Two-stage particle separation channel based on standing wave surface acoustic wave

Microuidic technology has great advantages in the precise manipulation of micro and nano particles, and the collection method of micro and nano particles based on ultrasonic standing waves has attracted much attention for its high eciency and simplicity of structure. This paper proposes a two-stage particle separation channel using ultrasound. In the microuidic channel, two different sound pressure regions are used to achieve the separation of particles with positive acoustic contrast factors. Through numerical simulation, the performance of three common piezoelectric substrate materials was compared qualitatively and quantitatively, and it was found that the output sound pressure intensity of 128°YX-LiNbO3 was high and the output was stable. At the same time, the inuence of the number of electrode pairs of the interdigital transducer and the electrode voltage on the output sound wave is studied. Finally, 15 pairs of electrode pairs are selected, and the electrode voltages of the two sound pressure regions are 2.0V and 3.0V respectively. After selecting the corresponding parameters, the separation process was numerically simulated, and the separation of three kinds of particles was successfully achieved. This work has laid a certain theoretical foundation for rapid disease diagnosis and real-time monitoring of the environment in practical applications.


Introduction
In recent years, the development of micro uidic technology in the elds of biology, chemistry, materials science, medicine and other elds has been particularly rapid. It has gradually shown a trend to replace the traditional methods of various functions realized in the above elds, involving cell sorting [1], reaction [2], mixing [3], cell location and culture [4] and many other multi-level applications [5]. In particular, a variety of new coronary pneumonia detection methods and vaccine development technologies developed by domestic and foreign researchers based on micro uidic technology have played a key role in the ght against COVID-19 this year [ 6].
With the rapid development of micro uidic technology, it has gradually begun to replace the functions of traditional conventional biochemical medical laboratories and has broad application prospects [7][8][9][10].Among the many applications of micro uidic technology, the sorting function is one of the most core functions. E cient sorting is of great signi cance to the elds of biology, chemistry, diagnostics, therapeutics, materials synthesis and drug development [11,12]. The sorting method using micro uidics can be divided into active method and passive method. The passive method uses the force exerted by the particles when they ow in the microchannel to realize the sorting without applying external force to the particles. There are mainly inertial force sorting [13], hydrodynamic sorting [14], micro-structure ltering and screening [15] and other technologies. The other is an active sorting method, which is to apply an external force eld to make different suspended particles in the micro ow channel move along different trajectories to achieve the purpose of sorting, mainly including dielectrophoresis sorting [16], sound force sorting [17,18], uorescence excitation sorting [19] and magnetic sorting [20], etc. These methods other than acoustic sorting are limited in practical applications due to their damage to biological particles or restrictions on speci c conditions. When using the ultrasonic standing wave method for particle manipulation, only the particles and the medium are required to have a difference in their density or compressibility properties. The realization conditions are relatively easy, and the separation e ciency is extremely high, thus obtaining a wider range of applications.
The cells or particles in the uid medium will be exposed to the acoustic radiation force when exposed to the sound eld [21], and the sound force depends on the size of the cells or particles and its acoustic contrast factor (Φ). The differences in the physical properties of various cells lead to differences in the size and sign of their acoustic contrast factors, so that the acoustic radiation force can be used to separate and classify cells according to their mechanical properties. When there is an acoustic standing wave, cells or particles with positive and negative acoustic contrast factors will move to the pressure node and pressure antinode, respectively. The use of acoustophoresis to separate particles with opposite contrast factors has been widely studied. Filip Petersson et al. [22] successfully realized the continuous separation of lipid particles and red blood cells using standing wave ultrasound and microchannel laminar ow. They used a microchannel with a width of 350 µm and a depth of 125 µm, and it operated in a half-wavelength standing wave mode with a pressure node in the center of the channel. Since the acoustic contrast factor of the red blood cells is negative and the lipid particles are positive, the red blood cells are collected in the middle of the channel, and nally ow out from the middle channel opening and the fat particles are collected to the position of the channel wall, and nally ow out from the two side channel openings. Carl Grenvall et al. [23] improved the separation device to achieve the separation of somatic cells and fat particles in milk. They added two target ow channels at the entrance of the channel, and avoided the problem of particle adhesion and blockage by changing the number of nodes in the channel.
However, most cells show a positive acoustic contrast factor in an aqueous solution. In the standing wave sound eld, these cells will move to the pressure node. Therefore, the use of cell diameter or the size of the acoustic contrast factor to perform cell separation methods with the same acoustic contrast factor sign has attracted widespread attention. Petersson et al. [24] proposed a micro uidic device for sorting based on cell size, which achieved the sorting of red blood cells, platelets and white blood cells by using acoustic methods. There is a pressure node in the center of the microchannel. They use the target ow to focus the cell ow on both sides of the channel. The cells begin to migrate to the pressure node due to the acoustic radiation force. Because the three kinds of cells receive different acoustic radiation forces, In the same time, the distance to the node is different, and the cells that experience different acoustic radiation force are separated and collected at different positions of the exit. Tony Jun Huang et al. [25] designed a new structure to sort white blood cells. They tilted two pairs of interdigital transducers with the ow channel at a certain angle, so that the particles have a greater migration distance, which solves the problem that the migration distance of ordinary structures is limited by the distance between pressure nodes when sorting. Augustsson et al. [26] used two acoustic standing waves to separate prostate cancer cells and white blood cells. They used two sets of standing waves at the upstream and downstream of the microchannel, the rst set of standing waves focused the cells on both sides of the ow channel wall, and the second set of standing waves made the cells migrate to the central node. Two types of cells with different nal volumes are collected at different outlets. Harris et al. [27] proposed using three acoustic standing waves with frequency switches to separate cells. Using the different speeds of the cells to pressure nodes at different positions at different frequencies, by switching the different acoustic eld resonance modes of the channel to separate cells of different sizes or contrast factors, this design greatly reduces the restriction on the residence time of the target cells in ordinary devices .
In this article, we propose a two-stage particle separation channel based on standing wave surface acoustic waves (SSAW) to separate three kinds of particles with positive acoustic contrast factors in micro uidic channels. The uid dynamics focusing technology is used to control the initial position of the particles, and the separation of the particles is achieved through two different sound pressure regions. The rst section is the low pressure zone, which is used to separate 9.4µm particles, and the second section is the high pressure zone, which is used to separate the remaining two particles with a smaller volume difference. This paper studies in detail the process of particle separation using acoustic surface standing wave devices. First, we selected piezoelectric substrate materials, and compared the properties of three common piezoelectric materials qualitatively and quantitatively. Subsequently, the in uence of the number of electrode pairs of the interdigital transducer and the electrode voltage on the output acoustic wave was studied. After selecting the corresponding appropriate parameters, the corresponding separation model was constructed and simulated, and the separation of three different sizes of particles was successfully achieved.

Methodology
This paper uses the nite element software COMSOL Multiphysics5.0, using surface acoustic wave devices to simulate the separation of particles in the microchannel. In order to reduce the amount of simulation calculation and ensure the accuracy of the simulation, we can adopt the following assumptions: 1. The surface acoustic wave only propagates on the surface of the substrate and shows a geometric attenuation in the thickness direction. Therefore, only 1-3 times the wavelength depth can be simulated to re ect its surface wave characteristics well; the surface acoustic wave device, which is composed of piezoelectric material and two sets of interdigital ngers on the surface. The transducer is composed, and its basic structure is shown in Fig. 1. As this article mainly studies the application of surface acoustic wave energy, both sets of interdigital transducers will be used as input terminals.
There, W is the acoustic aperture of the transducer, a is the spacing of the ngers, b is the width of the ngers, and M is the length of the periodic section. In addition, the number of interdigital pairs N determines the intensity of the excitation surface acoustic wave. When a = b = M/4, it is called uniform interdigital transducer, which is also the type of interdigital transducer used in this article. When the same excitation signal is applied to the interdigital electrodes at both ends, two series of SAWs with the same amplitude, the same frequency, and opposite directions will be generated. After these two waves are superimposed, a standing wave eld will be generated. The particle at the node after the superposition does not vibrate with time, and the amplitude of the particle at the antinode is the largest. According to the principle of wave interference, when the following conditions are met, the intensity of the surface acoustic wave generated by the transducer excitation is the largest: There, f is the frequency of the AC signal loaded on the transducer, f 0 is the resonant frequency of the transducer, λ is the wavelength of the acoustic wave, and v s is the propagation velocity of the surface acoustic wave in the substrate.

Governing equations
The principle of surface acoustic wave standing wave sorting is that when the surface acoustic wave standing wave acts on the uid in the micro channel, due to the acoustic ow effect, periodic pressure nodes and pressure anti-nodes will be formed in the channel. Suspended particles will migrate to the pressure node or the pressure inverse node under the action of the acoustic radiation force. The suspended particles of different properties (density, diameter, compressibility) receive different acoustic radiation force, so the migration speed and distance are also different, and then Realize sorting. Under the action of the sound eld, the expression of the acoustic radiation force acting on the particles in the uid is: There, P a is the peak sound pressure in the channel, V p is the particle volume, κ p and κ 0 are the compressibility of particles and water respectively, and ρ p and ρ 0 are the density of particles and water respectively. Φ is the acoustic contrast factor. When Φ > 0, the acoustic radiation force drives the particles to move toward the pressure node; when Φ < 0, the acoustic radiation force drives the particles to gather toward the pressure anti-node.
In addition to the acoustic radiation force, the particles are also affected by the hydrodynamic force from the surrounding uid. The force acting direction is orthogonal to the sound force and drives the particles out of the microchannel along the liquid ow direction. Since the uid ow in the microchannel is laminar and the particle volume is relatively small, the hydrostatic force can be approximated by the Stokes formula: Where η represents the dynamic viscosity of the uid, r represents the radius of the particle, v p represents the velocity of the particle, and v f represents the ow velocity of the ow eld where the particle is located.

Working mechanism
Most of the cells used in the experiment have a positive acoustic contrast factor. Therefore, driven by the sound radiation force, these particles will move toward the pressure node. This article uses polystyrene microspheres to replace blood cells and simulates the separation process in the microchannel. The speci c parameters are shown in Table 1. By setting two zones with different sound pressures in the microchannel, the separation of three different sizes of particles is achieved, and the speci c principle is shown in Fig. 2. The device uses two different transducer voltages corresponding to two different sound pressure regions in the microchannel. The standing waves passing through the microchannel form two pressure nodes in the width direction, so that the particles move toward both sides of the channel. The size of the acoustic radiation force received by the particles is different to realize the separation of the particles. The speci c process is that at the entrance of the microchannel, the target stream is used to pre-focus the particles in the center of the channel to make better use of the channel space. Next, the three particles will enter the low sound pressure zone. Since the particle with a diameter of 9.4µm (corresponding to white blood cells) is larger than the other two particles, according to the above formula of the acoustic radiation force on the particle, the larger particle will be affected The greater the sound force, the faster it moves to the nodes on both sides, so the 9.4µm particles will rst reach the exits on both sides of the channel to achieve separation. However, the smaller 5.0µm particles (corresponding to red blood cells) and 1.8µm particles (corresponding to platelets) will continue to enter the high sound pressure area. In the high sound pressure zone, the 5.0µm particles will eventually ow out from the outlets on both sides of the channel due to greater acoustic radiation force, while the 1.8µm particles will ow out from the middle outlet of the channel. Finally, the three kinds of particles were successfully separated based on size by using acoustic properties.

Simulation setup
According to the above discussion, the study of a complete physical model based on SSAW particle separation needs to consider the in uence of static electricity, elasticity and uid dynamics on the system. It is very di cult to simulate a complete three-dimensional system model and requires considerable computational cost. At the same time, since the displacement in the direction of the acoustic aperture is not coupled to the wave equation, the amount of eld remains unchanged along the length of the electrode. Therefore, we can simplify the three-dimensional structure model to a twodimensional structure model, as shown in Fig. 3.
As shown in Fig. 3, we carried out a two-dimensional modeling of the required device. On the 128°YX-LiNbO3 substrate, 15 pairs of interdigital electrodes are distributed on the left and right sides. The electrode material is metal aluminum, and the electrode width and spacing are both 75µm, the electrode thickness is 0.2µm, and the interdigital transducer period is 300µm. Since the surface acoustic wave decays exponentially as the depth of the material increases, the thickness of the substrate is set to 2.5 wavelengths. The middle part of the substrate surface is a microchannel with particles separated, and its width is designed to be 160 µm, which is just slightly larger than half the wavelength. There are three entrances in the microchannel, the left and right sides are the sheath ow inlets, which mainly pre-focus the particle ow in the middle of the channel, and the middle is the particle inlet. After passing through the low pressure zone, 9.4µm particles will ow out from the middle outlet of the microchannel, 5.0µm particles will ow out from the oulets on both sides of the microchannel tail after passing through the high pressure zone, and 1.8µm particles will ow out from the middle outlet at the end of the microchannel. Finally, the separation of the three particles is achieved.

Selection of piezoelectric substrate materials
Piezoelectric material is a single crystal or polycrystalline solid material that can generate electric charge under pressure. It is an important carrier for surface acoustic wave devices to conduct electroacoustic conversion and propagate surface acoustic waves. The performance of different piezoelectric materials will affect the surface acoustic wave devices made. This paper selects three common piezoelectric substrate materials, 128°YX-LiNbO3, ZnO single crystal and piezoelectric ceramic PZT-5H, and compares and analyzes their piezoelectric properties, so as to select a suitable substrate material.
Generally, the number of electrode pairs in interdigital transducers is relatively large. In order to reduce the amount of calculation, periodic boundary conditions can be used to further simplify the model. The simpli ed surface acoustic wave resonator model is shown in Fig. 4(a). The thickness and width of the piezoelectric substrate are equal to one wavelength, the electrode width is equal to a quarter of the wavelength, and the thickness is 0.2 µm. Since the surface acoustic wave only occurs in the 1-2 wavelength range of the substrate surface during the propagation process, the surface of the surface acoustic wave device can be divided more densely. At the same time, in order to retain the information of the surface acoustic wave within one period, one wavelength should be divided into at least 5 grids, as shown in Fig. 4(b).
After the mesh is divided, the model is analyzed with modal analysis and harmonious response analysis.
The speed of surface acoustic wave in the piezoelectric substrate 128°YX-LiNbO3, ZnO single crystal and piezoelectric ceramic PZT-5H is vs = 3990m/s, vs = 2684m/s and vs = 2099m/s[28-30], according to Eq. 2, it can be concluded that the theoretical resonance frequencies of the three materials are 13.30MHz, 8.95MHz and 6.99MHz. Based on this, Fig. 5 shows the actual resonance frequencies of the three materials are 13.13MHz, 8.98MHz and 6.71MHz. It can be seen from the Fig. 5 that when it is at the resonance frequency, the model vibration shape is a surface acoustic wave waveform, and the center node of the electrode has the largest displacement and the surface acoustic wave energy is the largest.
A two-dimensional model is established, and the central water area on the surface of the surface acoustic wave device is selected as the observation object, when the input signal frequency is the resonance frequency, the number of interdigital electrode pairs is 5, the terminal voltage is 10V, and the piezoelectric substrate is the above three materials, analyzing the sound pressure distribution in the water area, as shown in Fig. 6. It can be found that when the substrate is piezoelectric ceramic PZT-5H, the sound pressure in the water is the largest, followed by 128°YX-LiNbO3, ZnO single crystal is the smallest.
However, when the substrate is 128°YX-LiNbO3 and ZnO single crystal, the sound pressure distribution in the water is relatively more stable. Therefore, after comprehensive consideration, it is considered that the piezoelectric performance of 128°YX-LiNbO3 is relatively best, and it is selected as the device substrate material.

Selection of electrode pairs for interdigital transducer
The number of electrode pairs of interdigital transducers is one of the main factors affecting the energy output of surface acoustic wave devices. During the propagation of surface acoustic waves on the surface of the substrate, the amplitude of the particles on the substrate surface will gradually attenuate as the propagation distance increases, and the energy will gradually be dissipated. Generally speaking, the more electrode pairs, the greater the intensity of the excited surface acoustic wave. However, too many interdigital electrodes will also affect the stability of the acoustic wave output. Therefore, it is necessary to select a reasonable number of interdigital electrode pairs.
A two-dimensional model is established as shown in Fig. 3, and the surface center of the surface acoustic wave device is selected as the observation object. When the input signal frequency is 13.13MHz and the number of interdigital electrode pairs is 5 pairs, 10 pairs, 15 pairs and 20 pairs, the output waveform of the observation object is shown in Fig. 7.
It can be seen from the Fig. 7 that when the number of electrode pairs is small (the number of electrode pairs is less than 20), the output waveform is relatively stable, and the intensity of the surface acoustic wave increases as the number of electrode pairs increases. When the number of electrode pairs is 20, the surface acoustic wave output waveform uctuates and becomes extremely unstable, and the intensity of the acoustic wave will be reduced accordingly. The possible reason is that too many electrodes interfere with each other in addition to the superposition, and the interference has a greater impact on the sound wave, which leads to the instability and the decrease of the intensity of the sound wave. Therefore, the nal selection of the number of pairs of interdigital transducers is 15 pairs.

Selection of transducer electrode voltage
The electrode voltage of the interdigital transducer also affects the energy output of the surface acoustic wave device. Generally speaking, the greater the voltage, the greater the amplitude of the mass pointon the substrate surface and the greater the intensity of the sound wave. It is necessary to nd a suitable terminal voltage so that the microchannel can generate sound pressure conditions that meet the smooth separation of particles.
As shown in Fig. 3, the absolute value of the maximum sound pressure in the microchannel liquid is selected as the observation object. Under the condition that the frequency is 13.13MHz and the hard sound eld boundary is set on both sides of the water area, the absolute value of the maximum sound pressure in the liquid is analyzed when the electrode voltage is increased from 1.0V to 2.5V, and the result is shown in Fig. 8(a). It can be found that the electrode voltage has a linear relationship with the surface acoustic wave output intensity, and the acoustic output intensity will increase as the voltage increases. Through simulation analysis, the sound pressure in the low sound pressure zone of the microchannel that meets the separation conditions is 1.7e 5 Pa, the sound pressure in the high sound pressure zone is 2.56e 5 Pa, and the corresponding electrode voltages are 2.0V and 3.0V. The speci c sound pressure distribution is shown in Fig. 8(b).

The separation process of particles
After selecting the appropriate piezoelectric substrate material, the number of interdigital transducer electrode pairs, and the electrode voltage, the speci c separation process of the three particles is simulated, as shown in Fig. 9. Figu.9(a) shows the ow eld distribution diagram in the microchannel.
There are three entrances at the beginning of the channel, of which two sides are the sheath ow inlets, and the particle ow at the middle entrance is focused on the center of the channel. It can be found that the velocity of the ow eld in the center of the microchannel is the largest, and the closer to the sidewall, the lower the velocity. At the same time, the velocity of the ow eld in the rst half of the microchannel is relatively large, and the velocity of the ow eld in the second half of the microchannel is relatively low.
The reason is that the liquid splits at the two outlets in the middle of the channel, which makes the uid velocity drop. In addition, in order to prevent all uid from owing out of the middle section outlet, the corresponding boundary conditions need to be set: the uid at the outlet is controlled by pressure, the pressure at the terminal outlet is set to atmospheric pressure, that is P = 0, and the pressure at the middle section outlet of the channel is set to P = 0.45. Figure 9(b) shows the speci c separation process of the three kinds of particles under the combined action of the ow eld and the sound eld. When t = 0s, the particle ow is ready to enter the channel at the middle entrance of the beginning of the microchannel. At t = 0.25s, the particle stream is focused towards the center of the microchannel under the action of the sheath ows on both sides, and begins to enter the low sound pressure zone of the microchannel. At t = 0.85s, the 9.4µm particles have a larger volume difference from the other two kind of particles, so them receives a greater acoustic radiation force, and produces greater displacement to both sides during the process of passing through the low sound pressure zone, thus them ows out from the middle end of the microchannel, while the remaining two kind of particles continue to ow to the high sound pressure area of the channel. At t = 2.4s, under the action of the high sound pressure eld, the 5.0µm particles nally ow out from the outlets on both sides of the channel terminal, while the 1.8µm particles ow out from the middle outlet due to the small displacement to both sides. Finally, the three kinds of particles were successfully separated based on size by using acoustic properties.

Conclusion
We demonstrated a device that uses two different sound pressure regions to achieve particle separation in a uid microchannel. The separation process is completed by the combination of different intensities Surface acoustic wave device Page 18/19 The output waveform of the observed point in the Y direction