The enhancement of DNA fragmentation in a bench top ultrasonic water bath with needle-induced air bubbles: Simulation and experimental investigation

A. Bubble dynamics in an ultrasonic field

When subjected to an ultrasonic field, pressure fluctuations cause radial oscillations of the bubbles. The bubble radius, R(t), varies as the Rayleigh–Plesset–Noltingk–Neppiras–Poritsky equation,32–3432. F. Cavalieri, F. Chemat, K. Okitsu et al., Handbook of Ultrasonics and Sonochemistry (Springer, 2018).33. Y. Zhang, “Chaotic oscillations of gas bubbles under dual-frequency acoustic excitation,” Ultrason. Sonochem. 40, 151–157 (2018).34. J. B. Keller and M. Miksis, “Bubble oscillations of large amplitude,” J. Acoust. Soc. Am. 68(2), 628–633 (1980). https://doi.org/10.1121/1.384720 RR¨+32R˙2=1ρ[(P0+2σR0−Pv)(R0R)3κ−2σR−4μR˙R−P0−P(t)],(1)where R0 is the initial bubble radius, P0 is the hydrostatic pressure of the liquid, Pv is the vapor pressure, ρ is the liquid density, η is the viscosity, σ is the surface tension, and κ is the polytropic index of the gas within the bubble. P(t) is time-varying ultrasound pressure. The distribution of the standing-wave field is described as3535. Z. Xu, “Numerical simulation of the coalescence of two bubbles in an ultrasound field,” Ultrason. Sonochem. 49, 277–282 (2018). https://doi.org/10.1016/j.ultsonch.2018.08.014 P(z,t)=P0−2PAcos(kz)cos(ωt+ϕ0),(2)where PA is the amplitude, ω is the frequency, k is the wave number, z is the space axis, and φ0 is the initial phase. When a bubble in the liquid is subjected to a periodic sound field, a type of acoustic radiation force caused by an external sound field acts on bubbles-primary Bjerknes force.36,3736. T. J. Matula, S. M. Cordry, R. A. Roy, and L. A. Crum, “Bjerknes force and bubble levitation under single-bubble sonoluminescence conditions,” J. Acoust. Soc. Am. 102(3), 1522–1527 (1997). https://doi.org/10.1121/1.42006537. A. Doinikov, “Bjerknes forces and translational bubble dynamics[J],” in Bubble and Particle Dynamics in Acoustic Fields: Modern Trends and Applications (Research Signpost, 2005), Vol. 661, pp. 95–143. It is written aswhere V(t) is the body of volume and ∇P(z, t) is the pressure gradient. The primary Bjerknes force indicates the direct part of Eq. (3), and it has been deduced by Leighton, Fp=−[3PAkξ0V0sin(2kz)]/(2R0),(4)

where Fp is determined by the volume change and ξ0 and V0 are the amplitude of the bubble radial oscillation and the initial volume.

B. Simulation prediction of the bubble-enhanced ultrasound

The physical model is based on the inhomogeneous Helmholtz equation for the acoustic part and Navier–Stokes equations for the fluid dynamics. The simulation uses COMSOL Multiphysics, which contains the pressure acoustics module, the laminar flow interface, and the computational fluid dynamics (CFD) modules. An oscillating surface of a piezoelectric transducer is placed under the liquid, emitting high-amplitude acoustic waves into the solution. The distribution of the resulting sound field induces a body force described by an additional source term in the momentum balance of the fluid.35–3835. Z. Xu, “Numerical simulation of the coalescence of two bubbles in an ultrasound field,” Ultrason. Sonochem. 49, 277–282 (2018). https://doi.org/10.1016/j.ultsonch.2018.08.01438. D. Rubinetti, D. A. Weiss, J. Müller et al. “Numerical modeling and validation concept for acoustic streaming induced by ultrasonic treatment,” in Proceedings of the 2016 COMSOL Conference (COMSOL, 2016). The acoustic field is described by one variable, the pressure p (SI unit: Pa), and is governed by the wave equation:3939. See https://doc.comsol.com/5.3/doc/com.comsol.help.aco/AcousticsModuleUsersGuide.pdf and https://doc.comsol.com/5.3/doc/com.comsol.help.cfd/CFDModuleUsersGuide.pdf for Comsol CFD and acoustics Module User's Guide. 1ρ0c2∂2p∂t2+∇⋅(−1ρ0∇p)=0,(5)where t is time, ρ0 is the density of the fluid, and c is the (adiabatic) speed of sound. In the fluid domain, in the absence of volumetric sound sources and by assuming that the pressure varies harmonically in time, the wave equation describing the acoustic pressure distribution is ∇⋅(−1ρ0(∇p))−ω2pρ0c2=0,(6)

where ω is the angular frequency. The piezoelectric material is modeled by solving the solid mechanics and electrostatics interfaces that are coupled via linear constitutive equations. This model correlates stresses and strains to electric displacement and the electric field.

At the interface between the air and water domain, a normal component of the structural acceleration of the water boundary is used to drive the air domain. This is described by the following equation:where an is the normal acceleration. The acoustic pressure at the interface between the air and water domain acts as a boundary load on the interface,where σ is the body force. To analyze the grid dependency of results, the COMSOL built-in coarse mesh, regular mesh, thin mesh, thinner mesh, ultra-fine mesh, and ultra-finer mesh are used in simulations, and the results using the last three kinds of mesh are very close. Considering saving computation costs, the ultra-fine mesh with the middle grid density is used for further simulations. An AC electric potential of 200 V, 40 kHz ultrasonic energy is applied to the solution volume, which has a radius of 0.5 cm and a height of 2 cm, corresponding to the radius of the measuring cylinder and the height of the liquid level after loading the DNA solution. The speed of the sound wave in water and air is set to 340 and 1400 m/s, respectively. The reference pressure of the sound pressure level is set to the reference pressure of water pres.SPL = 1 μPa. Using spherical wave radiation as a boundary condition, the integration type selects a far-field integration approximation where the radius tends to infinity.The size and frequency of the bubbles are important information for acoustic simulation, which could be obtained in the flow field stimulation under ultrasound and verified by experiments. The simulated and experimental results of the bubble condition are shown in Fig. 2, the volume and frequency of bubble generation vary with inlet pressure, and they tend to change from a few large bubbles to many small bubbles in the presence of ultrasound due to the ultrasonic effects. Figure 2(a) shows the experimental results (images were taken at 500 frames per second by a high-speed camera FASTEC-IL5) and Fig.2(b) shows the corresponding simulation results. After bubble generation is stable, there are around six small bubbles with a diameter of about 1.5 mm in the solution at the same time under application of 20 kPa to the nozzle, and around five small bubbles with a diameter of about 2.0 mm under 50 kPa and under the application of ultrasound; without ultrasound, there are around three big bubbles with a diameter of about 2.0 mm under 20 kPa and around four bigger bubbles with a diameter of about 3.0 mm under application of 50 kPa. The upper speed of the rising bubbles is 0.3–0.4 m/s. The experimental results match well with the simulated results, as shown in Fig. 2. The bubble generation process with and without ultrasound under 50 kPa can be seen in the supplementary material Videos S1 and S2.The rising of the bubbles creates mixing in the solution, which could be beneficial to more effective mass transfer and enables the DNA molecular chains to be more evenly distributed in the solution.4040. L. Sun, M. K. Siddique, L. Wang, and S. Li, “Mixing characteristics of a bubble mixing microfluidic chip for genomic DNA extraction based on magnetophoresis: CFD simulation and experiment,” Electrophoresis 42(21–22), 2365–2374 (2021). https://doi.org/10.1002/elps.202000295 The simulated bubble forming and rising processes are shown in Fig. 3. Figure 3(a) shows the whole process from the first bubble generation to its burst under 50 kPa inlet pressure in the presence of ultrasound. The inset on the right of Fig. 3 shows an enhanced view of the simulated scenario of a bubble burst process; the phenomenon of bubble collapse is consistent with experimental observations in earlier studies.4141. J. C. Bird, R. De Ruiter, L. Courbin, and H. A. Stone, “Daughter bubble cascades produced by folding of ruptured thin films,” Nature 465(7299), 759–762 (2010). https://doi.org/10.1038/nature09069 With the bubbles rising to the liquid surface, the solution above the bubble becomes thinner and thinner and eventually forms a single-layer liquid film containing DNA molecule long chains. Then, this thin film bursts into multiple small fragments, while the long DNA strands contained in the film are also fragmented. The velocity distribution profiles with streamlines are shown in Fig. 3(b), the bubble’s rising speed is around 0.3 m/s and the bursted bubble formed an instant high-speed air jet (over 1.0 m/s). As the bubble rises, multiple micro-vortices are generated on both sides of the bubble’s rising trajectory symmetrically, forming a bottom-up mixing.Air bubbles in water have a significant effect on the propagation of underwater acoustics due to their ability to efficiently scatter sound.4242. Y. Ma and F. Zhao, “Nonlinear oscillation and acoustic scattering of bubbles,” Ultrason. Sonochem. 74, 105573 (2021). https://doi.org/10.1016/j.ultsonch.2021.105573 When subjected to an ultrasonic field, pressure fluctuations cause radial oscillations of the bubble and the radial oscillations will drive the surrounding fluid and create an acoustic streaming flow, leading to better energy absorption. The amplitudes of radial oscillations under different pressures are shown in Fig. 4. Figure 4(a) shows the bubble radial oscillation curves under different pressures, and the amplitude of the bubble under 20 kPa is around 0.18 mm and that under 50 kPa is around 0.30 mm. Figure 4(b) shows the corresponding bubble radial oscillation-induced acoustic streaming velocity distribution and the acoustic streamline patterns. The fluid close to the bubble is affected most and the flow velocity is higher than that far away from the bubbles, and the highest acoustic streaming velocity under 20 kPa reaches 0.2 m/s and reaches 0.24 m/s under 50 kPa. The streaming stress generated by the oscillating bubble reaches 0.45 kPa under 20 kPa and 0.51 kPa under 50 kPa.Figure 5 plots the bubble volume in the solution with and without ultrasound under different pressures and bubble oscillation-induced streaming velocity. The line with a circle is the experimental result of the bubble volume under different pressures without ultrasound, and the dashed line is the simulated result under the same parameters. The line with a triangle is the experimental result of the bubble volume under different pressures with ultrasound, the dotted line is the simulated result, and the experimental results are in good agreement with the simulation results. Generally, the volume of the bubble increases as the inlet pressure increases and bubbles without ultrasound are larger and fewer than the bubbles with ultrasound. The pink dotted line is the bubble oscillation-induced streaming velocity under different pressures—as the pressure rises, the bubbles become larger and the acoustic streaming flow also has a rising tendency.The simulated results of sound energy distribution are shown in Fig. 6, and the bubble size and distribution are chosen according to the simulation and experimental results obtained above: there are around five small bubbles with a diameter of around 1.5 mm in the solution at the same time under the pressure of 20 kPa, around five bigger bubbles with a diameter of about 2.0 mm under 50 kPa, and around four large bubbles with a diameter of about 6.0 mm under 100 kPa. It can be seen that the sound pressure distribution of the system without bubbles is concentrated, the center area of the solution is strong, and the edge is weak [see Fig. 6(a)]. The system with small bubbles (20–50 kPa inlet pressure) is characterized by a relatively uniform sound pressure, and the intensity of the middle area and the edge is similar. Obviously, reflected sound waves can be seen in the sound pressure level distribution with bubbles, compared with that without bubbles, as shown in Fig. 6(b). After multiple reflections of ultrasound waves by the bubble shell, the ultrasonic energy is better absorbed and leads to a higher sound pressure level in the entire area (around 200 dB) in both the bubbles' regular and random distributed cases. Without bubbles, only the center sound pressure level is high (200 dB) and the level surroundings are lower (almost 120 dB). The sound energy passes through the cylinder in the central area directly, and it cannot be fully absorbed and utilized without bubbles. As shown in the simulated results, due to the presence of bubbles, the sound energy can be better absorbed and distributed more evenly in the solution. This higher sound energy absorption leads to DNA fragmentation enhancement in the ultrasonic bath directly. At the same time, the presence of air bubbles creates a huge pressure gradient (around ±1.4 × 106 at the air/water interface) in the solution, which is also conducive to the fragmentation of DNA molecular chains.43–4543. C. Grygoruk, P. Sieczynski, J. A. Modlinski et al., “Pressure induced nucleus DNA fragmentation,” J. Assist. Reprod. Genet. 28(4), 363–368 (2011). https://doi.org/10.1007/s10815-010-9525-144. L. A. Schriefer, B. K. Gebauer, L. Q. Qui et al., “Low pressure DNA shearing: A method for random DNA sequence analysis,” Nucleic Acids Res. 18(24), 7455 (1990). https://doi.org/10.1093/nar/18.24.745545. M. A. Quail, “DNA: Mechanical breakage,” in Encyclopedia of Life Sciences (ElS) (John Wiley & Sons, 2010). https://doi.org/10.1002/9780470015902.a0005333.pub2 However, as the pressure continues to increase, the volume of the bubble grows and the proportion of bubbles in the liquid increases, larger bubbles (100 kPa inlet pressure) obstruct the transmission path of the sound waves, reducing the absorption of sound energy, which is bad for gene fragmentation improvement.

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