Long distance acoustic towing device and method based on line-defect phononic crystals

Abstract

The application discloses a long-distance acoustic traction device and method based on a line defect phononic crystal, and belongs to the technical field of acoustic traction. The long-distance acoustic traction device comprises a phononic crystal waveguide, which is arranged in a background fluid and has a periodic array of scatterer arrays, and a line defect is formed by removing a row of the scatterers; an acoustic source is used for emitting acoustic waves to the phononic crystal waveguide; wherein, when a manipulated object is placed in the phononic crystal waveguide, the object switches the waveguide transmission mode of the local area where the object is located from a guided wave mode to a forbidden mode, thereby self-inducing a continuous negative sound intensity gradient field in the object; meanwhile, the fixed lattice structure of the phononic crystal waveguide is configured to absorb the recoil momentum generated due to acoustic wave reflection, so that the net acoustic radiation force acting on the manipulated object is a traction force pointing to the acoustic source, and the long-distance acoustic traction device realizes long-distance acoustic wave traction.

Description

Technical Field

[0001] This invention relates to the field of acoustic traction technology, specifically to a long-distance acoustic traction device and method based on a line-defect phononic crystal. Background Technology

[0002] Acoustic tweezers have seen rapid development due to their unique advantages in the biological field, and are widely used in various non-contact manipulation scenarios. Since Marston first proposed the concept of acoustic traction, this counterintuitive phenomenon has attracted widespread attention in academia. Acoustic traction is a special mechanical effect in acoustic-matter interactions, manifested as the opposing force exerted by sound waves on an object under specific conditions—the acoustic radiation force (ARF)—is in the opposite direction to the sound wave propagation, thus achieving non-contact traction control of the target. Currently, researchers have developed various acoustic traction techniques, mainly focusing on suppressing backscattering, such as using Bessel beams, absorbing particles, enhancing forward scattering, or modulating incident waves. However, the high sensitivity of acoustic traction to incident wave reflection inherently limits its effective distance, hindering the realization of long-distance acoustic traction techniques.

[0003] Phononic crystals (PCs), with their artificially designed bandgap characteristics, exhibit unique advantages in the field of acoustic wave manipulation and can be widely used in cutting-edge fields such as vibration reduction design of engineering structures, acoustic filtering, energy harvesting, acoustic wave guiding, and acoustic superconducting wave transmission. However, current acoustic wave traction technology based on phononic crystals still faces two major bottlenecks: insufficient incident wave reflection sensitivity and poor traction mechanism efficiency. These limitations restrict the realization of long-distance acoustic wave traction force. Summary of the Invention

[0004] The purpose of this invention is to overcome the problems in the prior art and provide a long-distance acoustic traction device and method based on a line defect phononic crystal, thereby realizing long-distance acoustic wave traction.

[0005] This invention provides a long-distance acoustic traction device based on a line-defect phonon crystal, comprising: A phononic crystal waveguide, disposed in a background fluid, has a periodically arranged array of scatterers, with line defects formed by removing a row of the scatterers; a sound source for emitting sound waves into the phononic crystal waveguide; wherein, when a manipulated object is placed within the phononic crystal waveguide, the object switches the waveguide transmission mode of its local region from guided mode to forbidden mode, thereby self-inducing a continuous negative acoustic intensity gradient field within itself; simultaneously, the fixed lattice structure of the phononic crystal waveguide is configured to absorb the back impulse generated by the reflection of sound waves, such that the net acoustic radiation force acting on the manipulated object is a pulling force pointing towards the sound source.

[0006] Preferably, the phononic crystal waveguide is a two-dimensional square lattice structure composed of several square-arranged steel pillars, with the lattice constant a and the steel pillar diameter d set to 100µm and 0.9a, respectively.

[0007] Preferably, the width of the line defect is a.

[0008] Preferably, the frequency of the sound wave is within the frequency range of the induced bandgap generated when the object is placed inside the waveguide.

[0009] Preferably, the frequency of the sound wave emitted by the sound source is 10.27~10.41MHz.

[0010] Preferably, the manipulated object is rectangular or elliptical. When the manipulated object is rectangular, the length is greater than or equal to 3a and the width is 0.15a to 0.4a. When the manipulated object is elliptical, the major axis is greater than or equal to 3.1a and the minor axis is 0.21a to 0.6a.

[0011] Preferably, the background fluid is an iodixanol solution. Preferably, the design method of the phononic crystal waveguide includes: A basic model of the phononic crystal is established in a simulation environment. The basic model includes scatterers arranged periodically in a background fluid. A linear defect waveguide is formed in the basic model by removing a row of scatterers. A first band structure analysis is performed to determine the guided mode frequency range of the linear defect waveguide in the absence of an object. A model of a manipulating object is established in the linear defect waveguide, and a second band structure analysis is performed to verify that a band gap induced by the object appears in the guided mode frequency range after the object model is inserted. Based on the results of the second band structure analysis, the final design parameters of the phononic crystal waveguide are determined.

[0012] The present invention also provides a traction method for the above-mentioned long-distance acoustic traction device based on a line-defect phononic crystal, comprising placing the manipulated object in the phononic crystal waveguide; activating the sound source and emitting sound waves; and using the self-induced negative acoustic intensity gradient field and the momentum absorption of the fixed lattice structure to jointly exert continuous traction on the object towards the sound source.

[0013] Compared with existing technologies, the beneficial effects of this invention are as follows: This invention introduces object-induced bandgap transitions and lattice momentum absorption effects through the design of a phononic crystal waveguide. When an object is placed in the waveguide, it switches its transmission mode from the guided mode to the forbidden mode, thereby generating a continuous and powerful negative acoustic intensity gradient field internally, solving the problem of low traction efficiency in traditional technologies. Simultaneously, the fixed lattice structure of this device effectively absorbs the back impulse generated by sound wave reflection, ensuring that the net acoustic radiation force acting on the object is always a net pulling force pointing towards the sound source. Therefore, this invention, based on a line-defect phononic crystal, overcomes the limitation of the effective distance and realizes long-distance acoustic traction. Attached Figure Description

[0014] Figure 1 The acoustic traction force generated by the self-induced negative intensity gradient of an object in a phononic crystal is described in an embodiment of the present invention. in, Figure 1 (a) is a schematic diagram of a square lattice phonon crystal for a band-defect waveguide.

[0015] Figure 1 (b) in the diagram shows the band structure of the two guided modes in the phononic crystal waveguide with and without an object (red line).

[0016] Figure 1 In the diagram, (c) represents the absolute sound pressure field distribution at a frequency of 10.3 MHz when there is an object inside the phononic crystal (below) and when there is no object inside (above). Figure 1 (d) in the diagram is a schematic diagram of the formation mechanism of acoustic tension.

[0017] Figure 2 This is a schematic diagram of the continuous tensile force acting on an object in the PC channel of an embodiment of the present invention.

[0018] in, Figure 2 (a) shows the changes in absolute sound pressure inside and around the object; (a1) shows the absolute sound pressure distribution after the wave interacts with the manipulated object within the fluorescent green rectangle, the center of which is located at x=1.4a. (a2) shows the absolute sound pressure values ​​along the central axis from -6a to 9a, with the shaded area representing the location of the object.

[0019] Figure 2 (b) in the figure shows the curves of the force exerted on the object in the y direction as a function of the center position when x = 0, 0.2a, and 0.5a.

[0020] Figure 2 (c) shows the functional relationship between the acoustic tension on the object at different y-axis positions at a frequency of 10.3MHz and its position.

[0021] Figure 3 This is a force diagram of an object according to an embodiment of the present invention; in, Figure 3 (a) shows the sound pressure distribution and force distribution of the object and its surrounding lattice at x=0.9a.

[0022] Figure 3 (b) in the figure depicts the curve of the force acting on the object and its surrounding lattice as the position of the object's center changes.

[0023] Figure 3 Figure (c) shows the change in the resultant force on the object and the lattice as the object's center moves from 0 to 4a, as well as the evolution of the acoustic reflectivity.

[0024] Figure 4 This is a schematic diagram illustrating the influence of the size of a rectangular object and the frequency of sound waves on ARF according to an embodiment of the present invention.

[0025] in, Figure 4 Figure (a) shows the curve of acoustic radiation force as a function of the object's center position from 0 to 4a, measured at frequencies of 10.21, 10.27, and 10.32 MHz. The length and width of the rectangular object are 6a and 0.3a, respectively.

[0026] Figure 4 In (b), the length of the object changes from a to 10a, while the width remains fixed at 0.3a.

[0027] Figure 4 In the example (c), the object's width changes from 0.1a to 0.5a, while its length remains fixed at 6a. The object's position changes from 0 to 4a, and the sound wave frequency is set to 10.3 MHz.

[0028] Figure 5 This is a schematic diagram of the acoustic traction force acting on an elliptical object according to an embodiment of the present invention.

[0029] in, Figure 5 In the diagram, (a) represents the absolute sound pressure distribution after the wave interacts with the manipulated object, indicated by a fluorescent green elliptical outline, with its center located at x=1.5a.

[0030] Figure 5 (b) in the figure is the curve of the traction force on the elliptical object as a function of its position, with the center of the object moving from 0 to 4a.

[0031] Figure 5 In Figure (c), the effect of sound wave frequency variation on the traction force of the elliptical object is shown, with the frequency range between 10.27 and 10.34 MHz. The lengths of the major and minor axes of the ellipse are fixed at 6a and 0.3a, respectively.

[0032] Figure 5In the figure, (d) represents the change in acoustic radiation force corresponding to different lengths (a to 10a) of the major axis of the ellipse.

[0033] Figure 5 In the figure, (e) represents the change in acoustic radiation force corresponding to different lengths of the minor axis of the ellipse (0.1a to 0.7a). Detailed Implementation

[0034] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the described embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0035] Unless otherwise defined, the technical or scientific terms used herein shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms “first,” “second,” and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as “comprising” or “including” indicate that the elements or objects preceding “comprising” or “including” encompass the elements or objects listed following “comprising” or “including” and their equivalents, and do not exclude other elements or objects. Terms such as “connected” or “linked” are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as “upper,” “lower,” “left,” and “right” are used only to indicate relative positional relationships; when the absolute position of the described objects changes, the relative positional relationship may also change accordingly.

[0036] This invention provides a long-distance acoustic traction device based on a line-defect phonon crystal, comprising: A phononic crystal waveguide, disposed in a background fluid, has a periodically arranged array of scatterers, with line defects formed by removing a row of the scatterers; a sound source for emitting sound waves into the phononic crystal waveguide; wherein, when a manipulated object is placed within the phononic crystal waveguide, the object switches the waveguide transmission mode of its local region from guided mode to forbidden mode, thereby self-inducing a continuous negative acoustic intensity gradient field within itself; simultaneously, the fixed lattice structure of the phononic crystal waveguide is configured to absorb the back impulse generated by the reflection of sound waves, such that the net acoustic radiation force acting on the manipulated object is a pulling force pointing towards the sound source.

[0037] Because the traction force in this invention originates from the object's own induced, sustainable sound field attenuation, rather than a short-range interference effect, the object can be continuously pulled as long as the sound wave propagates, thus enabling long-distance acoustic traction. The acoustic radiation force generated by the self-induced, continuous negative acoustic intensity gradient field of this invention is highly efficient and directionally constant, overcoming the shortcomings of weak traction force and oscillation in traditional methods. The phononic crystal waveguide structure naturally forms an acoustic potential well in the lateral direction. When the object deviates from the center, it experiences a restoring force that pulls it back to the center, achieving stable directional transmission and preventing the object from going out of control during traction. The long-distance acoustic traction device and method of this invention are insensitive to changes in the size and shape of the object. As long as the object can effectively trigger mode switching, traction force can be generated, reducing the stringent requirements on the manipulated object and broadening the application scenarios.

[0038] It should be noted that, during the manufacturing of the phononic crystal waveguide of the present invention, silicon wafers or glass sheets can be selected as substrates, and a uniform array of steel micropillars can be fabricated on the substrate using raw processing techniques such as photolithography. At the same time, the positions for wire defect channels are reserved during processing.

[0039] In another preferred embodiment, the phonon crystal waveguide is a two-dimensional square lattice structure composed of several square-arranged steel pillars. The lattice constant 'a' and the steel pillar diameter 'd' are set to 100µm and 0.9a, respectively. In this embodiment, there is an extremely high acoustic contrast between the steel and the background fluid (such as iodixanol solution), which can generate a sufficiently wide complete phonon bandgap. The lattice constant 'a' and the steel pillar diameter 'd' are set to 100µm and 0.9a, respectively. By removing a row of steel pillars to form a line defect waveguide with a line defect width of approximately 'a', there is an extremely high acoustic contrast between the steel and the background fluid (such as iodixanol solution). This structure can generate a sufficiently wide complete phonon bandgap.

[0040] In another preferred embodiment, the frequency of the sound wave is within the frequency range of the induced bandgap generated when the object is placed inside the waveguide. This frequency promotes the generation of a self-induced negative acoustic intensity gradient field. Within this frequency range, the sound wave can be significantly attenuated inside the object, thereby generating a significant negative acoustic intensity gradient, ultimately producing a strong and reliable traction force, overcoming the shortcomings of weak and unstable traction forces in traditional methods.

[0041] In another preferred embodiment, the frequency of the sound wave emitted by the sound source is 10.27~10.41 MHz, which can better promote the generation of the self-induced negative sound intensity gradient field; more preferably, the frequency of the sound wave emitted by the sound source is 10.3 MHz, which is a preferred frequency within the induced bandgap range, at which the traction force reaches its maximum and the system operates most stably.

[0042] In another preferred embodiment, the manipulated object is rectangular or elliptical. When the manipulated object is rectangular, its length is greater than or equal to 3a and its width is 0.15a to 0.4a. When the manipulated object is elliptical, its major axis is greater than or equal to 3.1a and its minor axis is 0.21a to 0.6a. The manipulated object with the above-mentioned dimensions of the present invention can form a better match based on the above embodiments of the present invention, thereby reliably triggering the object-induced bandgap effect.

[0043] In another preferred embodiment, the background fluid is an iodixanol solution.

[0044] As another preferred embodiment, the design method of the phononic crystal waveguide includes: A basic model of a phononic crystal is established in a simulation environment. This basic model includes scatterers periodically arranged in a background fluid. A linear defect waveguide is formed by removing a row of scatterers from this basic model. A first band structure analysis is performed to determine the guided mode frequency range of the linear defect waveguide in the absence of an object. A model of a manipulating object is then established within the linear defect waveguide, and a second band structure analysis is performed to verify that an object-induced bandgap appears within the guided mode frequency range after the object model is inserted. Based on the results of the second band structure analysis, the final design parameters of the phononic crystal waveguide are determined. This invention aims to verify an object-induced bandgap, ensuring that the designed device can generate an efficient negative acoustic intensity gradient field. Furthermore, by comparing the two band structure analyses, it is possible to quickly and accurately determine whether a combination of structural parameters and an object can work, avoiding the enormous cost and time consumption of fabricating numerous physical samples for screening.

[0045] The present invention also provides a traction method for the above-mentioned long-distance acoustic traction device based on a line-defect phononic crystal, comprising placing the manipulated object in the phononic crystal waveguide; activating the sound source and emitting sound waves; and using the self-induced negative acoustic intensity gradient field and the momentum absorption of the fixed lattice structure to jointly exert continuous traction on the object towards the sound source.

[0046] This invention achieves inherent stability in the traction process through the synergistic effect of the negative acoustic gradient field generated by the object's self-induced acoustic properties and the momentum absorption of the fixed lattice structure of the phononic crystal. It automatically generates a lateral restoring force to maintain the motion trajectory and exhibits strong robustness to system fluctuations. This invention demonstrates good compatibility with manipulated objects; as long as the object's acoustic characteristics fall within the effective window of the induced bandgap, stable traction can be achieved without needing to re-optimize the device for different objects. In terms of energy efficiency, this method achieves energy directionality, greatly improving acoustic energy utilization efficiency. This invention breaks through the limitations of traditional acoustic tweezers in terms of operating distance, enabling long-distance continuous traction.

[0047] Please see Figure 1 ,in Figure 1(a) Schematic diagram of a square lattice phononic crystal with a band defect waveguide. The gray circle represents a steel cylinder, and the green rectangle represents the object. The lattice constant a is 100µm, and the diameter d of the steel cylinder is 0.9a. The length (h) and width (w) of the object are 6a and 0.3a, respectively. (b) Schematic diagram of the band structure of two guided modes in the phononic crystal waveguide with and without an object (black line). The figure shows a magnified view of the band structure, with the orange area representing the band gap (10.26-10.42 MHz) and the cutoff frequency f0=10.3 MHz. (c) Absolute sound pressure field distribution at 10.3 MHz with and without an object inside the phononic crystal. The fluorescent green rectangle indicates the manipulable rectangular object. (d) Acoustic pull formation mechanism: Unattenuated sound waves attenuate rapidly when they encounter an object, triggering the formation of a negative intensity gradient field inside the object, causing the object to be pushed towards the sound source.

[0048] like Figure 1 As shown in (a), the two-dimensional photoacoustic material consists of multiple circular steel pillars arranged in a square. The lattice constant *a* and the diameter *d* of the steel pillars are set to 100 µm and 0.9a, respectively. A photoacoustic waveguide is formed by removing a row of steel pillars along the x-axis, and the entire structure is immersed in an iodixanol solution. Furthermore, the length *h* and width *w* of the manipulated object are set to 6a and 0.3a, respectively. Detailed material parameters are shown in Table 1. We used cellular parameters as the parameters of the manipulated object and selected an iodixanol solution with a solubility of 60%. A 60% iodixanol solution is cell-friendly (commonly used as a contrast agent) and has been applied in isoacoustic focusing techniques. Therefore, a high-concentration iodixanol solution exhibits excellent properties as an acoustic manipulation medium.

[0049] Figure 1 (b) shows the predicted band structure of the PC in two different cases (defect-free structure and defect structure with an infinitely long object). The defect mode designed in the PC induces strong spatial confinement of the sound field, forming a guided wave mode. However, when an object (w=0.3a) is introduced at the center of the defect, a narrow band gap is generated within the original passband, thereby creating an attenuation field inside the manipulated object. Figure 1 (c) illustrates the sound field distribution at 10.3 MHz when the object is either not embedded (above) or embedded (below) in the PC channel (sound waves propagate from left to right). Notably, the sound waves rapidly attenuate upon interaction with the object, creating a negative intensity gradient field on the object's surface. This physical process is as follows: Figure 1 As shown in (d), in the absence of an object, sound waves do not attenuate when propagating through the PC defect channel. However, when an object is embedded in the defect channel, it triggers a bandgap transition, converting the propagation mode to a forbidden state. This causes the sound waves to attenuate rapidly as they pass through the object, thus creating a negative intensity gradient field across the entire object surface, generating a significant traction force.

[0050] Table 1. Acoustic parameters of PC and object.

[0051] For rectangular objects, we analyzed the absolute sound pressure distribution and calculated the ARF acting on the object (e.g., Figure 2 (As shown). The expression for ARF is as follows:

[0052] in ρ 0 As the background fluid density, c 0 This represents the longitudinal wave propagation velocity in the background fluid. p 1 and v 1 These represent the first-order sound pressure and velocity components in perturbation theory, respectively. The integration process applies to the time-averaged pressure and velocity fields, as well as to an arbitrarily selected region containing the object. S conduct.

[0053] Dimensionless radiative force can be calculated using a formula.

[0054] Where respectively represent effect ARF (Aspect-Resonance Frequency) of an object in the x and y directions. This indicates the sound wave's path through the same location when the object is not present. Energy density at that time.

[0055] Please see Figure 2 , Figure 2 This is a schematic diagram of the continuous tension acting on an object in the PC channel. (a1) Absolute sound pressure distribution after the interaction between the wave and the manipulated object within the fluorescent green rectangle, the center of which is located at x=1.4a. The black circle represents the PC steel cylinder. (a2) The figure below shows the absolute sound pressure values ​​along the central axis from -6a to 9a, with the shaded area representing the object's location. (b) Curves showing the force exerted on the object in the y-direction as a function of the central position when x=0, 0.2a, and 0.5a. (c) Functional relationship between the acoustic tension on the object at different y-axis positions at a frequency of 10.3MHz and its position.

[0056] Figure 2 (a) illustrates the variation in absolute sound pressure inside and around the object. The left side of the object is in a high-sound-intensity region, while the right side is in a low-sound-intensity region. This difference in sound intensity gradient exerts an attractive force on the object. The input sound field uses a point source model with a frequency set to f0 = 10.3 MHz.

[0057] The effect of ARF (acoustic buoyancy) on an object is as follows: Figure 2 As shown in (b) and (c). First, analyze the lateral stability (y-direction) of the object during the stretching process, as follows... Figure 2 As shown in (b), when the object's center is located at x=0, 0.2a, and 0.5a, the object is always subjected to a restoring force pointing towards the center (y=0) in the y-direction. This is because the sound pressure gradient field in the y-direction traps the object at the location of strongest sound pressure. Therefore, when the object deviates from the center of the PC channel, it will be subjected to a restoring force in the y-direction, causing it to automatically return to the central axis (y=0). Next, the ARF effect of the object in the x-direction is studied, such as... Figure 2 As shown in (c), when the object moves from 0 to 4a, it will be continuously subjected to a quasi-periodic tensile force, such as... Figure 2 As shown in (c), this periodically changing force originates from the periodic distribution of the sound field in the PC. Therefore, the longitudinal acoustic force acting on the object is a continuous and long-term acoustic tensile force. Notably, even with a finite y-axis displacement, the object can still maintain its motion towards the sound source along the x-direction.

[0058] To gain a more comprehensive understanding of the mechanism by which sound waves exert a pulling force on an object in the PC channel, we further explored the momentum relationship in the system. Theoretically, when sound waves interact with an object, some of the sound waves are reflected. According to the law of conservation of momentum, the object should experience a pushing force. However, we observed that the object continuously experiences a pulling force ( Figure 2 (c) This seems to violate the law of conservation of momentum. In fact, in our system, momentum exchange involves not only the sound wave and the object, but also the PC lattice. That is to say, the sound wave, the object, and the PC lattice together constitute a whole system in which the law of conservation of momentum is fully satisfied.

[0059] Please see Figure 3 , Figure 3 (a) The sound pressure distribution and force distribution of the object and its surrounding lattice at x=0.9a are shown. (b) The graph depicts the change in force acting on the object and its surrounding lattice as the position of the object's center changes. (c) This figure also shows the change in the resultant force on the object and the lattice, as the object's center moves from 0 to 4a, and the evolution of the sound wave reflectivity.

[0060] Against this backdrop, we calculated the net force acting on the PC lattice and found it to be positive. Figure 3 (b)). When the object and its surrounding lattice are considered as a composite system, their total force ΔFx is also positive. Figure 3 (c) This leads to an increase in momentum (positive momentum change). Simultaneously, when the sound wave is reflected by the object, its momentum undergoes a negative change. Under these conditions, all three components jointly satisfy the law of conservation of momentum, and the additional momentum provided by the PC lattice allows the object to continuously experience a pulling force. Figure 3 (c) shows the resultant force acting on the composite system (object and lattice) and the change in acoustic reflectivity as the object moves from 0 to 4a. The results indicate the existence of a persistent net positive force, the trend of which is highly correlated with the reflectivity curve.

[0061] Please see Figure 4 , Figure 4 The effect of rectangular object size and acoustic frequency on ARF. (a) Acoustic radiative force as a function of the object's center position from 0 to 4a, measured at frequencies of 10.21, 10.27, and 10.34 MHz. The length and width of the rectangular object are 6a and 0.3a, respectively. (b) The object's length changes from a to 10a, while the width remains constant at 0.3a. (c) The object's width changes from 0.1a to 0.5a, while the length remains constant at 6a. The object's position changes from 0 to 4a, and the acoustic frequency is set to 10.3 MHz.

[0062] We will now investigate the stability of acoustic traction force under different parameter conditions. Since the incident mode frequency and the size of the scattering body have a crucial influence on the acoustic traction effect, Figure 4 The variation of the Yx value with the incident wave frequency, the size of the scatterer, and the center position is shown. Figure 4 (a) shows the acoustic traction force (ARF) acting on the object at different frequencies. Clearly, sustained acoustic traction is only achievable within the bandgap-constrained frequency range. When the frequency exceeds the bandgap range, the sound waves penetrate the object with almost no attenuation, resuming their propagation mode and forming an oscillating ARF caused by periodic changes in the sound field. Figure 4 (b) illustrates the relationship between ARF and the object length h and center position. The ARF value is negative for most of the parameter space (x, h). When h < 3a, the thrust exceeds the traction force due to the weakened bandgap effect, resulting in the disappearance of the net traction force. However, when the object length reaches approximately 4.5a, the ARF value becomes positive again. The mechanism behind this phenomenon is that when the object length approaches 4.5a, its rear end resonates strongly with the sound wave within the PC material. This resonance effect weakens the bandgap effect, and when the strength of the negative force component is insufficient to offset the positive force component, a net positive force is ultimately generated. Figure 4 (c) illustrates the ARF under different x and w parameters. Continuous acoustic traction occurs only when the object width is between 0.15a and 0.4a. When the width is less than 0.15a, bandgap formation is suppressed; while above 0.4a, the coupling effect between polycarbonate (PC) and the incident sound wave is enhanced. This enhanced coupling effect confines the acoustic energy within the polycarbonate, reducing energy transfer with the object. Therefore, a positive force is generated at certain locations. The positive component dominates the negative component, resulting in a net thrust.

[0063] Please see Figure 5 , Figure 5 Schematic diagram of the acoustic traction force on an elliptical object. (a) Absolute sound pressure distribution after the interaction between the wave and the manipulated object, indicated by a fluorescent green elliptical outline, with its center located at x=1.5a. (b) Curve showing the traction force on the elliptical object as a function of position, with the center of the object moving from 0 to 4a. (c) Effect of sound wave frequency variation on the traction force of the elliptical object, with a frequency range between 10.27 and 10.34 MHz. The major and minor axes of the ellipse are fixed at 6a and 0.3a, respectively. (d) Changes in acoustic radiation force corresponding to different lengths of the major axis of the ellipse (a to 10a). (e) Changes in acoustic radiation force corresponding to different lengths of the minor axis of the ellipse (0.1a to 0.7a).

[0064] Next, we investigated the effect of changes in object shape on the traction force. The study found that this traction force implementation scheme is inherently robust to changes in object shape. In the experiment, we placed an elliptical object at the center of the PC channel, with a major axis (2rx) and a minor axis (2ry) of 6a and 0.3a, respectively. Figure 5 (a) shows the absolute sound pressure distribution when the object is centered. (and) Figure 2 (a) Similarly, a negative intensity gradient field is formed on the surface of the object, thereby producing an acoustic traction effect. Figure 5 (b)).

[0065] In this case, we obtained results similar to those for rectangular objects, such as... Figure 5 As shown in (c), (d), and (e), within the bandgap range, the object is always subjected to a tensile force due to the presence of the attenuation mode. Figure 4 (c)). Figure 5 (d) and (e) illustrate the variation of the acoustic thrust (ARF) of an elliptical object with the length of its major or minor axis. When the minor axis is fixed at 2ry = 0.3a, a sustained acoustic thrust occurs when the major axis exceeds 3.1a. Notably, compared to rectangular objects, elliptical objects no longer exhibit thrust within a length of 4.5a, thanks to the reduced backscattering caused by the geometry of the elliptical tip. In other words, unlike the strong scattering caused by the sharp corners of rectangular objects, the absence of sharp corners at the ends of an ellipse suppresses backscattering, thus reducing the positive portion of the ARF. Therefore, the net force acting on the elliptical object becomes a negative force. The wider operating range of the minor axis length also stems from the suppression effect of backscattering. Figure 5 (e)).

[0066] In summary, we have successfully achieved continuous acoustic traction within a designed photonic crystal (PC) substrate under the influence of a negative intensity gradient field. Theoretical analysis shows that this traction force primarily originates from a novel mechanism: inducing a negative acoustic intensity gradient within the object by manipulating the object's reaction to the incident mode. When the object is placed in a PC waveguide, the bandgap effect creates an imbalance in the positive and negative acoustic response fields (ARF) at the object's surface, resulting in continuous acoustic traction. Furthermore, this method offers significant advantages: for example, the bandgap frequency can be easily designed within the PC supercell, and continuous traction can be achieved across a wide range of object sizes. This invention significantly expands the application potential of acoustic manipulation techniques.

[0067] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A long-distance acoustic traction device based on a line-defect phonon crystal, characterized in that, include: A phononic crystal waveguide, disposed in a background fluid, has a periodically arranged array of scatterers, with line defects formed by removing a row of the scatterers; a sound source for emitting sound waves into the phononic crystal waveguide; wherein, when a manipulated object is placed within the phononic crystal waveguide, the object switches the waveguide transmission mode of its local region from guided mode to forbidden mode, thereby self-inducing a continuous negative acoustic intensity gradient field within itself; simultaneously, the lattice structure of the phononic crystal waveguide is configured to absorb the back impulse generated by the reflection of sound waves, such that the net acoustic radiation force acting on the manipulated object is a pulling force pointing towards the sound source.

2. The long-distance acoustic traction device based on a line-defect phonon crystal as described in claim 1, characterized in that, The phononic crystal waveguide is a two-dimensional square lattice structure composed of several square-arranged steel pillars. The lattice constant a and the diameter d of the steel pillars are set to 100µm and 0.9a, respectively.

3. The long-distance acoustic traction device based on a line-defect phonon crystal as described in claim 2, characterized in that, The width of the line defect is a.

4. The long-distance acoustic traction device based on a line-defect phonon crystal as described in claim 1, characterized in that, The frequency of the sound wave is within the frequency range of the induced bandgap generated when the object is placed inside the waveguide.

5. The long-distance acoustic traction device based on a line-defect phonon crystal as described in claim 4, characterized in that, The sound source emits sound waves with a frequency of 10.27~10.41 MHz.

6. The long-distance acoustic traction device based on a line-defect phonon crystal as described in claim 1, characterized in that, The manipulated object is rectangular or elliptical, and when the manipulated object is rectangular, its length is greater than or equal to 3a. Width 0.15a~0.4a; when manipulating an elliptical object, the major axis is greater than or equal to 3.1a; the minor axis is 0.21a~0.6a.

7. The long-distance acoustic traction device based on a line-defect phonon crystal as described in claim 1, characterized in that, The background fluid is an iodixanol solution.

8. The long-distance acoustic traction device based on a line-defect phonon crystal as described in claim 1, characterized in that, The design method for the phononic crystal waveguide includes: A basic model of the phononic crystal is established in a simulation environment. The basic model includes scatterers arranged periodically in a background fluid. A linear defect waveguide is formed in the basic model by removing a row of scatterers. A first band structure analysis is performed to determine the guided mode frequency range of the linear defect waveguide in the absence of an object. A model of a manipulating object is established in the linear defect waveguide, and a second band structure analysis is performed to verify that a band gap induced by the object appears in the guided mode frequency range after the object model is inserted. Based on the results of the second band structure analysis, the final design parameters of the phononic crystal waveguide are determined.

9. The traction method of the long-distance acoustic traction device based on a line-defect phonon crystal as described in any one of claims 1 to 7, characterized in that, This includes placing the manipulated object within the phononic crystal waveguide; The sound wave is initiated and emitted; through the self-induced negative acoustic intensity gradient field and the momentum absorption of the fixed lattice structure, the object is continuously pulled towards the sound source.

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