding sugar to the particle suspension can achieve a uniform distribution of particles on the cover layer.²² On the other hand, random collisions among particles during their flight contribute to a uniform distribution of captured particles. However, determining the precise influence of these two effects is a challenging task. For applications involving suspension injection, the primary concern is typically the penetration depth, and the particle distribution in a horizontal plane would not be an essential matter.

The image analysis also introduced a projected area of each particle A_p, and we defined the equivalent radius r_p,equ as r_p,equ ≡ (A_p/π)^½. The normalized histogram of the estimated r_p,equ is shown in Fig. 10 (gray box), with curve fitting using a Gaussian function (red line). As mentioned above, the particle originally had a mean radius of 17.5 µm (the black arrow in Fig. 10), and the maximum and minimum radii were controlled for 25 and 10 µm, respectively. Because the deposited particles formed clusters, the obtained histogram had a mean value at r_p,equ = 22.5 µm and larger r_p,equ than the maximum r_p observed. However, a smaller r_p,equ suggests that the particle collapses during ballistic flight, as observed in Ref. 23.

In this study, we investigate the potential of a low-power exploding foil initiator as an electrical microparticle accelerator. The accelerator contains a substrate, a copper conductive layer, and a polyimide cover layer. The conductive land cover layers included a converged square-shaped section (“bridge”). When the condenser-charged energy was released, intensive Joule heating occurred at the bridge, and the conductive bridge was vaporized. Consequently, the cover layer experienced a high-speed deformation driven by the confined copper gas. Under the threshold level for fragmentation, the deformation velocity increased with increasing input energy up to 800 m/s, which is more than two times faster than that reported in previous studies. Therefore, pulsed discharge is an attractive method for driving high-speed membrane deformation. The energy transfer from the input electrical energy to the membrane kinetic energy was 8.5%, irrespective of the bridge dimensions. Based on the biaxial state of stress, 90% of the stresses induced by the applied impulsive loading were contained as surface extensions, and the other 10% were surface bending. In addition, we demonstrated needle-free drug delivery applications as a possible usage of the proposed electrical microparticle accelerator. Because the theoretically estimated energy loss through the particle dislodging process is negligible, the particles deposited onto the cover layer obtained an initial velocity corresponding to the maximum cover layer deformation velocity, as previously mentioned. Considering particle clustering and deceleration by the drug force during supersonic ballistic flight with an assumption of normal incident angle, half of the ejected particles would reach the human dermic layer that is 200 µm below the skin surface. These results indicate that the electrical microparticle accelerator can facilitate needle-free drug delivery. Although existing research supports our assumptions and estimations, precise penetration-depth measurement using a confocal fluorescence microscope is desired, which is left for future work.

This study was supported by the JST FOREST Program (Grant No. JPMJFR2058, Japan). Kentaro Hayashi and Hidenari Naito (Ricoh Elemex Corp.) were technically supported, particularly in electrical circuits. The authors acknowledged enlightening discussion with Akihiro Sasoh (Nagoya University).

The authors have no conflicts to disclose.

D. Ichihara: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Funding acquisition (lead); Investigation (lead); Methodology (lead); Project administration (lead); Resources (lead); Software (lead); Supervision (lead); Validation (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (lead). R. Takata: Data curation (equal); Methodology (equal).

The data that support the findings of this study are available within the article.