CN112055644B

CN112055644B - Acoustichoretic force modulation in acoustophoretic printing

Info

Publication number: CN112055644B
Application number: CN201980029031.0A
Authority: CN
Inventors: D·福雷斯蒂; J·A·路易斯
Original assignee: Harvard College
Current assignee: Harvard College
Priority date: 2018-04-30
Filing date: 2019-04-25
Publication date: 2022-11-29
Anticipated expiration: 2039-04-25
Also published as: JP2021523032A; JP7361049B2; CN112055644A; WO2019212845A1

Abstract

A method, comprising: disposing a nozzle having a nozzle opening within a first fluid; and generating an acoustic field within the first fluid by oscillating the transmitter. A second fluid ("ink") is expelled from the nozzle, forming a pendant drop of the second fluid at the nozzle opening. The acoustic field at the nozzle opening is modulated and the sound generated by the acoustic field is directed to promote the hanging drop detachment. Thus, the second fluid or ink is controllably ejected as ejected drops in the first fluid. For acoustophoretic printing, the nozzle opening can be positioned opposite the print substrate, and the ejected drops can be deposited on or in the print substrate.

Description

Acoustichoretic force modulation in acoustophoretic printing

RELATED APPLICATIONS

This patent document claims priority from U.S. provisional patent application serial No. 62/664,467, filed 2018, 4, 30, 35u.s.c. § 119 (e), which is incorporated herein by reference in its entirety.

Technical Field

The present disclosure relates generally to printing technology, and more particularly to acoustophoretic printing.

Background

Due to the limitations of existing 2D and 3D printing methods in the art, inks are typically designed to have physical properties that meet the requirements of existing printers. A typical way to make the material printable is to use additives to adjust the rheology of the ink. While improving printability, such additives can act as impurities in the printed structure or otherwise be detrimental to the printed structure.

In drop-based printing technologyIn the art, inkjet technology represents a standard in industry and research. Despite the widespread use of inkjet technology, only a narrow range of materials with the appropriate combination of properties (e.g., viscosity and surface tension) can be successfully ejected from an inkjet printhead. This limitation can be attributed to the droplet detachment mechanism based on the Rayleigh-Plateau instability. In inkjet technology, the ink needs to be mechanically stimulated to break up the meniscus and eject a defined amount of liquid. This dynamic process implies a strong correlation between interfacial and viscous forces. From a physical point of view, defining the drop formation of the ink can be used as a dimensionless number, an Olympic number Oh and its inverse Z = Oh ^-1 ＝(ρσ2R) ^1/2 μ, where R is the characteristic length of the drop, ρ is the density of the liquid, σ is its surface tension, and μ is the viscosity of the ink. Not surprisingly, the scientific literature reports that successful printing requires that the ink physical properties yield Z values within a narrow range (1 < Z < 10).

Many practical inks are based on colloids or polymers, have relatively high viscosities, and require dilution with additives for successful printing. Truly decoupling the printing process from the dependence on ink physical properties may allow for unprecedented freedom in the type and complexity of materials that can be printed in 2D and 3D. Descriptions of earlier work on how to solve this problem can be found in Foesti et al, "Acousophosphoric Printing Apparatus and Method," U.S. Pat. Nos. 9,878,536 and 10,214,013 and Foresti et al, "Apparatus and Method for Acousophosphoric Printing," WO2018/022513, the entire contents of which are incorporated herein by reference.

Disclosure of Invention

A method, comprising: disposing a nozzle having a nozzle opening within a first fluid; and generating an acoustic field in the first fluid by oscillating the transmitter. A second fluid ("ink") is expelled from the nozzle, forming a pendant drop of the second fluid at the nozzle opening. The acoustic field at the nozzle opening is modulated and the sound generated by the acoustic field is directed to promote the hanging drop detachment. Thus, the second fluid or ink is controllably ejected as ejected drops in the first fluid. For acoustophoretic printing, the nozzle opening can be positioned opposite the print substrate, and the ejected drops can be deposited on or in the print substrate.

Drawings

FIG. 1A is a schematic diagram illustrating the forces acting on a hanging drop at the nozzle opening during acoustophoretic printing.

Fig. 1B shows how drop volume varies with acoustic force and nozzle diameter at break-off.

Fig. 2A is a schematic diagram illustrating acoustophoretic printing with pulse modulation.

Fig. 2B-2H illustrate how drop volume varies upon detachment depending on the printing parameters used for pulsing.

Fig. 3A is a schematic diagram illustrating acoustophoretic printing with a constant sound field.

Fig. 3B-3E show how drop volume varies upon detachment depending on the printing parameters for a constant sound field.

Fig. 4A is a schematic diagram illustrating a typical drop shape upon constant mode acoustophoretic printing and detachment of a viscoelastic fluid.

Fig. 4B is a schematic diagram illustrating a typical drop shape upon pulsed mode acoustophoretic printing and detachment of a viscoelastic fluid.

FIG. 5A is a graph including 4wt.% during constant mode printing

Images of jetted drops of solution.

FIG. 5B is a graph including 4wt.% during pulse mode printing

Images of jetted drops of solution.

Fig. 5C is an image of jetted drops comprising 3wt.% alginate solution during constant mode printing.

Fig. 5D is an image of jetted drops comprising 3wt.% alginate solution during pulse mode printing.

Fig. 6A to 6C show synchronization achieved by pulse modulation.

Fig. 7 shows a typical acoustophoretic nozzle-substrate configuration and ejected drop trajectory.

Fig. 8 shows a typical acoustophoretic drop deposition with relative substrate-printhead motion, where deposition error can be divided into components orthogonal and parallel to the printing direction.

Fig. 9 shows the natural oscillation frequency of the water droplet (first mode) according to equation 5.

Fig. 10A-10C compare drop ejection with constant acoustic effort and drop ejection with acoustophoretic force amplitude modulation.

Fig. 11A and 11B show how track errors are reduced by amplitude modulation.

Fig. 12 shows different ways for controlling the amplitude of the drive frequency to influence the acoustophoretic force.

Detailed Description

Described herein are methods of acoustophoretic field modulation during acoustophoretic printing to allow unprecedented control over drop ejection and size, shape, and trajectory of ejected drops. The method is applicable to inks having a wide range of Z values (such as 0.001 to 1000), including both newtonian and non-newtonian fluids, viscoelastic fluids, yield stress fluids, polymer solutions, hydrogels, colloids, emulsions, and complex fluids in general.

The method comprises the following steps: arranging a nozzle having a nozzle opening in the first fluid, and generating a sound field in the first fluid by oscillating or vibrating the emitter. The first fluid is capable of transmitting sound waves. A second fluid ("ink") is expelled from the nozzle, forming a pendant drop of the second fluid at the nozzle opening. The acoustic field at the nozzle opening is modulated and the sound generated by the acoustic field is directed to promote the hanging drop detachment. Thus, the second fluid or ink is controllably ejected as ejected drops in the first fluid. For acoustophoretic printing, the nozzle opening can be positioned opposite a print substrate, which can comprise a solid, liquid, or gel, onto or into which the ejected drops can be deposited.

The modulation may comprise modulating the frequency and/or amplitude of the acoustic wave from the oscillating emitter so as to vary the acoustophoretic force on the pendant drop. Before describing the sound field modulation approach in detail, the physical principles that influence drop detachment using acoustophoretic forces are explained, and various aspects of the acoustophoretic printing method are described.

Fig. 1A shows a hanging drop at the nozzle end (nozzle opening) with gravity as the external body force independent of the nozzle/reservoir system. When the gravity F _g ＝4/3πR ³ ρ g = V ρ g (where V is drop volume and g is gravitational acceleration) exceeds the opposing capillary force F at a given nozzle diameter d _c Where σ is the surface tension of the droplet, detachment occurs. It is to be noted that this manner allows the ejection of ink drops of almost any viscosity, for example, even with a viscosity higher than 10 ⁸ Pa · s asphalt droplets. To reduce drop volume at detachment V = pi σ d/ρ g, an external force (> 1 g) may be applied to substantially pull the hanging drop.

Acoustophoretic forces are independent of any electromagnetic properties and have been used to capture or manipulate droplets within an acoustic field in air. When spherical droplets are generated in a standing wave configuration, they are dominated by the following force balance:

F _c ＝πσd＝F _g +F _a ＝Vρ(g+g _a )→V＝πdσ/ρg _eq (1)

wherein, F _c Capillary force of = pi σ d is determined by gravity F _g Harmony swimming force F _a ∝R ³ P ² ∝VP ² The two are antagonistic, where R is the drop radius and P is the sound pressure. Fig. 1A and 1B illustrate drop detachment as described by equation 1.

The acoustophoretic droplet ejection process described in equation 1 is a quasi-static system. The above description can also be extended to employ dynamic models to explain the evolution of drop size with respect to time. By feeding the nozzle at a constant flow rate Q, the pendant drop volume can be evolved in terms of V (t) = Q · t, where t represents time. At this approximate level the capillary force Fc is constant, i.e. F _c = pi σ d = constant. Equation 1 becomes:

F _g (t)+F _a (t)＝V(t)ρ(g+g _a (t))＝Q·t·ρ(g+g _a (t)) (2)

in equation 2, it is assumed that Q is constant and within the range of the drop of the nozzle liquid. This approach may also be true in the case of Q (t) (i.e., the flow rate is a function of time).

The sound field may be a constant sound field, where g _a Is a constant; or the sound field may be modulated such that g _a Is a function of time.

In the case of a constant sound field, g _a And a constant. Thus, detachment can occur in the following cases:

V(t)ρ(g+g _a (t))＝Q·t·ρ(g+g _a )＝F _c ＝πσd (3)

drops can be released at a specific time, V (t) _d )＝V _d ，V＝πdσ/ρg _eq 。

When acoustophoretic acceleration g _a As a function of time (i.e. in the variable sound field g) _a (t) case), jet evolution and drop break-off may be g _a (t) as a function of. In this case, drop detachment may follow the inequality (equation 4):

Q·t·ρ(g+g _a (t))＞＝F _c ＝πσd (4)

the ga (t) modulation mode has an influence on the bond detachment of the droplet, and the acoustophoretic droplet ejection operation mode can be fundamentally changed.

The present disclosure now returns to a general description of a method in which an acoustic field is modulated to control the ejection and deposition of drops during acoustophoretic printing. As described above, a wide range of inks ("second fluids"), including inks having Z values in the range of 0.001 to less than 1, 1 to 10, or from greater than 10 to 1000, can be successfully printed. The ink or second fluid may comprise, for example, a synthetic or naturally derived biocompatible material with or without cells (e.g., human cells, such as stem cells, primary cells, or other cell types), a conductive or ionically conductive material such as a liquid metal (e.g., gallium indium eutectic (EGaIn)), and/or a polymer such as an adhesive, hydrogel, or elastomer.

The Method may be performed in an acoustic chamber partially or completely enclosed by an acoustically reflective wall, such as described in "Apparatus and Method for acoustophoric Printing" WO2018/022513, forest et al, incorporated herein by reference. The acoustic chamber may comprise a first fluid, for example a gas or a liquid, such as ambient air, water or oil. The acoustic chamber may be immersed in the first fluid. In some cases, the first fluid may be forced through the acoustic chamber at a constant or variable flow rate.

The oscillating transmitter may take the form of a piezoelectric transducer, a metal oscillator, or other acoustic wave source. Suitable drive frequencies may be in the range of 1kHz to 2MHz, more typically in the range of 20kHz to 250 kHz.

The nozzle through which the second fluid is ejected may take the form of a glass pipette, a micro-machined feature (e.g., comprising silicon), or other fluid conduit. Typically the diameter of the nozzle opening is in the range of about 1 micron to about 1mm, more typically in the range of about 10 microns to about 100 microns. To prevent wetting of the nozzles during printing, the nozzles may include a hydrophobic coating at or near the nozzle openings. Examples of suitable nozzles are described in U.S. provisional patent application No. 62/826,436 to forest et al, "non Design for Acoustic Printing," incorporated herein by reference.

The advantage of this method is that the size and shape of the ejected drop can be controlled. Typically, the width or diameter of the ejected drop is less than about 2mm (or less than about 4mm by volume) ³ ). At higher acoustic fields or where the acoustic field is modulated, as described below, smaller sized droplets, such as droplets having a width or diameter of less than about 200 microns or a volume of less than about 0.004mm, may be ejected ³ Is dropped. In some cases, the diameter of the ejected drop can be as small as about 120 microns, or even as small as about 50 microns. The lower limit of the droplet diameter may be about 10 microns. Generally, the width or diameter of the jetted drops is in the range of about 10 microns to about 2mm, with a width or diameter range of 50 microns to 2mm or 200 microns to 2mm being more typical. The shape of the ejected droplets may range from teardrop or pear shapes to spherical or oval shapes depending on how the acoustic field is modulated.

As described above, sound field modulation may involve controlling the frequency and/or amplitude of oscillation from an oscillating transmitter.

Pulse modulation

In one example, sound field modulation may involve pulsing the sound field in what may be referred to as a "pulse mode" or PM modulation. The pulsing may be performed at a frequency of about 0.01Hz to about 10,000khz, more typically 1Hz to about 1,000khz. The pulse may be an on-off pulse, wherein the pulse amplitude is 0% or 100% of the peak amplitude. Alternatively, the pulse amplitude may vary between 0% and 100% of the peak amplitude. In some cases, the pulse amplitude may not return to zero. For example, the pulse amplitude may vary from greater than 0% to 100% of the peak amplitude, 50% to 100% of the peak amplitude, or 80% to 100% of the peak amplitude. The pulses may be represented by a waveform selected from a square wave, a triangular wave, a sawtooth wave, or a sine wave. The duty cycle of the pulses may range from greater than 0% to less than 100%, typically 10% to 90% or 30% to 70%. The ejection speed of the ejected drop may increase as the duty cycle of the pulse increases.

The frequency of detachment of the pendant drop may be determined by the pulse frequency. The effect of pulse modulation on drop ejection is illustrated in fig. 2A-2H. In this example, g _a (t) is a square wave function, max g _a ＝g _amax =5g and a duty cycle of 10%. In this case, when g _a(t) With =0, the minimum drop size that can be detached is equivalent to a simple drop, i.e. V _d ＝V _{Drip down} . In g _a(t) ＝g _amax In the case of (2), the minimum possible value is V _min ＝V _{Drip down} /(g _amax +1). According to the inequality of equation (4), the disengagement can be by the pulse modulation period τ _PM And its corresponding frequency f _PM To decide. By pulse modulation, the frequency of ejection f of drops _eq Is constant and determined by the pulse pattern, and drop volume V at break-off _d Depending on the flow rate Q. Note that g may be selected _amax And f _pm Consider Q. In general, for periodic injection, f _pm V _d ＞Q＞f _pm V _min 。

And no sound field modulation (i.e. for g) _a = constant ("constant mode"), the impact of pulse modulation on drop ejection can be understood as described above with reference to equation 3. In this case, for constant Q and g _a In other words, the injection is periodic, so V _d ＝Q·τ _ej Wherein, τ _ej Is a drop ejection cycle. As can be seen from FIGS. 3A-3E, by increasing Q, the drop break-off period can be reduced and the corresponding drop ejection frequency f _ej ＝1/τ _d May be increased and vice versa. Note that in all of these cases where Q is varied, the drop volume V at break-off _d Remain unchanged. By changing g only _a The drop size changes. At the same time, for equal Q, increased g _a To f _ej With a linear effect as shown.

The main difference between using the pulsed mode and using the constant mode is that: in the latter mode, drop volume V upon detachment _d Is constant regardless of flow. By contrast, with pulse modulation, the ejection frequency f of the drops _eq Is constant and determined by the pulsation pattern, and drop volume V at break-off _d Depending on the flow rate. Both Constant Mode (CM) and Pulsed Mode (PM) approaches have advantages, and the selection of one or the other or a combination of both may depend on the particular application. For example, if monodispersity is a priority for noisy/variable flow, constant mode is a good choice. The pulse mode is more suitable if it is preferred for noisy/variable flow to keep the injection frequency constant. Notably, the drop volume is proportional to the third power of its diameter D. This means that V _d A 15% variation still maintained the monodispersity of the droplets (diameter variation less than 5%). On the other hand, a 15% variation in drop ejection frequency is problematic in the case of printing on a substrate due to resolution/accuracy loss.

Pulsing the acoustic field has many advantages when dealing with high viscosity and viscoelastic fluids (e.g., inks with Z values from greater than 10 to 1000). In fact, the presence of a constant field may begin to pull the drop while it is still attached, stretching the drop before detachment, forming a teardrop/pear shape or may be described as a tailed drop, as shown in fig. 4A. By using a pulsed acoustic field, this defect can be controlled and/or eliminated, as schematically shown in fig. 4B. Two typical examples of high viscosity/viscoelastic fluids are: yield stress fluids, e.g. cross-linkingPolyacrylic acid polymers (e.g., 4wt. -%)

) (ii) a Or a shear thinning fluid such as a 3wt.% alginate solution. These inks were subjected to constant mode and pulsed mode acoustophoretic printing, and the shape of the printed drop was studied, for 4wt.% of

The solutions are shown in fig. 5A and 5B, and in fig. 5C and 5D for a 3wt.% alginate solution. For the

Solution with d =100 μm, g _a =60g constant mode experiment was performed and d =100 μm, g _a =60g and f _PM Pulse mode experiments were performed at =0.3 Hz. For alginate solutions, d =90 μm, g _a =60g constant mode experiment with d =90 μm, g _a =60g and f _PM Pulse mode experiments were performed at =3.9 Hz. By comparing the images, it can be observed that the ejected drops produced in the constant mode experiment (fig. 5A and 5C) exhibited tails that were reduced (fig. 5B) or eliminated (fig. 5D) in the pulse mode experiment. Thus, depending on how the acoustic field is modulated, the jetted droplets may have a non-spherical shape with a tail (e.g., a teardrop or pear shape), or the jetted droplets may appear spherical.

As already mentioned, the pulse pattern may provide control over the drop ejection frequency. For certain applications, it may be important to control the injection period τ _ej Such that drop ejection occurs periodically (or aperiodically, if desired). This capability can be used to synchronize drop ejection from multiple nozzles, as shown in fig. 6A-6C. For multiple (two or more) nozzles disposed in a first fluid, pulsing each pendant drop can cause lift-off such that drop ejection is synchronized; in other words, drop ejection from multiple nozzles can be controlled to occur simultaneously. If the pulses applied to each drop can be independently controlled, then synchronizing may include directing pulses from multiple nozzlesDrop ejection of (a) is controlled to occur simultaneously or sequentially (if desired).

This approach is particularly beneficial because manufacturing imperfections can lead to inconsistencies between the various nozzles. In addition, parameters (such as flow Q and/or maximum applied acoustophoretic force g _amax ) May vary with respect to the expected value. As shown in fig. 6B and 6C, even for different g _amax The values or spray periods of the plurality of nozzles may also be synchronized for different flow rates Q through the nozzles. Advantageously, using pulsed mode acoustophoretic printing, a pendant drop can be detached from a nozzle at a predetermined time, ideally with a detachment error of about 200ms or less. Further, for a known ejected drop velocity and distance from the substrate, the ejected drops can be deposited onto or into the print substrate at a predetermined time.

Synchronization is also beneficial to improve printing accuracy. As explained below, the tracking error epsilon _t And a disengagement error e _d May be inherent to the electrophoretic printing process.

Fig. 7 shows a typical acoustophoretic nozzle-substrate configuration and ejected drop trajectory. The spray trajectory may have an angle alpha compared to a vertical trajectory. The accuracy analysis is based on Δ α. For simplicity, α =0 is considered, but the description made can be extended to any α as well.

There are different ways to calculate and measure accuracy. For example, (1) the change in the spray angle α can be measured and/or (2) the placement of the drops on the substrate can be analyzed in a static or dynamic manner. In the first case, the motion of each drop can be tracked in two planes (xz and yz) in order to reconstruct the deposition of the drop on the substrate (fig. 7, right). The result may give a specific error component, namely the trajectory error ε _t This is inherent to the acoustophoretic printing process. In the second case, the drops may be printed on the substrate. A clear advantage is that a large number of drops can be printed and the position of individual drops can be analyzed simply by a single map. The disadvantages are that: for static objects/substrates, the number of printable drops is limited, as the drops soon overlap (fig. 7, right).

Thus, an alternative is to move the substrate while printing. To be provided withIn this way, error is recovered by comparing drop positions along the ideal trajectory, as shown in FIG. 8. Besides being simple, this approach has another advantage: it not only helps to find out the track error epsilon _t And also helps to find the release error epsilon _d . Drop-off errors are due to uncertainty in drop ejection timing. This uncertainty can lead to accuracy errors when there is a moving target. Errors can also be divided into quadrature errors and parallel errors, defined as being orthogonal and parallel to the printing direction, respectively. The quadrature error is due to the track error epsilon _t And (4) causing. The parallelism error is due to two components, i.e. the trajectory error epsilon _t And a disengagement error e _d And (4) causing. In case of symmetry being assumed, the trajectory error should be the same in both orthogonal and parallel directions. This means that the trajectory error component in the parallelism error should be equal to the quadrature error. At this time, by subtracting the quadrature error, the slip-off error can be found by the parallel error.

Drop ejection synchronization can be used to reduce drop-out error epsilon _d . As described above, this can be accomplished by using pulsing to control drop release/ejection. Track error ε can be reduced by using amplitude modulation to modulate signals in different ways and time scales _t As described below.

Amplitude modulation

Acoustophoretic forces can be used to cause oscillation of the droplet. When the force is periodic, it can excite a specific natural oscillation mode n of the droplet. Rayleigh has studied and described this phenomenon for small amplitude, non-sticking spherical droplets. Within these approximate ranges, the natural frequency of oscillation can be calculated as:

f _n ＝1/2π·((σ·n(n+1)(n-1)(n+2))/R ³ Γ) ^1/2 (5)

wherein Γ = ρ ₀ n + ρ (n + 1), and ρ ₀ Is the density of the surrounding fluid (in this case the acoustic medium). Fig. 9 shows the natural frequency (n = 2) of the first resonance mode of the water droplet in the air. The drop radius is selected to be within a range of interest for acoustophoretic printing (in particular, magnification)Figure, right side), but generalizations are also possible for larger and smaller droplets. Of particular interest is the case of a droplet radius with a resonance frequency comparable to the ultrasound frequency, for example about 25kHz for R =30 μm (see circle in fig. 9, left). It is believed that very interesting phenomena may occur in this frequency range.

For acoustophoretic printing, the acoustic effort can be modulated by superimposing waveforms of different frequencies from the sound field frequency to implement amplitude modulation. For example, a frequency f matching the natural frequency of the pendant drop may be used _AM To modulate acoustophoretic acceleration g _a (t) of (d). Generally speaking, the frequency f _AM May be within +/-50% of the natural frequency of the pendant drop. Fig. 10A to 10C show schematic evidence and experimental evidence of such a modulation scheme. Each top image of fig. 10C is by jetting d =80 μm, g _a =60g of water and shows drop behaviour at constant or continuous acoustophoretic force; each bottom image of fig. 10C is by jetting d =80 μm, g _a =60g and f _AM Water of =270Hz, and shows the drop behaviour under acoustophoretic forces after amplitude modulation.

Amplitude modulation can be used to reduce lateral oscillations of the hanging drop and improve the trajectory accuracy of the ejected drop. In other words, the track error or deviation ε may be reduced _t As shown in fig. 11A for an exemplary constant mode experiment and Amplitude Modulation (AM) mode experiment. The data of FIG. 11B shows the standard deviation of drop deposition locations for constant mode and AM mode, where g is achieved by spraying a water-glycerol solution (50 wt.%), with _a =87, d =60 μm, Q =296nL/s, printing speed =500mm/min, f _AM =2.5kHz, acoustophoretic printing. Advantageously, the ejected drops can be deposited onto or into the print substrate at predetermined locations, the trajectory error ε being compared to a situation without amplitude modulation _t Reduced to less than 50% and angular trajectory error Δ α < 10 °.

Amplitude modulation can also be used to reduce drop size upon ejection because the oscillations cause additional acceleration of the drop resulting in additional force to assist detachment. As noted above, a spray width or diameter of less than about 200 microns may be usedOr a volume of less than about 0.004mm ³ Is dropped. In some cases, the ejected drop may be as small as about 120 microns in diameter, or even as small as about 50 microns, where the lower limit of the drop diameter may be about 10 microns. Generally, the ejected drops have a width or diameter in the range of about 10 microns to about 2mm, with a width or diameter generally in the range of 50 microns to 2mm, 200 microns to 2mm, and/or 50 microns to 200 microns.

Amplitude modulation can impart a specific shape to the drop as it is ejected (by resonating at a different natural mode, i.e., n =2,3,4.), which can be used to generate a specific shape of the particle. For example, the jetted droplets may solidify in flight while still oscillating to produce microparticles. In general, amplitude modulation may allow for a pendant drop having a predetermined shape (e.g., teardrop, spherical, ovoid) to be obtained upon detachment. It is also important to consider the special case where f _AM Near the natural oscillation frequency fn and within the same order of magnitude of the main (driving) frequency f or one of its harmonics (e.g., f =25kHz, harmonics of 2f,3f,. Et cetera).

To control g of acoustophoretic printing _a (t), several solutions can be implemented: (1) the amplitude of the driving frequency f can be controlled; (2) the geometry of any resonator can be controlled; (3) the acoustic properties of the medium can be controlled; and/or (4) combinations of these.

One straightforward way to affect acoustophoretic forces is to vary the amplitude of the acoustic wave, for example, to control the amplitude of the drive frequency (carrier signal). The sound waves may have any shape and modulation thereof. An example is shown in fig. 12. The carrier signal f without modulation corresponds to Constant Mode (CM) printing. Using at a frequency f _pm The pulse pattern of modulating the carrier signal f having any waveform results in pulse Pattern (PM) printing. By at a frequency f different from the carrier frequency _AM And the waveform to obtain amplitude modulation, resulting in Amplitude Modulation (AM) mode printing. As shown in fig. 12, the frequency of the waveform may be lower than the sound field frequency. It is also possible to combine all these ways. In certain cases where the injection accuracy is improved, both PM and AM may be used simultaneously.

In addition or alternatively, the main frequency f may be varied, for example, by using a resonator, for example by a waveguide or subWAVE (e.g., as described in U.S. patent No. 10,214,013 acostophoretic Printing Apparatus "to forest et al and WO/2018/022513a1" to forest et al, the entire contents of which are incorporated herein by reference). In this case, the magnitude of the force depends on the matching between the resonator geometry and the excitation frequency. By varying the sound frequency, the resonator may or may not resonate, thereby directly affecting the amplitude and distribution of the sound field within the chamber (e.g., within the chamber outlet or within the wavelet), and thus affecting the acoustophoretic force on the droplet. In addition or as an alternative, the geometry of the resonator may be controlled. Since the resonator can be designed for a specific wavelength, a change in the geometry of the resonator can change the resonant frequency. In addition or as an alternative, sound field modulation can be achieved by modifying the oscillating emitter. For example, the size (size) or geometry of the oscillating emitter may be varied.

Additionally or alternatively, an acoustic medium ("first fluid") may be selected to affect g (t), which may be a gas such as air or a liquid such as water or oil. The wavelength of the acoustic wave depends on the medium. By changing the properties of the medium (e.g., density or temperature), the wavelength of the acoustic wave can also be changed. This can be used to set the system on/off resonance, thereby affecting the final acoustophoretic force. Indeed, during acoustophoretic printing, modulation of the sound field may be achieved by varying the temperature of the first fluid.

In summary, sound field modulation can be implemented to affect acoustophoretic printing using any combination of the following ways: modulating amplitude, frequency, resonator size or geometry, emitter size or geometry, and/or temperature of the first fluid.

Although the present invention has been described in considerable detail with reference to certain embodiments, other embodiments are possible without departing from the scope of the invention. Therefore, the spirit and scope of the appended claims should not be limited to the description of the preferred versions contained herein. All embodiments that come within the meaning of the claims are to be embraced within their literal or equivalent scope.

Moreover, the advantages described above are not necessarily the only advantages of the invention, and it is not necessarily expected that all of the described advantages will be achieved by each embodiment of the invention.

Claims

1. A method of acoustophoretic printing, the method comprising:

disposing a nozzle within the first fluid, the nozzle having a nozzle opening;

generating an acoustic field in a first fluid by an oscillating transmitter;

expelling the second fluid from the nozzle to form a pendant drop of the second fluid at the nozzle opening; and

the sound field at the nozzle opening is modulated,

wherein sound generated by the acoustic field is directed to promote detachment of the pendant drop, thereby causing the second fluid to be ejected as a jetted drop in the first fluid;

wherein the pendant drop breaks off from the nozzle at a predetermined time with a break off error of less than 200 ms.

2. The method of claim 1, wherein modulating the acoustic field comprises pulsing the acoustic field and the pendant drop detaches at a detachment frequency determined by the pulsing.

3. The method of claim 2, wherein the frequency of pulsing is 0.01Hz to 10,000khz.

4. The method of claim 2, wherein the pulsing is performed by a waveform selected from the group consisting of: square wave, triangular wave, sawtooth wave, sine wave.

5. The method of claim 2, wherein the amplitude of the pulse modulation varies from greater than 0% to 100% of the peak amplitude.

6. The method of claim 5, wherein the amplitude of the pulse modulation varies from 50% to 100% of the peak amplitude.

7. The method of claim 2, wherein the ejection speed of the ejected drop increases as the duty cycle of the pulse modulation increases.

8. The method of claim 1, further comprising a plurality of nozzles disposed in the first fluid and synchronizing the release of the pendant drop from each nozzle opening.

9. The method of claim 1, wherein the ejected drop comprises a sphere.

10. The method of claim 1, wherein the second fluid comprises a Z value in the range of 0.001 to 1000.

11. The method of claim 10 wherein the Z value is from greater than 10 to 1000.

12. The method of claim 1, wherein the nozzle opening is positioned opposite a print substrate comprising a solid, liquid, or gel.

13. The method of claim 12, wherein the ejected drop is deposited onto or into the print substrate at a predetermined position with an angular trajectory error Δ α < 10 °.

14. The method of claim 1, wherein the pendant drop, when detached, has a predetermined shape selected from the group consisting of a sphere, an oval, and a teardrop.

15. The method of claim 1, wherein the modulation of the acoustic field is by any combination of modulating amplitude, frequency, resonator size or geometry, emitter size or geometry, and/or temperature of the first fluid.

16. The method of claim 1, wherein modulating the sound field comprises superimposing a waveform having a frequency different from the sound field frequency, thereby effecting amplitude modulation of the sound field.

17. A method of acoustophoretic printing, the method comprising:

disposing a nozzle within the first fluid, the nozzle having a nozzle opening;

generating an acoustic field in a first fluid by an oscillating transmitter;

the sound field at the nozzle opening is modulated,

wherein modulating the sound field comprises superimposing a waveform having a frequency different from the sound field frequency, thereby performing amplitude modulation of the sound field.

18. The method of claim 17, wherein the frequency of the waveform is within +/-50% of the natural frequency of the pendant drop.

19. The method of claim 17, wherein the frequency of the waveform is lower than the soundfield frequency.

20. The method of claim 17, wherein the pendant drop size upon detachment is reduced due to amplitude modulation, the pendant drop having a width or diameter of less than about 200 microns.

21. The method of claim 17, wherein modulating the acoustic field further comprises pulsing the acoustic field and the pendant drop detaches at a detachment frequency determined by the pulsing.