Acoustic balance for non-contact measurement of mass and density of millimeter-scale objects

Abstract

Acoustic traps use forces exerted by sound waves to confine and transport small objects. The dynamics of an object moving in the force landscape of an acoustic trap can be significantly influenced by the inertia of the surrounding fluid medium. These inertial effects can be observed by setting a trapped object in oscillation and tracking it as it relaxes back to mechanical equilibrium in its trap. Large deviations from Stokesian dynamics during this process can be explained quantitatively by accounting for boundary-layer effects in the fluid. The measured oscillations of a perturbed particle then can be used not only to calibrate the trap but also to characterize the particle.

Description

Atty. Dkt. No.: 046434-0861 ACOUSTIC BALANCE FOR NON-CONTACT MEASUREMENT OF MASS AND DENSITY OF MILLIMETER-SCALE OBJECTS CROSS-REFERENCE TO RELATED PATENT APPLICATION

[0001] This application claims the benefit and priority of U.S. Provisional Patent App. No. 63 / 530,913, filed on August 4, 2023, the entirety of which is incorporated herein by reference. STATEMENT OF GOVERNMENT INTEREST

[0002] This invention was made with government support under DMR2104837 awarded by the National Science Foundation. The government has certain rights in the invention. TECHNICAL FIELD

[0003] The present disclosure relates generally to acoustic balance for non-contact measurement of mass and density of millimeter-scale objects. BACKGROUND

[0004] Particle and object observation and / or measurement is a critical aspect of a wide range of endeavors. While determining the weight or mass of an object is generally considered a trivial exercise for the modern world, challenges present themselves when considering particles at the millimeter-scale or below. Further, many approaches determine weight as the measurement system is influenced by the gravitational forces at the measurement site. This has ramifications not only for how the system is used, for example terrestrial vs extraterrestrial, but also for precision and accuracy at very light objects such as millimeter-scale particles, as the impact of gravity as well as other influences such as drag, inertia, and other such forces are more impactful.

[0005] Acoustic manipulation of granular media was first demonstrated by Kundt in 1866 as a means to visualize the nodes and antinodes of sound waves. After a century and a half of gestation, acoustic trapping is emerging as a focal area for soft-matter physics and a practical platform for noncontact materials processing thanks to recent advances in the theory of wave- matter interactions and to innovations in techniques for projecting acoustic force landscapes. An object’s trajectory through such a landscape encodes information about the wave-matter interaction and therefore can be used to characterize the object, as well as to calibrate the trap.

[0006] Correctly interpreting the measured trajectory of an acoustically trapped particle can be challenging because the drag force deviates substantially from the standard Stokes form, as has 1 4880-1385-9786Atty. Dkt. No.: 046434-0861 been noted in previous studies. The measurement of particles or objects becomes limited by these considerations. These limitations prevent the meaningful use of existing acoustic trapping to contribute to the development of mass measurement devices.

[0007] The methods described herein incorporate non-Stokesian drag into a self-consistent measurement framework by invoking the Prandtl-Schlichting hydrodynamic boundary-layer approximation to account for the fluid’s inertia. This approach appears not to have been demonstrated previously and provides a fast and accurate way to measure physical properties of the trapped object without requiring separate calibration of the acoustic trap. The same measurement also yields an absolute calibration of the trap’s stiffness for that specific object. SUMMARY

[0008] One embodiments relates to an acoustic trapping system. The system comprises an acoustic levitator having a first bank of acoustic transducers and a second bank of acoustic transducers, the first bank of acoustic transducers and the second bank of acoustic transducers positioned opposite each other. The system further includes the acoustic levitator configured to receive an object between the first bank of acoustic transducers and the second bank of acoustic transducers. The first bank of acoustic transducers and the second bank of acoustic transducers are configured to emit ultrasonic waves towards each other, impacting the object when received within the acoustic levitator. An imaging apparatus configured to capture information about the object received within the acoustic levitator.

[0009] In another embodiment, a method is provided for determining mass of an object. The method comprises positioning an object within an acoustic levitator between a first bank of acoustic transducers and a second bank of acoustic transducers. An imaging apparatus is engaged to capture information about the positioned object. Counterpropagating ultrasonic waves are emitted from the first bank of acoustic transducers and the second bank of acoustic transducers. The method further comprises interacting at least a portion of counterpropagating waves, forming a standing pressure wave and causing an oscillation in the object within the acoustic levitator. A trajectory of the object is measured and the measured trajectory is compared to a predicted trajectory to determine the object’s mass density and / or mass.

[0010] In another embodiment, a computer controlled acoustic trapping system comprises an acoustic levitator having at least one bank of acoustic transducers, the acoustic levitator is configured to receive an object, the at least one bank of acoustic transducers configured to emit ultrasonic waves forming an acoustic trap within the acoustic levitator, an imaging apparatus 2 4880-1385-9786Atty. Dkt. No.: 046434-0861 configured to capture information about the object received within the acoustic levitator. The computer controlled acoustic trapping system further includes one or more processors and one or more memories operatively coupled to the one or more processors, the one or more memories having instructions stored thereon which, when executed by the one or more processors, cause the one or more processors to perform operations comprising: positioning the object within the acoustic trap; engaging the imaging apparatus to capture information about the positioned object; causing an oscillation in the object within the acoustic levitator; measuring a trajectory of the object; and comparing the measured trajectory to a predicted trajectory to determine the object’s mass density and / or mass.

[0011] It should be appreciated that all combinations of the foregoing concepts and additional concepts discussed in greater detail below (provided such concepts are not mutually inconsistent) are contemplated as being part of the subject matter disclosed herein. In particular, all combinations of claimed subject matter appearing at the end of this disclosure are contemplated as being part of the subject matter disclosed herein. BRIEF DESCRIPTION OF THE FIGURES

[0012] The foregoing and other features of the present disclosure will become more fully apparent from the following description and appended claims, taken in conjunction with the accompanying drawings. Understanding that these drawings depict only several implementations in accordance with the disclosure and are therefore not to be considered limiting of its scope, the disclosure will be described with additional specificity and detail through use of the accompanying drawings.

[0013] Fig.1A is a schematic diagram of the reference acoustic trap. Fig.1B is a typical video frame of a millimeter-scale Styrofoam sphere levitated in the acoustic trap together with a schematic diagram of the forces acting on the particle. Fig. 1C shows measured trajectory (symbols) of a Styrofoam bead returning to mechanical equilibrium in an acoustic trap compared with predictions of the damped oscillator model (curve).

[0014] Fig.2A shows frequency dependence of the damping rate ^^^Ω^, Plot symbols present results from fits to measured trajectories, such as the example in Fig.1C. The solid curve is a fit to the boundary-layer model in Eq.14 that yields ^^^= 28.9(3) kg m−3. The horizontal dashed line reflects the standard Stokes result, ^^^= (1.50 ± 0.03) s−1. Fig.2B shows correlation of the axial offset, ^^^, with the observed oscillation frequency, Ω. The horizontal dashed line represents the nodal plane of the acoustic trap. 3 4880-1385-9786Atty. Dkt. No.: 046434-0861

[0015] Fig.3 shows dependence of the measured trap stiffness ^^ on the peak-to-peak voltage ^^^used to power the acoustic trap’s transducer banks. The solid curve is a fit to Eq.20b for the calibration constant ^^.

[0016] Fig.4 illustrates a computer system for use with certain implementations.

[0017] Reference is made to the accompanying drawings throughout the following detailed description. In the drawings, similar symbols typically identify similar components, unless context dictates otherwise. The illustrative implementations described in the detailed description, drawings, and claims are not meant to be limiting. Other implementations may be utilized, and other changes may be made, without departing from the spirit or scope of the subject matter presented here. It will be readily understood that the aspects of the present disclosure, as generally described herein, and illustrated in the figures, can be arranged, substituted, combined, and designed in a wide variety of different configurations, all of which are explicitly contemplated and made part of this disclosure. DETAILED DESCRIPTION

[0018] Acoustic traps use forces exerted by sound waves to confine and transport small objects. The dynamics of an object moving in the force landscape of an acoustic trap can be significantly influenced by the inertia of the surrounding fluid medium. These inertial effects can be observed by setting a trapped object in oscillation and tracking it as it relaxes back to mechanical equilibrium in its trap. Large deviations from Stokesian dynamics during this process can be explained quantitatively by accounting for boundary-layer effects in the fluid. The measured oscillations of a perturbed particle then can be used not only to calibrate the trap but also to characterize the particle. Described herein are systems and methods for extracting information through machine-vision measurements of trapped objects’ oscillations in the face of the combined influences of gravity, the trap’s restoring force and drag due to displacement of the surrounding fluid medium.

[0019] Described herein are embodiments using an acoustic optical trapping system to levitate or suspend a particle or object within a defined space. The object can be measured for physical attributes including but not limited to shape, size, mass, weight, and composition. The action of the acoustic forces, such as the traveling wave and including secondary forces, results in anomalous motion within the trap. It is this movement that can be measured and used for determination of physical properties. Such acoustic optical trapping systems enable the direct measurement of mass, that is are able to ignore gravity’s influence on the object. Due to the 4 4880-1385-9786Atty. Dkt. No.: 046434-0861 relative immunity to certain influencing forces such as gravity, the resultant measurement is able to measure mass at the microgram, milligram and nanogram scale.

[0020] Embodiments described herein relate generally to acoustodynamic mass determination. Fig. 1A schematically represents an acoustic trapping system 100 of one embodiment, though it should be appreciated that other forms of acoustic trapping may be utilized. In the illustrated embodiment, the acoustic trapping system 100 is based upon a standard TinyLev design. An acoustic levitator 103 is included in the system. The acoustic levitator 103 comprises one or more banks 105 of ultrasonic transducers 107 having an arrangement and focus to define a spherical volume of air for a traveling wave to be projected into. Fig. 1A illustrates an embodiment with two opposing transducer banks. However, in some embodiments, a single transducer bank may be utilized with a reflector. Further, the one or more acoustic banks may comprise a single transducer or more than one transducer. The acoustic trapping system 100 may include a housing 110 for containing and positioning the acoustic levitator 103. The housing 110 may be such that it accommodates a continuous measurement of different particles or a batched approach. In some embodiments, each of one ore more banks of ultrasonic transducers are an arcuate shape, in others a three-dimensional shape such as a semi sphere.

[0021] In one embodiment illustrated in Fig. 1A, the acoustic levitator 103 consists of two banks 105 of piezoelectric ultrasonic transducers 105 (MA40S4S, Murata, Inc.) having, in one embodiment each bank at the same frequency and amplitude such as a frequency of 20 kHz to 2 MHz and an amplitude of 70 dB to 120dB, such as with a resonance frequency around 40 kHz. The first acoustic bank 105 and the second acoustic bank 105 may be positioned opposite each other to form the acoustic trap therebetween. In one embodiment, each bank includes 36 transducers. Each bank of those transducers 105maybe driven sinusoidally by a function generator (for example, DS345, Stanford Research Systems) (not show) and projects a traveling wave into a spherical volume of air. Interference between the two waves creates an array of acoustic traps along the instrument’s vertical axis.

[0022] In some embodiments, the acoustic trap is associated with a defined environment or atmosphere, for example within the housing 110. The acoustic trap may be defined within an ambient fluid, such as air, or alternatively within a selected environment such as a controlled liquid or gas.

[0023] In one embodiment, the acoustic trap is loaded with an object. The acoustic trap maybe loaded by various mechanisms including by use of a gravity. Alternatively, a loading apparatus may be provided to impart movement to the particle to position it within the acoustic trap defined 5 4880-1385-9786Atty. Dkt. No.: 046434-0861 by the one or more acoustic banks. The loading apparatus may be, in addition to gravity induced, a force applied to the object such as from a mechanical impulse, a pulse of fluid / air, a transient electric field, a transient magnetic field, a transient field gradient, or other environmental aspect that results in a motive force to the object to induce oscillation.

[0024] The object will remain static with equal acoustic profiles from the acoustic banks, that is equal application of force upon the object. The object may be acted upon via an impulse to initiate an oscillation. For example, one or more parameters of at least one of the acoustic banks may be altered to be different, such as a different frequency and / or amplitude from the opposing acoustic bank. Alternatively, or in addition, an additional force may be applied such as from a mechanical impulse, a pulse of fluid / air, a transient electric field, a transient magnetic field, a transient field gradient, or other environmental aspect that results in a motive force to the object to induce oscillation. It should be appreciated that the impulse may be imparted by the same mechanism as the loading of the object or by a different mechanism.

[0025] In order to capture information regarding the particle, the traveling wave, and the changes indicative of particle properties, an observation device is utilized. In one embodiment, that may be accomplished by an imaging device. The imaging device may comprise one or more of imaging optics, non-imaging optics, or acoustic imaging / tracking. In one embodiment, the imaging optics utilizes a camera. A video camera maybe positioned to capture images of the particle within the acoustic trapping system 100. Fig.1B presents a video image of a millimeter- scale sphere of expanded polystyrene localized in fluid, here air, within one of the acoustic traps. The camera (Blackfly S USB3, FLIR) records the particle’s motions at 170 framess-1with an exposure time of 2 ms and an effective magnification of 61 μm / pixel. Under these imaging conditions, the height of the particle in the trap, ^^^^^^^െ ^^^, can be measured in the imaging plane to within ∈௭= 15 μm by fitting for the image’s least bounding circle. This method has the advantage over light-scattering techniques that it also yields an estimate for the particle’s radius, ^^^. For the particle in Fig.1B, ^^^= 1.346(7) mm.

[0026] The particle can be made to oscillate in its trap by rapidly displacing it from its equilibrium position. This can be accomplished by abruptly changing the amplitude, frequency or relative phase of the signals driving the two banks of transducers. The discrete symbols in Fig. 1C show the trapped particle’s displacement from its equilibrium position, ^^^^^^^െ ^^^, after an abrupt change of drive amplitude causes a displacement of Δ ^^ = −0.31(1) mm. The curve is a fit to the standard result for a damped harmonic oscillator, 6 4880-1385-9786Atty. Dkt. No.: 046434-0861 ^^ି^ ఊ௧^^ ^^^ ൌ ^^^^ ∆ ^^ ^^ଶ cos^Ω ^^^Eq. 1for the oscillation frequency, Ω = 122.1(2) rads−1= 19.43(3) Hz and the damping rate ^^ = 6.3(3) s−1, in addition to Δ ^^ and the equilibrium position, ^^^. Although this fit appears to be satisfactory, the estimated parameters must be interpreted with care.

[0027] To illustrate the challenge, consider the standard Stokes result, 6^^ ^^^ ^^^2for the drag rate experienced by awith dynamic viscosity ^^^. An expanded polystyrene sphere has a density of roughly ^^^= 30 kg m−3, so that ^^^ ൌ43^^ ^^^ଷ^^^ ൌ 0.3 mg.Eq. 3The viscosity of air under standard conditions is ^^^= (1.825 ± 0.005) × 10−5Pa s. Eq.2 therefore predicts ^^^= 1.4 s−1, which is a factor of four smaller than the measured value. Previous studies on similar systems have reported comparably large discrepancies between predicted and observed drag rates, and have addressed them phenomenologically with nonlinear drag models, if at all.

[0028] Described herein are embodiments where the linear drag model underlying Eq. 1 is demonstrated to be appropriate for analyzing the oscillations of acoustically trapped objects, provided that the parameters are suitably modified to account for the inertia of the displaced fluid, such as air. The enhanced model provides a basis for precisely measuring the density and mass of trapped objects without requiring the acoustic trap to be independently calibrated. The same approach can be used to calibrate the trap’s stiffness while accounting naturally for the influence of external forces such as gravity. It should be appreciated that other systems for providing an acoustically trapped object may also be utilized without varying from the scope of the concepts herein. In particular, this embodiment relates to the determination of inertial mass rather than gravitational mass. In contrast to gravitational mass determinations, which rely upon comparing a calibrated force acting on a calibrated object vs gravity acting on the object, here the measurement is of the inertia of the object in a known fluid based on the influence of known acoustic forces.

[0029] The force landscape experienced by an acoustically trapped object is dictated by the structure of the sound field. The counterpropagating waves in the acoustic trapping system interfere to create a standing pressure wave along the central axis whose spatial dependence is approximately sinusoidal, 7 4880-1385-9786Atty. Dkt. No.: 046434-0861 ^^^^^^ൌ 2 ^^^ sin^ ^^ ^^^ Eq. 4near the midplane at ^^ = 0. Here, ^^^is the pressure amplitude due to a single bank of transducers and ^^ ൌ ^^ / ^^^is the wave number of sound at frequency ^^ in a medium whose speed of sound is ^^^. For acoustic levitation in air, ^^^= 343.5(5) ms−1under standard conditions.

[0030] The time-averaged acoustic force experienced by an object at height ^^^in the standing wave has the form: ^^^^ ^^^^ ൌ െ ^^^sin^2 ^^ ^^^^5with an overall scale,^^^ ൌ ^^ ^^ ^^^ଶ Eq. 6that depends on the frequency and amplitude of the sound wave, and on properties of the object and the medium through ^^. For a small spherical particle ( ^^ ^^^< 1), the acoustic response function is 7where ^^^and ^^^are the densities of the particle and medium, respectively, and ^^^and ^^^are their respective isentropic compressibilities. Dense incompressible particles have ^^ > 0 and therefore tend to be trapped at nodes of the pressure field.

[0031] External forces can displace the particle from the center of the acoustic trap, as depicted in Fig.1B. Gravity, in particular, acts on the particle’s buoyant mass,8and displaces it from the pressure node at ^^ = 0 into mechanical equilibrium atEq. 9where ^^ = 9.81ms−2is the acceleration due to gravity.

[0032] As long as the particle does not move too far from the nodal plane, the acoustic trap exerts an approximately Hookean force on theെ െ 10 with a stiffness, ^^ ൌ 2 ^^ ^^^cos^2 ^^ ^^^^ Eq.11 that depends on properties of the sound wave, properties of the particle and the strength of the external force. Calibrating the trap generally involves determining ^^. Eq.11 clarifies that the trap 8 4880-1385-9786Atty. Dkt. No.: 046434-0861 cannot be calibrated with a reference object, as has been proposed, but instead requires a separate calibration for every set of experimental conditions. Inertial corrections.

[0033] An object moving in the trap’s potential energy well displaces the surrounding fluid medium and therefore experiences viscous drag. The standard Stokes result from Eq.2 neglects the inertia of the fluid. For the special case of a sphere undergoing harmonic oscillations, inertial effects can be incorporated into a linear drag model, 12 by defining a dynamical13and a renormalized 14that both depend on the oscillation frequency, Ω, through the thickness of the Prandtl-Schlichting boundary layer surrounding the sphere 15This model is derived from the Basset-Boussinesq-Ossen approximation for drag by non-steady flows, described further in paragraphs

[0034] -

[0036] . The inertia-corrected equation of motion for an acoustically levitated sphere is then analogous to the standard equation of motion for the damped harmonic oscillator,െ ൌ 16 with a natural frequency,Eq. 17that is related to the measuredൌ418Unlike the standard harmonic oscillator, whose drag and restoring forces are independent of frequency, the natural frequency of an acoustically trapped object must be found by solving Eq. 18 self-consistently. 9 4880-1385-9786Atty. Dkt. No.: 046434-0861

[0034] The derivation of Eq. 16 from boundary-layer theory establishes that Eq. 1 suitably models the dynamics of an object oscillating in an acoustic trap. Unlike dynamical models with nonlinear drag, the damping rate predicted by Eq. 14 does not depend on the amplitude of the motion. This is consistent with the observation in Fig. 1C that a single constant value for ^^ successfully accounts for viscous damping over the oscillating particle’s entire trajectory.

[0035] As indicated by the examples below, abruptly changing the trapping characteristics of an acoustic levitator sets a trapped object into a free oscillation that is damped by viscous drag in the surrounding medium. The resulting trajectory can be described with the standard model for a damped harmonic oscillator provided that inertial effects in the displaced fluid are taken into account self-consistently with hydrodynamic boundary-layer theory. These inertial corrections quantitatively resolve the large discrepancy between the measured drag rate and the Stokes prediction that has been noted in previous studies, but previously has been unexplained. The boundary-layer model is applicable for particle speeds substantially smaller than the speed of sound and Reynolds numbers, Re = ^^^^^^^^^ / ^^^, well below the threshold for turbulence. For the present examples, ^^^< 0.25 m s−1and Re23, so that both conditions are satisfied. The observation that Re > 1 explains why the standard Stokes result substantially underestimates the drag rate.

[0036] Fitting measured trajectories to predictions of the boundary-layer model yields precise estimates for the trapped particle’s mass density and mass. Dynamic acoustic trapping therefore can be used to weigh millimeter-scale objects without requiring direct contact, including sub- milligram objects that can be challenging to weigh individually. Generalizing this approach to accommodate aspherical objects, powders and fluids will be addressed in future studies.

[0037] Using the acoustic force field itself to set an object into oscillation provides a simple and effective method to calibrate the stiffness of an acoustic trap. This approach does not require the external intervention used in complementary calibration techniques, such as mechanically moving the sample relative to the levitator.

[0038] Acoustodynamic mass determination should have near-term applications in the pharmaceutical industry for weighing individual pills and capsules, in the jewelry industry for weighing gemstones and precious metals, and in the nuclear power industry for massing individual fuel pellets. Many such applications currently rely on ultra-micro balances to cover the relevant mass range with good precision. Acoustodynamic mass determination offers several advantages. The measurement is inherently self-calibrated and is robust against environmental perturbations. 10 4880-1385-9786Atty. Dkt. No.: 046434-0861 Levitated samples never come in contact with surfaces, which is inherently beneficial for sensitive and hazardous materials, minimizes the likelihood of cross-contamination and simplifies integration with robotic sample handlers. Unlike conventional techniques, furthermore, acoustodynamic mass determination can operate freely in challenging environments such as microgravity. Reaping these benefits will require extensions to the tracking method and the dynamical model to accommodate the shapes of such general granular materials.

[0039] An acoustic trapping system may be implemented in various embodiments such as a quantitative research tool, an in-line inspection / verification tool, or a real-time tracking / observation device. It should be appreciated that the acoustic trapping system may be configured for a measurement of the object without physical contact of the object, allowing for use in situation where physical contact is undesirable due to potential contamination or spoilage or due to danger or safety concerns.

[0040] In further embodiments, the acoustic trapping system may be positioned within or on isolating equipment, such as a antivibration and / or gyro-stabilizing device to reduce or eliminate the impact of vibration or motion from the environment. Similarly, the housing 110 or other aspects of the acoustic trapping system may provide an isolated environment in which the acoustic trap is formed, such as by blocking or reducing exposure to air currents, drafts, and the like. Experimental Examples

[0041] Measurements of ^^^Ω^ can be interpreted with Eq.14 to estimate the mass density of the particle. The discrete points in Fig. 2A are measured by fitting recorded trajectories of the expanded polystyrene bead in Figs. 1A-1C. Different oscillation frequencies are obtained by adjusting amplitude ^^^of the sinusoidal voltage powering the trap. It is not necessary to know how the trap strength ^^^depends on ^^^to perform this measurement because ^^ and Ω are both obtained directly from each measured trajectory. Taking the density of air to be ^^^= 1.220(5) kg m−3leaves the particle’s density ^^^as the only undetermined parameter in the model. The solid curve in Fig. 2A is a fit to Eq. 14 that yields ^^^= 28.9(3) kg m−3, which is consistent with expectations for expanded polystyrene beads. Inertial corrections quite convincingly account for the previously unexplained enhancement of the oscillating particle’s drag rate. In so doing, they also provide the basis for a precise and robust way to measure the mass density of millimeter- scale objects. Combining ^^^with the optically measured radius yields the levitated object’s mass, ^^^= 0.31(1) mg. Repeating this measurement on 10 different beads from the same batch yields an average density of ^^^= 30.5(2) kg m−3and an average mass of ^^^= 0.295(3) mg. 11 4880-1385-9786Atty. Dkt. No.: 046434-0861

[0042] The precision of acoustodynamic mass determination is limited by run-to-run variability in the measured values of ^^^Ω^ which in turn can be ascribed to spurious transverse motions of the particle in its trap and to environmental factors such as vibrations and drafts. Even with these practical limitations, the 3 μg precision achieved in this representative realization is comparable to the performance of a conventional ultra-micro balance.

[0043] Previous acoustic trapping studies have attempted to measure the masses of levitated objects by interpreting their static displacements with Eq. 9 or by interpreting their oscillation frequencies directly without inertial corrections. Like conventional scales and balances, these approaches rely on independent calibration of the trap’s stiffness, ^^. The present acoustodynamic approach avoids the need for such calibrations by comparing two independent time scales represented by Ω and ^^, rather than two independent force scales.

[0044] Increasing the acoustic trap’s strength increases the oscillation frequency and lifts the particle toward the trap’s center. This correlation is reflected in the dependence of ^^^on Ω that is plotted in Fig. 2B. These measurements can be interpreted within the boundary-layer model by combining Eq.9 with Eq.11 to obtain 19where ^^^୰ୟ୮is the height of the trap’s nodal plane in the camera’s field of view. The solid curve in Fig.2B shows this model’s prediction using the value of ^^^obtained from ^^^Ω^. The data in Fig.2B have been offset so that ^^^୰ୟ୮= 0(5) μm. The excellent agreement between measurement and theory in this comparison serves to validate the acoustodynamically determined values of ^^^and ^^^. Accurately identifying ^^^୰ୟ୮also is valuable for force-extension measurements once the trap’s stiffness is calibrated. Dynamic Trap Calibration.

[0045] The trap’s stiffness at each value of ^^^can be inferred from the particle’s damped oscillations through ^^^Ω^ൌ ^^^Ω^Ωଶ^^Ω^ Eq. 20aAssuming that the pressure amplitude, ^^^, is proportional to the driving voltage, ^^^, Eq.6 and Eq. 11 lead to anെ ൩^12 4880-1385-9786Atty. Dkt. No.: 046434-0861 that can be compared with measurements based on Eq.20a to obtain ^^, the required calibration constant for this specific particle in the levitator. This result is valid when the particle is stably trapped against gravity, ^^^^ ^^ ^^ ^^. Fig.3 shows the calibration obtained from the data set in Figs. 2A-2B and yields ^^ = (6.02 ± 0.15) × 10−4N m−1V−2. Ignoring inertial corrections by using ^^^in Eq. 20a would have yielded a significant underestimate for the calibration constant, ^^^= (5.77 ± 0.14) × 10−4N m−1V−2. Adding to the challenge, an accurate value for ^^^generally would not be known a priori for a millimeter-scale object. The analytical framework described here solves this problem by providing self-consistent measurements of ^^^, ^^^and ^^^Ω^. The estimated calibration constant, ^^, therefore should yield reliable predictions for the trap stiffness, ^^. Inertia-Corrected Equation of Motion

[0046] The trajectory of an acoustically trapped particle may be modeled by the equation of motion for a damped harmonic oscillator: ^^^ ^^^^ ^ ^^ௗ^^^^, ^^^^^ ^^൫ ^^^ െ ^^^൯ ൌ 0 Eq. 21This differs from the canonical expression because the drag force experienced by a sphere of radius ^^^accelerating along ^^̂ through a fluid of viscosity ^^^and mass density ^^^is enhanced by the inertia of the displaced fluid,where ^^ ൌ 6 ^^ ^^^^^^Eq.22b is the Stokes drag coefficient and ^^^^ ൌ ^9^^^^^ଶEq.22c ^ is the viscous relaxation time for non-steady flows.

[0047] Equation 22a represents an average over the period of the acoustic pressure field, which is appropriate because the sphere’s period of oscillation is very much longer. Substituting Eq.22 into Eq.21 yields the Basset-Boussinesq-Oseen equation for this system.

[0048] The inertia-corrected equation of motion is satisfied by the trajectory for a linearly damped harmonicexp ൬െ2 േ2313 4880-1385-9786Atty. Dkt. No.: 046434-0861 The resulting expressions for the oscillation frequency Ω and damping rate ^^ are greatly simplified by invoking the weak-damping approximation, ^^^^ ^^^ ^ ^^ exp^ ^^Ω ^^^Eq. 24in Eq.22, which reduces the expression for the drag force to ^^ ^^25Substituting thisequation of motion, Eq. 16, with expressions for the effective mass ^^^Ω^, drag rate ^^^Ω^, and natural frequency Ω^^Ω^ that are given in Eqs.13, 14, and 17, respectively. The approximation implicit in Eq.25 is valid when Ω ≫ ^^^Ω^ / 2, which is the case for the data described herein. Definitions

[0049] As used herein, the singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, the term “a member” is intended to mean a single member or a combination of members, “a material” is intended to mean one or more materials, or a combination thereof.

[0050] As used herein, the terms “about” and “approximately” generally mean plus or minus 10% of the stated value. For example, about 0.5 would include 0.45 and 0.55, about 10 would include 9 to 11, about 1000 would include 900 to 1100.

[0051] It should be noted that the term “exemplary” as used herein to describe various embodiments is intended to indicate that such embodiments are possible examples, representations, and / or illustrations of possible embodiments (and such term is not intended to connote that such embodiments are necessarily extraordinary or superlative examples).

[0052] As used herein, the terms “coupled,” “connected,” and the like mean the joining of two additional intermediate members being integrally formed as a single unitary body with one another or with the two members or the two members and any additional intermediate members being attached to one another.

[0053] As shown in Fig.4, e.g., a computer-accessible medium 120 (e.g., as described herein, a storage members directly or indirectly to one another. Such joining may be stationary (e.g., permanent) or moveable (e.g., removable or releasable). Such joining may be achieved with the two members or the two members and any device such as a hard disk, floppy disk, memory stick, CD-ROM, RAM, ROM, etc., or a collection thereof) can be provided (e.g., in communication 14 4880-1385-9786Atty. Dkt. No.: 046434-0861 with the processing arrangement 110). The computer-accessible medium 120 may be a non- transitory computer-accessible medium. The computer-accessible medium 120 can contain executable instructions 130 thereon. In addition or alternatively, a storage arrangement 140 can be provided separately from the computer-accessible medium 120, which can provide the instructions to the processing arrangement 110 so as to configure the processing arrangement to execute certain exemplary procedures, processes and methods, as described herein, for example. The instructions may include a plurality of sets of instructions.

[0054] System 100 may also include a display or output device, an input device such as a keyboard, mouse, touch screen or other input device, and may be connected to additional systems via a logical network. Many of the embodiments described herein may be practiced in a networked environment using logical connections to one or more remote computers having processors. Logical connections may include a local area network (LAN) and a wide area network (WAN) that are presented here by way of example and not limitation. Such networking environments are commonplace in office-wide or enterprise-wide computer networks, intranets and the Internet and may use a wide variety of different communication protocols. Those skilled in the art can appreciate that such network computing environments can typically encompass many types of computer system configurations, including personal computers, hand-held devices, multi- processor systems, microprocessor-based or programmable consumer electronics, network PCs, minicomputers, mainframe computers, and the like. Embodiments of the invention may also be practiced in distributed computing environments where tasks are performed by local and remote processing devices that are linked (either by hardwired links, wireless links, or by a combination of hardwired or wireless links) through a communications network. In a distributed computing environment, program modules may be located in both local and remote memory storage devices.

[0055] Various embodiments are described in the general context of method steps, which may be implemented in one embodiment by a program product including computer-executable instructions, such as program code, executed by computers in networked environments. Generally, program modules include routines, programs, objects, components, data structures, etc. that perform particular tasks or implement particular abstract data types. Computer-executable instructions, associated data structures, and program modules represent examples of program code for executing steps of the methods disclosed herein. The particular sequence of such executable instructions or associated data structures represents examples of corresponding acts for implementing the functions described in such steps. 15 4880-1385-9786Atty. Dkt. No.: 046434-0861

[0056] Software and web implementations of the present invention could be accomplished with standard programming techniques with rule-based logic and other logic to accomplish the various database searching steps, correlation steps, comparison steps and decision steps. It should also be noted that the words “component” and “module,” as used herein and in the claims, are intended to encompass implementations using one or more lines of software code, and / or hardware implementations, and / or equipment for receiving manual inputs.

[0057] It is important to note that the construction and arrangement of the various exemplary embodiments are illustrative only. Although only a few embodiments have been described in detail in this disclosure, those skilled in the art who review this disclosure will readily appreciate that many modifications are possible (e.g., variations in sizes, dimensions, structures, shapes and proportions of the various elements, values of parameters, mounting arrangements, use of materials, colors, orientations, etc.) without materially departing from the novel teachings and advantages of the subject matter described herein. Other substitutions, modifications, changes and omissions may also be made in the design, operating conditions and arrangement of the various exemplary embodiments without departing from the scope of the present invention.

[0058] While this specification contains many specific implementation details, these should not be construed as limitations on the scope of any inventions or of what may be claimed, but rather as descriptions of features specific to particular implementations of particular inventions. Certain features described in this specification in the context of separate implementations can also be implemented in combination in a single implementation. Conversely, various features described in the context of a single implementation can also be implemented in multiple implementations separately or in any suitable subcombination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a subcombination or variation of a subcombination. 16 4880-1385-9786

Claims

Atty. Dkt. No.: 046434-0861 WHAT IS CLAIMED IS:

1. An acoustic trapping system comprising: an acoustic levitator having a first bank of acoustic transducers and a second bank of acoustic transducers, the first bank of acoustic transducers and the second bank of acoustic transducers positioned opposite each other; the acoustic levitator is configured to receive an object between the first bank of acoustic transducers and the second bank of acoustic transducers; the first bank of acoustic transducers and the second bank of acoustic transducers configured to emit ultrasonic waves towards each other, impacting the object when received within the acoustic levitator; and an imaging apparatus configured to capture information about the object received within the acoustic levitator.

2. The acoustic trapping system of claim 1, wherein the first acoustic bank and the second acoustic bank are configured to emit ultrasonic energy with within a frequency of 20 kHz to 2MHz and an amplitude of 70 dB to 120 dB .

3. The acoustic trapping system of claim 1, wherein the imaging apparatus is selected from a non-imaging optic, an imaging optic, and an acoustic imaging device.

4. The acoustic trapping system of claim 1, wherein the first bank of acoustic transducers and the second bank of acoustic transducers are independently controlled.

5. A method of determining mass of an object, comprising: positioning an object within an acoustic levitator between a first bank of acoustic transducers and a second bank of acoustic transducers; engaging an imaging apparatus to capture information about the positioned object; emitting counterpropagating ultrasonic waves from the first bank of acoustic transducers and the second bank of acoustic transducers; interacting at least a portion of counterpropagating waves, forming a standing pressure wave; causing an oscillation in the object within the acoustic levitator; measuring a trajectory of the object; and comparing the measured trajectory to a predicted trajectory to determine the object’s mass density and / or mass. 17 4880-1385-9786Atty. Dkt. No.: 046434-0861 6. The method of claim 5, wherein causing the oscillation comprises altering at least one property of either the first bank of acoustic transducers or the second bank of acoustic transducers.

7. The method of claim 5, wherein causing the oscillation comprises application of a motive force to the object.

8. The method of claim 5, wherein the motive force is selected from the group consisting of a mechanical impulse, a pulse of air, a transient electric field, a transient magnetic field, and transient field gradient.

9. The method of claim 5, further comprising determining an estimate of the particle’s radius based upon displacement of the object.

10. The method of claim 5, wherein the imaging apparatus is selected from a non-imaging optic, an imaging optic, and an acoustic imaging device.

11. A computer controlled acoustic trapping system comprising: an acoustic levitator having at least one bank of acoustic transducers; the acoustic levitator is configured to receive an object; the at least one bank of acoustic transducers configured to emit ultrasonic waves forming an acoustic trap within the acoustic levitator; an imaging apparatus configured to capture information about the object received within the acoustic levitator; a one or more processors; and one or more memories operatively coupled to the one or more processors, the one or more memories having instructions stored thereon which, when executed by the one or more processors, cause the one or more processors to perform operations comprising: positioning the object within the acoustic trap; engaging the imaging apparatus to capture information about the positioned object; causing an oscillation in the object within the acoustic levitator; measuring a trajectory of the object; and comparing the measured trajectory to a predicted trajectory to determine the object’s mass density and / or mass. 18 4880-1385-9786Atty. Dkt. No.: 046434-0861 12. The method of claim 1, the memories further include instructions, when executed, to cause the oscillation comprises altering at least one property of the at least one bank of acoustic transducers.

13. The method of claim 11, the memories further include instructions, when executed, to determine an estimate of the particle’s radius based upon displacement of the object.

14. The method of claim 11, wherein the imaging apparatus is selected from a non-imaging optic, an imaging optic, and an acoustic imaging device.

15. The method of claim 11, wherein the at least one bank of acoustic transducers comprises a first bank of acoustic transducers and a second bank of acoustic transducers positioned opposite to the first bank of acoustic transducers, further comprising memories including instructions, when executed to emit counterpropagating ultrasonic waves from the first bank of acoustic transducers and the second bank of acoustic transducers. 19 4880-1385-9786

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