SAW-driven droplet jetting technology in microfluidic: A review

Abstract

The introduction of surface acoustic wave (SAW) technology on microfluidics has shown its powerfully controlling and actuating fluid and particle capability in a micro-nano scale, such as fluid mixing, fluid translation, microfluidic pumping, microfluidic rotational motor, microfluidic atomization, particle or cell concentration, droplet or cell sorting, reorientation of nano-objects, focusing and separation of particles, and droplet jetting. The SAW-driven droplet jetting technology enjoys the advantages of simple structure to fabricate with little hindrance, compact size to integrate with other components, high biocompatibility with biological cells or other molecule samples, large force in realizing fast fluidic actuation, and contact-free manipulation with fluid. The realization of this technology can effectively overcome some bottleneck problems in the current micro-injection technology, such as mechanical swear, complicated and bulky structure, and strict limitation of requirements on fluidic characteristics. This article reviews and reorganizes SAW-microfluidic jetting technology from decades of years, referring to the interaction mechanism theory of SAW and fluid, experimental methods of SAW-microfluidic jetting, effects of related parameters on objected pinch-off droplets, and applications of individual structures. Finally, we made a summary of the research results of the current literature and look forward and appraise where this discipline of SAW-microfluidic jetting could go in the future.

I. INTRODUCTION

Microdroplet drop-on-demand jetting technology can be widely used in inkjet printing of industrial production,¹ microcircuit manufacturing² and dispensing in microelectronics,³ DNA and protein distribution in biomedicine,⁴ and intricate material device molding in aviation and construction field⁵ and other industries. The jetting requirements are rigorous, especially in precise droplet volumes, highly accurate droplet placement, high droplet jetting frequency, variable droplet size capability, and unrivaled reliability.^6–8 The mechanism of microdroplet drop-on-demand jetting technology is to break the equilibrium state to form a jet by applying a specific external force to the liquid and control the jet to pinch-off into droplets at the same time. At present, droplet jetting methods mainly contain pneumatic type,⁹ thermal bubble type,¹⁰ piezoelectric type,¹¹ electromagnetic type,^12,13 mechanical type,¹⁴ and ultrasound focusing type¹⁵ according to the driving source. The pneumatic jetting device directly uses air pressure as the driving force with a simple structure and a wide range of material forming; however, the shortcoming is the limited driving force and inconvenient control.⁹ The principle of the thermal bubble inkjet technology is heating and vaporizing the liquid in contact with a heating element to generate bubbles and to squeeze the liquid out from the nozzle. This technology is capable of ejecting small droplets of low-viscosity fluid (≤30 cps), but only can be used for liquids that are heated and evaporated quickly.¹⁰ The principle of the piezoelectric micro-injection device is using the piezoelectric characteristics of the piezoelectric ceramic material as the driving force to generate the radial volume contraction and expansion deformation that causes the liquid in the tube to form a pressure pulse to spray the droplets. The most significant advantage of this technology is that an array of injectors can work simultaneously so that the droplets can be generated at a high frequency. Nevertheless, their typical suitable viscosity range of fluid is also below 30 cps. Apart from some problems of nonlinearity, creep, aging, and hysteresis in piezoelectric ceramics, an additional amplification mechanism is required to improve the output displacement and ejection quality.¹¹ Mechanical ejections create pressure fluctuations in the fluid through the movement of the valve stem and eject the fluid as a beam. The advantage of this technology is that the nozzle position can achieve high partial pressure and then can spray those highly viscous fluids. The disadvantage is that severe mechanical wear of moving parts exists in the cavity.¹⁴ The electromagnetic ejection works in limitation by ejecting a conductive metal liquid from a micro-sized nozzle under the action of a Lorentz force in a magnetic field.^12,13 The ultrasonic focusing micro-ejection devices focus the pulsed ultrasonic wave on the free liquid surface utilizing a spherical acoustic lens to form a high sound pressure in a localized range to overcome the surface tension of the fluid. Thereby, microdroplets are ejected, which is entirely determined by the ultrasonic frequency and the acoustic properties of the fluid. The whole ultrasonic system is highly complicated and costly.¹⁵ Due to a variety of the above issues, exploring a new micro-ejection technology never stops.

In the past 10 years, surface acoustic wave (SAW) technology has been increasingly applied in manipulating microfluidics. So far, SAW technology has widespread lab-on-a-chip applications of microfluidic mixing,^16,17 microfluidic translation,^18–20 microfluidic pumping,^21–23 microfluidic rotational motor,²⁴ microfluidic atomization,^25–28 particle or cell concentration,^29,30 droplet or cell sorting,^31,32 reorientation of nano-objects,³³ cell synchronization,³⁴ and focusing and separation of particles,^35,36 which demonstrates an effective manner in controlling and manipulating fluids and particles. SAW is a kind of acoustic wave that propagates along the surface of an elastic piezoelectric material with the energy mainly constrained on the surface and exponentially decaying in the depth direction. These SAW-based microfluidic actuators offer the advantages of simple structure to fabricate with little hindrance, compact size to integrate with other components, high biocompatibility with biological cells or other molecule samples, large force in realizing fast fluidic actuation, and versatility in various fluid driving modes.^37,38 Therefore, more and more attempts have been paid to the SAW-microfluidic jetting technology over these years. Microfluidic confinement mechanisms such as nozzles or orifices are not necessary to accelerate the fluid to produce droplet jetting, and only a simple structure of the SAW device is required for realizing objects jetting, i.e., piezoelectric single crystal material and finger-crossed metal inter-digital transducers (IDTs).^39–43 Although some articles in SAW-microfluidic jetting have been published, no review paper has been found which addresses the interaction mechanism of SAW and microfluidic, the principle and performance of liquid jet, key features of various SAW jetting methods, and the versatility and difficulty of applications simultaneously. This review paper tries to provide a comprehensive review of SAW-microfluidic jetting technology during the past 20 years as well as the potential applications and future development. We first introduced the interaction mechanism theory of SAW-microfluidic jetting technology from the SAWs in microfluidic actuation, the generation of “SAW streaming,” to the principle of liquid ejection and droplet breakup. Then, we summarized the influence of experimental methods and parameters on jetting performance, i.e., piezoelectric materials, driving single forms, contact angle, excitation frequency, input power, initial parent drop state, heat effect, and phononic crystals and micromachined platforms application in shaping fluids. Finally, we concluded the achievements and potential application areas of SAW-microfluidic ejection and look forward to exploring the research direction of this technology in the future.

II. INTERACTION MECHANISM OF SAW AND FLUID

A. SAWs in microfluidic actuation

The SAW is a nanometer order amplitude electro-elastic wave at megahertz mechanical vibration frequency that propagates along the surface of piezoelectric substrate material, and the energy is concentrated near the surface. Different boundary conditions and propagation medium conditions can excite different modes of SAWs, such as Rayleigh SAW,⁴⁴ leaky SAW,⁴⁵ shear-horizontal (SH) SAW,⁴⁶ and Lamb SAW⁴⁷ presented on a semi-infinite substrate, Love waves,⁴⁸ Sezawa waves,⁴⁹ and Stoneley waves⁵⁰ in the layered structure. The most straightforward SAW device is composed of a piezoelectric substrate with positive and inverse piezoelectric properties and finger-crossed metal IDTs printed on the surface of the piezoelectric substrate. When a matching alternating electrical signal is applied to the metallic IDTs bus electrode, the electrical signal will convert into mechanical energy by the inverse piezoelectric effect of the piezoelectric substrate that propagates on the surface of the substrate in the form of SAW displacement amplitude [Figs. 1(a) and 1(b)]. The structure parameters of the IDTs, such as electrode shape, aperture, electrode width and spacing, film thickness to wavelength ratio, and electrode pair numbers, determine the response frequency, propagation directivity, and bandwidth of the generated SAW. In the field of microfluidic actuating, both traveling-wave SAWs⁵¹ and standing-wave SAWs^52,53 have been effectively applied. Traveling-wave SAWs are obtained by absorbing the acoustic energy with the gel material, while standing-wave SAWs are usually obtained by allowing the wave to reflect from reflecting grating on the substrate or superimposing multi-column acoustic waves. Accordingly, the structure of the IDT mainly includes traditional straight IDT,⁵⁴ focused IDT,²⁸ chirped IDT,⁵⁵ and slanted finger IDT⁵⁶ [Figs. 1(c)–1(g)]. With a flexible electrode structure design, the sound wave can be transmitted along only one direction, which is called electrode width-controlled, single-phase unidirectional transducers (EWC-SPUDTs^57,58) shown in Fig. 1(h).

FIG. 1.

The schematic diagram of SAW generation. [(a) and (b)] A metallic IDT deposited on the piezoelectric substrate generates SAWs that propagate along the substrate surface. d₁ is the electrode width, d₂ is the electrode spacing, λ is the SAW wavelength, and W is the aperture of IDTs. (c) Traveling-wave SAW for straight IDTs. (d) Standing-wave SAW for superimposing two columns of SAWs with the same frequency. (e) Focused IDTs. (f) Chriped IDTs. (g) Slanted finger IDTs (SFIT). (h) Electrode width-controlled, single-phase unidirectional transducers (EWC-SPUDTs).

Generation of SAWs on a piezoelectric material can be mathematically modeled, even though it is extremely complicated by the presence of the electromechanical coupling effect and the anisotropy exhibited in both mechanical and electrical properties of piezoelectric materials. There are some reference works in learning about modeling acoustic wave propagation in solid piezoelectric media, but a challenging aspect of proper analysis is the possibility of a variety of wave types appearing simultaneously for the anisotropy in the piezoelectric material, such as Rayleigh waves,⁴⁴ SH-SAW,⁴⁶ leaky SAW,⁴⁵ Scholte waves,⁵⁹ Sezawa waves,⁴⁹ pseudo-SAW,⁶⁰ and surface-skimming bulk wave (SSBW).⁶¹ The constitutive equations governing the relationship among stress, strain, electric field, and electric displacement field in piezoelectric motion are as follows:^62,63

$$D_i=e_{ikl}{S}_{kl}+{\epsilon }_{ik}^S{E}_k,$$ (1)

$$T_{ij}=c_{ijkl}^E{S}_{kl}-e_{kij}{E}_k,$$ (2)

where D_i is the electrical displacement (C/m²), e_ikl is the piezoelectric matrix (C/m²), $S_{kl}$ is the strain tensor (C/m²), ${\epsilon }_{ik}^S$ is the permittivity matrix (F/m), T_ij is the stress vector, $c_{ijkl}^E$ is the elasticity matrix (N/m²), and E_k is the electric field vector (V/m). The electric field displacement equation arises from the relation between electric displacement and electric field,⁶⁴ $D_i={\epsilon }_{ik}{E}_k$, while the stress equation arises from Hooke's law,⁶⁵ $T_{ij}=c_{ijkl}{S}_{kl}$. With a particular coordinate system be used, both piezoelectric matrix and strain tensor are symmetrical to simplify the equations. In general, the electromagnetic wave propagates five orders of magnitude faster than the elastic wave, then the electromagnetic wave coupled with the SAW can be approximated as an electrostatic field, which is known as the quasi-static assumption.⁶⁶ The electric field intensity can be expressed as a gradient of a potential function, $E_k=-\mathrm{\partial }\mathrm{\Phi }/\mathrm{\partial }{x}_k$. Since the medium is an insulator without free charge, the gradient of electric displacement vector D must be equal to zero, $\mathrm{\partial }{D}_i/\mathrm{\partial }{x}_i=0$.

B. SAW streaming force

Figure 2 shows the acoustic radiation mechanism for driving liquid by SAW. When a column of SAW contacts with a liquid, the propagation mode of the wave will change from the original SAW that propagates along the substrate surface to the leaky SAW that continues to propagate on the substrate surface and longitudinal pressure wave that propagates along the Rayleigh angle in the fluid, ${\theta }_R=\arcsin ({\mathrm{v}}_f/v_s)$, with energy leaking into the liquid, where v_f and v_s are the acoustic wave velocities in fluid and the piezoelectric substrate, respectively.^67,68 A non-linear phenomenon that transforms the SAW energy into a steady fluid flow is called SAW-induced acoustic streaming, which is also known as “SAW streaming.” When a high-intensity beam of the SAW source radiates into a liquid, SAW streaming would be generated. For a general viscous fluid, the principle equations of mass and momentum conversation that govern the motion of continuous media are as follows:⁶⁸

$${\displaystyle \frac{\mathrm{\partial }\rho }{\mathrm{\partial }\mathrm{t}}+\mathrm{\nabla }\cdot (\rho u)=0,}$$ (3)

$$\rho {\displaystyle \frac{\mathrm{\partial }\mathrm{u}}{\mathrm{\partial }t}+\rho (u\cdot \mathrm{\nabla })u=-\mathrm{\nabla }p+\mu {\mathrm{\nabla }}^{2}u+({\mu }_B+{\displaystyle \frac{\mu }{3})\mathrm{\nabla }(\mathrm{\nabla }\cdot u),}}$$ (4)

where ρ is the mass density, u is the flow velocity, p is the fluid pressure, μ is the shear viscosity of fluid, and μ_B is the bulk dynamic viscosity of fluid. Combining Eqs. (3) and (4),

$$\begin{array}{r}{\displaystyle \frac{\mathrm{\partial }\rho u}{\mathrm{\partial }t}+\rho (u\cdot \mathrm{\nabla })u-u\mathrm{\nabla }\cdot \rho u=-\mathrm{\nabla }p+\mu {\mathrm{\nabla }}^{2}u+({\mu }_B+{\displaystyle \frac{\mu }{3})\mathrm{\nabla }(\mathrm{\nabla }\cdot u).}}\end{array}$$ (5)

Definition:

$$F_0={\displaystyle \frac{\mathrm{\partial }\rho \mathrm{u}}{\mathrm{\partial }t},}$$ (6)

$$-F_1=\rho (u\cdot \mathrm{\nabla })u-u\mathrm{\nabla }\cdot \rho u.$$ (7)

FIG. 2.

The schematic diagram of acoustic radiation mechanism for driving liquid by SAW. The Rayleigh SAW is generated from IDTs and transmitted into liquid at x = 0 that transforms into Leaky SAW and longitudinal pressure wave. Here, λ_SAW, k_R, and w are the wavelength, wave number, and angular frequency of Rayleigh SAW; k_L is the wave number of Leaky SAW.

A thermodynamic equation of state⁶⁹ can be used as a supplement to the above set of equations,

$$p-p_0=c_0^2(\rho -{\rho }_0)+{\displaystyle \frac{1}{2}({\displaystyle \frac{\mathrm{\partial }{c}^2}{\mathrm{\partial }\rho })|{(\rho -{\rho }_0)}^2+{\displaystyle \frac{\mathrm{\partial }p}{\mathrm{\partial }s}(s-s_0)+\cdots ,}}}$$ (8)

where c is the sound speed, s is the entropy, the subscript “0” refers to equilibrium properties associated with the ambient conditions, i.e., u₀ = 0 m/s, p₀ = 101 kPA, and ρ₀ = 998 kg/m³ for water. To simplify the nonlinear system, an asymptotic expansion approach in which fluid velocity, density, and pressure fields are assumed to have the following forms:

$$u=u_0+\epsilon u_1+{\epsilon }^2{u}_2+O({\epsilon }^3)+\cdots ,$$ (9)

$$p=p_0+\epsilon p_1+{\epsilon }^2{p}_2+O(p^3)+\cdots ,$$ (10)

$$\rho ={\rho }_0+\epsilon {\rho }_1+{\epsilon }^2{\rho }_2+O({\rho }^3)+\cdots .$$ (11)

Here, the subscript “1” refers to the first-order approximations and the subscript “2” refers to the second-order field. Substituting Eqs. (9)–(11) into Eqs. (3) and (4), the first-order approximations for the mass and momentum conservation equations are as follows:

$${\displaystyle \frac{\mathrm{\partial }{\rho }_1}{\mathrm{\partial }\mathrm{t}}+\mathrm{\partial }{\rho }_0(\mathrm{\nabla }\cdot u_1)=0,}$$ (12)

$${\rho }_0{\displaystyle \frac{\mathrm{\partial }{\mathrm{u}}_1}{\mathrm{\partial }\mathrm{t}}=-\mathrm{\nabla }{p}_1+\mu {\mathrm{\nabla }}^2{u}_1+({\mu }_B+{\displaystyle \frac{\mu }{3})\mathrm{\nabla }\mathrm{\nabla }\cdot u_1.}}$$ (13)

From Eq. (8), the first-order approximation of the state equation for an adiabatic process (s = s₀) is⁷⁰

$$p_1=c_0^2{\rho }_1.$$ (14)

At the second order, the fluid motion consists of a superposition of the steady-state and harmonic flows. The second-order approximation for the continuity, momentum, and state equations are as follows:

$${\displaystyle \frac{\mathrm{\partial }{\rho }_2}{\mathrm{\partial }\mathrm{t}}+\mathrm{\nabla }\cdot ({\rho }_0{u}_2)+\mathrm{\nabla }\cdot ({\rho }_1{u}_1)=0,}$$ (15)

$$\begin{array}{r}{\rho }_0{\displaystyle \frac{\mathrm{\partial }{u}_2}{\mathrm{\partial }t}+{\rho }_1{\displaystyle \frac{\mathrm{\partial }{u}_1}{\mathrm{\partial }t}+{\rho }_0(u_1\cdot \mathrm{\nabla })u_1=-\mathrm{\nabla }{p}_2+\mu {\mathrm{\nabla }}^2{u}_2+({\mu }_B+{\displaystyle \frac{\mu }{3})\mathrm{\nabla }\mathrm{\nabla }\cdot u_2,}}}\end{array}$$ (16)

$$p_2={\displaystyle \frac{c_0^2}{{\rho }_0}\left[{\displaystyle \frac{1}{2}{\displaystyle \frac{B}{A}{\rho }_1^2+{\rho }_0{\rho }_2}}\right],}$$ (17)

where $A={\rho }_0{\mathrm{c}}_0^2$ is the adiabatic bulk elastic modulus and $B={\rho }_0^2{(\mathrm{\partial }{c}^2/\mathrm{\partial }\rho )}_s$ is the nonlinear modulus.^71,72 Consider sound waves that vary sinusoidally in time with frequency ω and retain the terms up to second order and take the time average over a suitable number of cycles in Eqs. (6) and (7). The time average of F₀ must be zero in the steady state, and the result may be rewritten

$$-F_1=⟨-F_1⟩=⟨{\rho }_0(u\cdot \mathrm{\nabla })u+u\mathrm{\nabla }\cdot {\rho }_{0}u⟩.$$ (18)

Hence, F₁ is determined once the first-order velocity u in principle. The nonlinear quantity F₁ is the exact force of SAW streaming. Assuming the propagation constant for SAW is k_R and propagation constant for leaky SAW is k_L, the particle displacement in the liquid can be put in the following form:⁷³

$${\mathrm{S}}_{x_1}=A{e}^{j\omega t}{e}^{-j{k}_L{x}_1}{e}^{-\alpha k_L{x}_3},$$ (19)

$$S_{x_3}=-j\alpha A{e}^{jwt}{e}^{-j{k}_L{x}_1}{e}^{-\alpha k_L{x}_3},$$ (20)

where A is the SAW amplitude, α is the attenuation constant as ${\alpha }^2={(1-u_l/u_s)}^2$, u_l is the sound speed in liquid and u_s is the sound speed in the substrate, k_L is the wave number that can be calculated by extending the method of Campbell and Jones into the liquid/solid structures, assuming that the boundary conditions of both displacement and stress at z = 0 are continuous. Furthermore, the SAW amplitude A is proportional to the input RF power and can be characterized by the input RF power and wavelength using the following equation:⁷⁴

$$A/\lambda =8.15\times {10}^{-6}{P}_D^{0.225}+5\times {10}^{-6}{P}_D^{0.8},$$ (21)

where P_D is the input RF power in Watt. Letting the particle displacement of Eqs. (19) and (20) be replaced by particle velocity and substituting the particle velocity into Eq. (18), the derived SAW streaming force is⁷⁵

$$F=-{\rho }_0{(1+{\alpha }_1^2)}^{3/2}{A}^2{\omega }^2{k}_i{e}^{2(k_i{x}_1+{\alpha }_1{k}_i{x}_3)},$$ (22)

where k_i is the imaginary part of the leaky SAW wave number k_L. Therefore, SAW streaming is a second-order nonlinear acoustic effect. Due to nonlinear terms in the governing equations, the momentum can be transferred from the acoustic field to the fluid field, which results in an inertial volume force acting on the contact point of fluid with SAWs. The fluid motion will be governed by the balance between viscous force, surface tension, gravity, and the acoustic radiation force.

C. The principle of liquid ejection and droplet breakup

When a liquid drop is placed on a horizontal piezoelectric substrate surface with a vertical vibration displacement component, as shown in Fig. 3, the external SAW streaming forces input in promoting interfacial instabilities for droplet jetting and pinching off. The initial contact angle of the droplet on the surface of the piezoelectric substrate is θ, and the initial height of the droplet at rest is H₀. If there is only one column of traveling SAW leaking energy into the liquid drop, the liquid will jet along the Rayleigh angle (θ_R)⁶⁷ direction for the SAW streaming force F_SAW, as shown in Fig. 3(a). However, if there are two columns of opposite traveling SAWs leaking energy into the liquid drop simultaneously, the direction in which the drop stretched and ejected will change. The ejection direction actually can be tuned by controlling the energy of the two opposite SAWs or, in fact, the input RF power to the two symmetric IDTs. As shown in Fig. 3(b), when the energy of the two opposite SAWs is precisely the same, the drop ejection would be perfectly perpendicular to the SAW propagation direction on the piezoelectric substrate for the superposition of two equal and opposite SAW streaming forces (F_SAW1, F_SAW2) from left and right sides.³⁹ However, if the energy of the two opposite SAWs is not the same, then the drop ejection will deviate from the vertical axis and shift toward the side with the smaller energy distribution. Overall, the ability to tune the ejection angle for water can be controlled within a range of ±22°.⁷⁶ The governing equation for a droplet jetting dynamics system in the absence of phase change and evaporation is⁷⁷

$$\mathrm{\nabla }\cdot \mathbf{u}=0,$$ (23)

$$\begin{array}{r}\rho ({\displaystyle \frac{\mathrm{\partial }\mathbf{u}}{\mathrm{\partial }t}+\mathbf{u}\cdot \mathrm{\nabla }\mathbf{u})=-\mathrm{\nabla }p+\mathrm{\nabla }\cdot (\mu (\mathrm{\nabla }\mathbf{u}+\mathrm{\nabla }{\mathbf{u}}^T))+{\mathbf{f}}_{st}+\rho \mathbf{g}+{\mathbf{f}}_{SAW},}\end{array}$$ (24)

where ρ is the density of liquid (kg/m³), p is the pressure (Pa), u is the velocity (m/s), t equals time (s), μ is the viscosity (Pa s), g is the gravity acceleration (m/s²), f_st is the force due to surface tension, and f_SAW is the SAW streaming force.

FIG. 3.

The principle of liquid ejection induced by SAW. (a) Liquid jetting with only one column of traveling SAW from the left side. (b) Liquid jetting with two columns of opposite traveling SAWs from left and right sides simultaneously. H₀ is the height of the initial sessile drop, H is the height of the drop deformation induced by SAW leaking energy into the liquid drop, and R is the radius of the elongated jet.

The governing equations are established for the viscous, incompressible, Newtonian fluid of viscosity μ, density ρ, and the surface tension of the liquid/gas interface of σ. Four types of forces, including viscous force, inertial force, surface tension, and gravity, govern the droplet jetting. Under these conditions, several dimensionless parameters would be defined adequately in studying the whole jet decay. Furthermore, assume that the contact radius of the sessile drop on the piezoelectric substrate is L/2 and the radius of the elongated jet is R. By choosing R ∼ L/2 as the characteristic length scale and quantity $\sqrt{\rho R^3/\sigma }$ as the characteristic time scale, the corresponding velocity and pressure scales are found to be $\sqrt{\sigma /\rho R}$ and $\sqrt{\sigma {\mu }^2/\rho R^3}$, respectively.^78,79 As shown in Table I, the dimensionless groups that govern the dynamics of the liquid drop are the Reynolds number,⁸⁰ the gravitational Bond number,⁸¹ the Weber number,⁸² the Capillary number,⁸³ and the Ohnesorge number.⁸⁴ For microfluidic jetting, single droplet pinching off occurs at 0.1 < We < 0.4.³⁹ As the Weber number is increased, the fluid jetting phenomenon evolves from simple forming a jet, single droplet pinch-off, to generate multiple droplets.

TABLE I.

Dimensionless parameters control the droplet jetting process in microfluidic.

Symbol	Name	Formula	Value range	Physical meaning
Re	Reynolds number	Re = ρvR/μ	10−6–10	Inertial force∕viscous force
Bo	Bond number	Bo = ρgR2/σ	≪1	Gravity force∕surface tension
We	Weber number	We = ρRv2/σ	0–1	Inertial force∕surface tension
Ca	Capillary number	Ca = μv/σ	10−3–10	Viscous force∕surface tension
Oh	Ohnesorge number	$\mathrm{Oh}=\mu /\sqrt{\rho R\sigma }$	10−2–10	Viscous force∕Inertial force∕ surface tension

III. SAW-LIQUID EJECTION PERFORMANCE

A. Piezoelectric materials effect

Piezoelectric materials for surface acoustic wave devices include piezoelectric bulk materials, such as piezoelectric single crystals (Quartz, LiTaO₃, LiNbO₃, Bi₁₂GeO₂₀)^85,86 and piezoelectric ceramics (PbTiO₃–PbZrO₃),⁸⁷ and piezoelectric thin films (ZnO, AIN)^88,89 on various substrates (silicon, glass, or polymer). For piezoelectric bulk materials, driving microfluidic by SAWs mainly concentrated on Rayleigh SAW on the surface of the 128° Y-X LiNbO₃ piezoelectric single crystal for its high electromechanical coupling coefficient (5.5%) and low-temperature coefficient (−75 × 10⁻⁶/°C).^90,91 Besides, phononic crystal, one kind of metamaterial, can be engineered on a silicon wafer and placed on the piezoelectric substrate to filter, reflect, and scatter SAW for controlling the microcentrifugation of particles in a frequency-dependent manner.⁹² The SAW in the piezoelectric substrate couples into the superstrate to excite Lamb waves, which interact with the phononic crystal resulting in a body force that shapes the liquid droplet. However, for the layered structure, like AIN/diamond^93,94 or ZnO/Si⁹⁵ SAW devices shown in Figs. 4(a) and 4(c), there were two bright transmission bands. The first peak was attributed to the conventional Rayleigh wave mode, and the second peak could be either the Sezawa waves shown in Fig. 4(b) or the higher frequency-guided wave mode shown in Fig. 4(d), which was determined by the velocities of the piezoelectric layer and the substrate. When the velocity of the piezoelectric layer is generally smaller than that of the substrate, the second band with higher frequency-guided wave mode propagating through the interface between the films and substrate is the Sezawa waves. Both the resonant frequencies of Rayleigh and Sezawa waves decrease with increasing film thickness. Nevertheless, the Sezawa wave has a much higher acoustic velocity and larger signal amplitude (typically five to ten times) than those of Rayleigh SAW, increasing with piezoelectric film thickness. Table II shows that the experimental RF powers were required in microfluidic streaming, pumping, and jetting based on the 128° Y-X LiNbO₃ device, ZnO/diamond, and AIN/Si SAW devices.

FIG. 4.

The SEM image and typical reflection measurement of the layered structure SAW device. (a) The SEM image of the ZnO/UNCD SAW device with 1.2 μm UNCD layer and 6 μm ZnO layer.⁹⁵ Reproduced with permission from Fu et al., Biomicrofluidics 6, 024105–024111 (2012). Copyright 2012, AIP Publishing LLC. (b) Reflection coefficient corresponding to the layered ZnO/UNCD SAW device in (a). (c) The SEM image of the AIN/Si SAW device with 4.7 μm AIN layer. Reproduced with permission from Zhou et al., Sens. Actuators B 202, 984–992 (2014). Copyright 2014, Elsevier B.V. (d) Transmission and reflection coefficient corresponding to the layered AIN/Si SAW device in (c). Reproduced with permission from Zhou et al., Microfluid. Nanofluid. 18, 537–548 (2015). Copyright 2014, Springer-Verlag.

TABLE II.

Input RF power range in microfluidic streaming (S), pumping (P), jetting (J), and atomization (A) based on piezoelectric bulk material for 128° Y-X LiNbO₃ and piezoelectric film material for AIN/diamond and ZnO/Si SAW devices.

References	Piezoelectric material	Water droplet	Wave types	Microdroplet actuating
Fu et al.95	Zno/diamond/Si	5 μl	Rayleigh wave (65.36 MHz)	S			P			J
Guo et al.96	128° YX-LiNbO3	5 μl	Rayleigh wave (61.7 MHz)	S	P	J
	ZnO/Si	5 μl	Rayleigh wave (67.2 MHz)	S			P		J
Zhou et al.97	AIN/Si	3 μl	Rayleigh wave (80.3 MHz)	S							P		J
		3 μl	High-frequency guided wave (157.3 MHz)	S										P	J
Wang et al.27	128° YX-LiNbO3	3 μl	Rayleigh wave (20 MHz)	S	P	J
Jangi et al.98	ZnO/Si	2 μl	Rayleigh wave (12.2 MHz)	S					J
	128° YX-LiNbO3	2 μl	Rayleigh wave (9.5 MHz)	S			J
Lei et al.99	128° YX-LiNbO3	10 μl	Rayleigh wave (29.4 MHz)	S		J
RF power (W)				0–0.7	0.7–1.6	1.6–4	4–8	8–12	12–14	14–16	16–32	32–36	36–51	51–68	68–

LiNbO₃-based SAW device is more capable of actuating microfluidics with much smaller input RF power needed to realize similar SAW streaming phenomena than using ZnO/Si and AIN/Si piezoelectric materials for its larger piezoelectric constant and better electromechanical coupling coefficient than ZnO or AIN thin-film materials. Also, the resonance frequency of LiNbO₃ bulk material would be a constant value when setting the wavelength at a fixed value for this material has no thickness variation effects. In contrast, the resonance frequency of film piezoelectric material would be changed with the variation of material thickness. For example, the resonance frequency of the Rayleigh wave changes from 136 MHz to 108 MHz as the ZnO thickness changes from 1.5 μm to 6.6 μm.¹⁰⁰ For those reasons, LiNbO₃ bulk materials are much accessible in SAW microfluidic devices. However, piezoelectric bulk materials are brittle, and the cracking phenomenon was always observed for the high temperature at high driving RF power. Conversely, it has been found that the layered structure SAW has excellent advantages for the application of high-frequency SAW devices with high SAW velocity, small temperature coefficient, and high-power durability. So, piezoelectric thin films can be easily integrated with controlling electronics to realize multiple wave modes or flexible complex electrodes structure design. Additionally, AIN/sapphire layered structure as a potential substrate for SAW devices can be used in high-temperature applications (up to 950 °C).¹⁰¹

B. Driving signal forms

SAWs are generated on the surface of the piezoelectric material with the inverse piezoelectric effect when an alternating electric field is applied in the polarization direction of the dielectric. Therefore, it is only necessary to apply an alternating electric field to the bus electrodes of IDTs on the surface of the piezoelectric material; that way, SAWs can be generated to drive the microfluidic motion. Generally, a continuous sine wave signal was used as the driving signal source for SAW actuators. Shiokawa et al.^68,102 used an exciting frequency of 50 MHz with a pulse frequency of 100 Hz and a power of 2 W to drive a drop with a volume of 6 μl on the surface of the SAW device with a normal IDT of ten finger pairs and an aperture width of 2 mm. A string-like jet was exhibited, and a droplets diameter of 0.5 mm with an ejection velocity of 1.5 m/s was observed. However, a very fine fog was produced under the pulse frequency of 1 kHz. It was shown that the pulse frequency would affect fluid streaming mode. Bennes et al.¹⁰³ measured the ejection distance in the case of short pulse duration below150 ms for water droplets with a volume of 1 μl, 500 nl, and 100 nl under 78 MHz excitation frequency and an input RF power of 5 W. For pulse duration below 50 ms, the ejection distance of the drop increases with the pulse duration and droplet volume. For pulse duration equal to or larger than 50 ms, the ejection distance of the drop seems to be constant. However, atomization could be observed for long pulse duration higher than 1 s, where the atomized particle size distributed in the range of 10 μm–40 μm. Further, Ju et al.¹⁰⁴ applied the intermittent driving with a 10% duty ratio during a 1 kHz burst interval in the central operating frequency of 10 MHz to test the effect of the atomized drop size distribution. The distribution range becomes narrower by adopting continuous drive than intermittent drive on the standing-wave type device. Friend and co-workers¹⁰⁵ studied the effect of amplitude modulation on the nebulization rate of de-ionized water at each sinusoidal amplitude modulation frequency from 500 Hz to 40 kHz under the central operating frequency of 30 MHz. The amplitude modulation-driven nebulization occurred at a rate three times the continuously driven version at the input power of 1.5 W. From another perspective, the power supply requirements would be reduced with the intermittent drive for achieving the same atomization effect. The nebulization rate is slightly reduced as the amplitude modulation frequency is increased, particularly beyond 10 kHz. Darmawan et al.¹⁰⁶ applied RF square AC signals to maximize the V_rms values to generate standing focused SAWs. In general, there are currently three types of excitation signals that are commonly used, which are sine waves, square waves, and pulse wave signals. For high-power devices, the intermittent drive can effectively protect the SAWs chip from cracking caused by high-temperature effects.

C. Contact angle on jetting

The contact angle is a parameter used to measure the wettability of a liquid on a solid surface, the magnitude of which depends on the properties of the liquid and the solid surface.¹⁰⁷ The most significant properties of the solid surface are the surface free energy (SFE) of the solid surface and the nature of its molecular forces, such as polar and non-polar forces. Other properties of the solid surface include some other physical and chemical properties, such as the flatness, the smoothness, or the roughness, and chemical composition inhomogeneity of the surface. Shiokawa et al.¹⁰⁸ found that the SAW streaming motion strongly depends on the chemical condition of the piezoelectric substrate surface, which means whether it is hydrophobic or hydrophilic. When stearyltrichlorosilane [CH₃(CH₂)₁₇SiCl₃] was used to form a chemically hydrophobic surface, a string of droplets was ejected from the liquid upward at a Rayleigh angle instead of only moving in the SAW propagation direction. Similarly, to increase the static contact angle between the de-ionized water drop and the substrate surface, a 100 nm thick layer of Teflon was coated on the substrate by Tan et al.³⁹ and Bhattacharjee et al.⁴⁰ The substrate surface was treated by a self-assembled monolayer (SAM) of octadecyltricholorisilane (OTS), making it hydrophobic with a static contact angle of 98° by Bussonniere et al.⁴³ Darmawan and Byun⁴² encompassed an experimental observation in water droplet deformation with modified surface wettability on hydrophobic substrate and superhydrophobic substrate. The hydrophobic film with a 3 μl water drop contact angle of about 105° was realized by spin coating the Teflon layer of 300 nm thick on the 128° Y-cut LiNbO₃ substrate, and the superhydrophobic substrate with a water drop contact angle of about 155° was achieved by a straightforward plasma treatment with a proper gas composition of He, CH₄, and C₄F₈. Due to the SAW refraction directly at the pinning point, the entire liquid droplet was deformed into an elongated string as the inertial body force started overcoming the surface tension of the droplet on the hydrophobic surface. However, an unfamiliar droplet jetting formation was observed on the superhydrophobic substrate that a sharp jetting pinching point was formed at the apex of the droplet rather than at the droplet's pinning point. Furthermore, the jetting formation, therefore, progressively changed into multiple jetting due to the high inertial force and small jet radius under the same input power of 12 W. On the other hand, the contact line dynamics showed that the input power within the range of 10–14 W does not affect the magnitude of the expansion, and the droplet–substrate detach time in the hydrophobic case. In contrast, small and rigid contact line changes were observed at the lowest input power of 10 W on the superhydrophobic substrate as the acoustic radiation force barely overcome the pinning force threshold. The results showed that the relatively longer droplet's expansion and detachment time on the superhydrophobic substrate had a smaller active SAW propagation area than the hydrophobic substrate.

In summary, for the SAW microfluidic ejection, the larger the droplet contact angle of the same liquid, the more likely the ejection phenomenon occurs. With the increase in the contact angle, the contact area decreases, and the reflection of the longitudinal waves within the droplet will be much more effective in forming a jet thread, thus the energy required to drive the droplet ejection is correspondingly reduced. On the other hand, the number of satellite droplets is also considerably reduced by increasing the surface contact angle. Furthermore, the ejection is more directional with hydrophobic treatment than without one.¹⁰³ Finally, the droplet–substrate contact area on different surface wettability would affect the droplet's expansion and detachment time.⁴²

D. Frequency and power effect

The resonant frequency and the input RF signal power of the SAW devices are the most crucial parameter for microfluidic jetting applications. Guo et al.⁹⁶ performed a jetting phenomenon for a 5 μl water liquid droplet on 128° Y-X LiNbO₃ bi-directional SAW devices with different resonant frequencies (61.7 MHz, 110.8 MHz, 199.4 MHz, and 250.1 MHz), and the results of the water jetting experiments are exhibited in Table III and Fig. 5. The jetting angle significantly depends on the liquid droplet size, RF power, hydrophobic surface treatment, and IDT configuration, but merely the jetting angle decreases as the frequency increases. Further, increasing the RF frequency of the SAW device resulted in an increased power threshold for the jetting phenomenon. As the resonant frequency increases, the length of the droplet jetting column beam and the droplet pinch-off time all become shorter.⁴⁶

TABLE III.

Jetting parameters under different resonant frequencies.

Resonant frequency (MHz)	Jetting angle (deg)	RF power threshold (W)	Jetting beam length (mm)	Droplet pinch-off time (ms)
61.7	∼26 ± 2	1.6	∼7	68
110.8	∼15 ± 2	1.8	∼5	60
199.4	∼0 ± 2	5.4	∼3.5	51
250.1	∼0 ± 2	8.2	∼2	48

FIG. 5.

Jetting phenomena for a 5 μl water droplet on the 128° Y-X LiNbO₃ SAW device with different resonant frequencies. [(a)–(d)] SAW device with a resonance frequency of 61.7 MHz, 110.8 MHz, 199.4 MHz, and 250.1 MHz and an input RF power of 1.6 W, 1.8 W, 5.4 W, and 8.2 W, respectively. Reproduced with permission from Guo et al., J. Appl. Phys. 116, 024501 (2014). Copyright 2014, AIP Publishing LLC.

The attenuation length, L_SAW, of the SAW into a liquid is defined as the inverse of α_L, which is attenuation coefficient per unit length scale of the Rayleigh wave,¹⁰⁹

$$L_{SAW}={\displaystyle \frac{1}{{\alpha }_L}={\displaystyle \frac{{\rho }_s{v}_s\lambda }{{\rho }_f{v}_f}={\displaystyle \frac{{\rho }_s{v}^2}{{\rho }_f{v}_{f}f},}}}$$ (25)

where ρ_s and ρ_f are the density of the piezoelectric substrate material and the liquid, respectively; v_s is the SAW velocity in the substrate, v_f is the sound velocity in the liquid, λ is the SAW wavelength, and f is the SAW resonant frequency. So, the SAW excitation frequency directly influences the SAW attenuation length and hence the SAW acoustic energy absorbed by the liquid. At higher frequency, the SAW dissipated into liquid decays more rapidly with a much shorter decay length. So the increased thresholds for increasing frequency are attributed to a greater absorption rate of SAW energy that leaks into the liquid at high frequencies, which reduces the attenuation length of the SAW streaming force, then requires higher power to achieve a similar jetting effect.

The fluid dynamics of SAW streaming due to interaction between SAW and liquid, such as vibration, translation, droplet formation, and atomization, are strongly influenced by the SAW amplitude. It is essential to know the relationships between SAW amplitude and SAW input voltage. The SAW streaming force is directly proportional to the square of the SAW amplitude, as shown in formula (22). The vibration amplitude within the nanometer range measured by an optical method is proportional to the RF input voltage or RF power.^74,110 As the SAW amplitude increases with increasing input RF power, the SAW streaming force increases. The jetting angle, jetting height, and jetting speed all increase with increasing SAW input RF power. As the input RF power increases, droplet ejection also develops from single droplet ejection to multiple droplet ejection.³⁹ Beyond that, the volume of the ejected droplet is concerned with its parent source drop, the input energy to the SAW, and hence the jet, which can be controlled through the input RF power applied to the IDTs and the pulse duration. Castro et al.⁷⁶ have shown that the ejected droplet volume, normalized against the initial parent drop volume, was a function of input RF power proportionally increasing. For the examined liquid of 50% DI water/glycerol, it was possible to tune the ejected droplet volume from approximately 35% to 70% of the initial parent drop volume by simply changing the input RF power and pulse duration. In particular, Rezk et al.¹¹¹ got the conclusion that the ejected droplet size can be tuned by simply varying the input RF power applied to the SAW device. When setting the initial water liquid volume at 200 μl and a pulse duration of 7 ms, the ejected droplet size decreases from about 730 μm to 340 μm as the input RF power increases from 2.9 W to 3.55 W.

E. Sessile and pendant drops

Because SAW possesses sufficient energy transferring into the fluid to overcome the restoring capillary forces without requiring any fluid confinement mechanisms such as nozzles and orifices, the research on sessile drop jetting becomes the basis for successful applications of this technology. Since the first time that Shiokawa et al.⁶⁷ have done a sessile drop jetting experiment and found that SAW can drive the liquid to eject. Until 2009, Tan et al.³⁹ studied the nature of jet formation using a pair of elliptical focusing EWC-SPUDTs at two opposite ends of the substrate to drive a liquid placed at the focal point, which is the radiation intensity convergence point of two SAWs on the substrate [Fig. 6(a)]. A robust standing-wave SAW is generated through the superposition of the two F-SAWs that transmit into the liquid drop from the aligned electrodes at both ends of the substrate and cause the drop to deform into a coherent elongated liquid column, as shown in Fig. 6(b). The dynamics of the SAW jetting phenomenon is captured [Fig. 6(c)], in which they characterized jetting length as a function of the driving force and the elongated column pinch-off to eject a single droplet or breaking up to form multiple droplets is depend on the jet Weber number, which is defined as

$$\mathrm{W}{\mathrm{e}}_j=\rho U_j^2{R}_j/\gamma ,$$ (26)

where ρ is the fluid density, U_j is the jet velocity, R_j is the jet radius, and γ is the interfacial tension. They also predicted the axial jet velocity as a function of the acoustic Reynolds number by introducing an acoustic forcing term to the leading order axisymmetric jet momentum balance derived by Eggers, shown as

$$U_j={[2L_{\mathrm{j}}(F_s^y-g)]}^{1/2},$$ (27)

where L_j is the jet length prior to breakup, $F_s^y\approx {\alpha }_0\beta {\dot{\xi }}_{x3}^2{\mathrm{Re}}_A$ is the force associated with the acoustic streaming in the jet, g is the gravitational acceleration, ${\mathrm{Re}}_A=\rho {\dot{\xi }}_{x3}{\lambda }_f/(2\pi b)$ is the acoustic Reynolds number, $b=4\mu /3+{\mu }_B$, ${\mu }_B$ is the bulk viscosity of the fluid, ${\alpha }_0=\pi bf/(\rho c_l^3)$ is the coefficient of nonlinearity, and $\beta =1+B/2A$, B/A is a value determined by experiment. In this case, the jets observed here present opportunities for inkjet printers, soft biological printing, and fiber synthesis.

FIG. 6.

Sessile drop jetting phenomenon induced by two circular focusing electrode width-controlled SPUDTs. (a) Circular focusing electrode width-controlled SPUDTs fabricated at the ends of a 128° Y-X LiNbO₃ substrate with Teflon coated around focal point. (b) Droplet, placed at the focal point, deforms into a coherent elongated jet process. (c) Images showing the transition from (i) drop vibration, (ii) jetting, (iii) pinch-off of a single droplet to (iv), (v) jet breakup into multiple droplets with increasing the jet Weber number We_j.³⁹ Reproduced with permission from Tan et al., Phys. Rev. Lett. 103, 024501 (2009). Copyright 2009, The American Physical Society.

Bhattacharjee et al.⁴⁰ used a pair of 30 MHz pulsed FSAW to eject a jet from an inverted sessile droplet to form capillary bridges of low-viscosity Newtonian and non-Newtonian fluids. A sessile drop was placed at the focal point of the SAW device, and a glass plate was placed directly opposing the plate containing the SAW device [Fig. 7(a)]. A non-dimensional number was defined as $\mathrm{\Pi }=P/c_s\gamma R_d$ that represent the ratio of SAW forcing imposed on the droplet to the resistance offered by surface tension, where P is the SAW power, c_s is the speed of the acoustic wave in the fluid, and R_d is the original droplet radius. Another dimensionless number was the Ohnesorge number, which was defined as $\mathrm{Oh}={\tau }_v/{\tau }_R=14.1{\eta }_0/\sqrt{\rho \gamma R_d}$ measuring the ration of viscous over inertial effects, where ${\tau }_R=\sqrt{\rho R_{\mathrm{d}}^3/\gamma }$ is the timescale quantified by the Rayleigh time. Lighthill¹¹² suggested that acoustic streaming could be expected when the ratio $\rho P/\sqrt{c_s{\eta }_0^2}=\mathrm{\Pi }/O{h}^2$ exceeds a value of around 10. The relationship between Π and Oh was plotted in Fig. 7(c), in which they found that at relatively low dimensionless values of power, the droplet only slightly deforms into a “stub,” and there was a transition from stub to jetting as power increased. When the input power was high enough, jet atomization could be observed. Interestingly, they also found that drops tend to atomize directly as power increased without forming any jets at large Oh values. The bridge formation and necking behavior were demonstrated in Fig. 7(b) that the liquid bridge was formed at about 7.5 ms and broken up at about 12 ms. Furthermore, McDonnell et al.¹¹³ measured the extensional viscosity of cell suspensions using this novel acoustically driven microfluidic capillary-breakup extensional rheometer (CaBER) developed by Bhattacharjee et al. In CaBER, a liquid bridge is usually first formed between two end-plates, and then the bridge subsequently begins to thin due to the Rayleigh-Plateau instability. It is feasible to obtain the viscosity by monitoring the neck radius as a function of time because the rate of a liquid bridge thinning is mainly determined by the balance of the capillary stress, the inertial, and the viscous stress induced by the extensional flow about the necking plane. Obtaining reliable measurements for highly viscous samples is very easy; however, measurements for low-viscosity complex fluid such as aqueous cell suspensions would face considerable challenges in quickly breaking up the liquid bridge, in which the motion with the liquid bridge following a sudden stopping is complex and is not simply described by a stress balance. These problems were overcome by using acoustically driven microfluidic CaBER, wherein the liquid-bridge can be formed and stabilized against capillary forces initially by radiating RF power from SAWs. The observations indicated that the particle motility has a clearly measurable influence on the rheology or precisely the viscosity of suspensions. Moreover, capillary thinning of liquid bridges progressed more slowly in suspensions of algal pullers than those of dead cells at the same volume fraction, whereas bacterial and sperm pushers tended to hasten thinning.

FIG. 7.

Liquid capillary bridges formation by using a pair of traveling-wave FSAW. (a) Schematic system for creating the liquid bridge by placing drop at the focal point of two focusing electrodes at the end of a LiNbO₃ substrate. (b) A coherent jet formation from the droplet and subsequently becoming a liquid bridge as it reaches the opposite surface. (c) A map of the phenomena that associated with the dimensionless numbers Π and the Ohnesorge number Oh.⁴⁰ Reproduced with permission from Bhattacharjee et al., New J. Phys. 13, 023005 (2011). Copyright 2011, IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.

Bussonniere et al.⁴³ investigated and compared the dynamics of sessile and pendant drops excited by traveling-wave SAWs and tried to identify the gravity effect. Two relevant dimensionless numbers have been defined as the Bond number Bo and the acoustic Weber number We_ac,

$$\mathrm{Bo}={\rho }_{l}g{L}^2/\sigma ,$$ (28)

$$\mathrm{W}{\mathrm{e}}_{\mathrm{ac}}=p_r/p_{cap}={\rho }_l{A}_s^2{\omega }_{ac}^{2}R/\sigma {\cos }^2({\theta }_R),$$ (29)

where ρ_l is the density of the liquid, g is the standard gravity acceleration, L is the characteristic size of the system, σ is the surface tension of the liquid, p_r is the radiation pressure, p_cap is the pressure at the interface due to the capillary effect, A_s is the amplitude of the normal acoustically induced displacement at the surface of the substrate, ω_ac is the frequency of the acoustic wave, R is the radius of the drop, and θ_R is the Rayleigh angle. The sessile droplet was sketched by the effect of the wave radiation pressure and then fell due to gravity under low power. For the pendant drop, three regions (no detachment, intermediate, and detachment) were observed as a function of We_ac and Bo experimentally. A new regime was observed close to the detachment threshold with the appearance of a quasi-static equilibrium with large deformation but almost no oscillation and translation (Fig. 8). For a droplet detachment from the substrate, the drop was stretched vertically into forming a quasi-cylindrical liquid column. Then, the base of the drop was squeezed and pinched off for the Rayleigh-Plateau instability. They found that the droplet detachment occurs when h_c/R_c ≈ 4.5 (i.e., λ_R/2), where h_c and R_c are the critical height and radius of the liquid column before a breakup occurs. In the case of pendant drop, the drop stretching was mainly induced by stationary effects of gravity and radiation pressure that both act in the same direction. In contrast, drop stretching was mainly induced by nonlinear dynamical effects for gravity and radiation pressure acts in the opposite direction in sessile drops. Even for relatively small droplets, gravity strongly affects the drop dynamics. However, the role of gravity could be negligible at the small scales of system with Bo ≪ 1.⁷⁶ Taking de-ionized water as an example to elucidate the specified interval that whether to take into account the gravity effect, in which ρ_l = 1000 kg/m³, g = 9.8 m/s², σ = 72 × 10³N/m. We can predict the threshold value of the characteristic size of the system is about 2.7105 mm. Accordingly, the effect of gravity can no longer be ignored when the volume of hemispherical water droplets reaches approximately 5 μl.

FIG. 8.

Gravity effects in dynamics of sessile and pendant drops excited by SAWs. (a) A sessile drop of de-ionized water is excited with a Rayleigh SAW frequency of 20 MHz, an aperture of 2 cm. (b) The deformation and translation of a drop excited by a Rayleigh SAW at translation velocity V, oscillations of amplitude Δh, initial drop radius R₀, and average drop height h_m by radiating acoustic wave. (c) Successive images of drop deformation with a volume of 15 μl, a Bo of 0.5, and a We_ac of 0.38. (d) Successive images of drop deformation and detachment with a volume of 10 μl, a Bo of 0.24, and a We_ac of 0.41. The parameters h_c and R_c represent the critical height and radius of the liquid column before breakup occurs. Reproduced with permission from Bussonnière et al., Phys. Rev. E 93, 053106 (2016). Copyright 2016, The American Physical Society.

F. Phononic crystals for shaping fluids

Cooper and co-workers⁴¹ have engineered a cone-shaped phononic crystal structure to focus the energy at particular locations and locally enhance the intensity of the acoustic field in a tunable frequency-dependent manner and the geometry of the phononic crystal on a non-piezoelectric substrate. The SAW device contained 20 pairs of 160 ± 7.5 μm width electrodes with a 20-nm titanium adhesion layer and a 100-nm gold layer and an aperture of 10 mm on 128° Y-cut X-propagating LiNbO₃ substrates. Appropriate phononic crystal lattice, including a square array of disks of diameter d = 160 μm, a pitch p = 200 μm, and a fill fraction ($\pi d^2/4p^2$) of 0.5, was engineered on a ⟨100⟩ silicon wafer with a thickness of 470 μm and placed in contact with the LiNbO₃ substrate to scatter acoustic waves into the superstrate and to transform the Rayleigh wave into Lamb waves. As shown in Fig. 9(a), the depth of the engineered hole was 235 μm, the aperture of the cone was 10 mm to coincide with the aperture of the IDTs, and the apex was approximately 3 mm wide. The finite element (FE) method based on COMSOL software was used to analyze the spatial acoustic intensities, which differ from the acoustic waves at different frequencies generated [shown in Fig. 9(b)]. Three droplets placed on position A/B/C on the superstrate, the maximum intensity for 12.6 MHz was at position A while for 12.2 MHz it was at position B. Thus, the energy localization and intensity can be tuned by the input frequency and the geometry of the phononic crystal. For high input powers at the dimensionless Reynolds number $\mathrm{Re}=\rho U_s{R}_d/\mu \approx {10}^3$, enough inertial force induced by acoustic streaming could overcome the capillary stress acting on the interface of the liquid, and a column of water could be deformed, as shown in Fig. 9(c).

FIG. 9.

Jetting phenomenon induced by Lamb waves by using a superstrate on the piezoelectric substrate. (a) Schematic of the SAW device comprising IDTs and phononic crystal superstrate with a conic structure on the LiNbO₃ substrate, and three water droplets positioned on top of the non-piezoelectric phononic crystal superstrate. (b) Images of the jetting phenomenon induced by the lamb SAW for a droplet of 10 μl at an input RF power of 2 W. (c) Finite element simulation of the conic structure for phonocic crystal superstrate at three different excitation frequencies of 12.6 MHz, 12.3 MHz, and 12.2 MHz. Reproduced with permission from Bourquin et al., Adv. Mater. 23, 1458–1462 (2011). Copyright 2011, WILEY-VCH Verlag GmbH & Co. KGaA.

G. Micromachined platforms application in fluid ejection

Although SAW can achieve free droplet ejection without any confinement mechanisms, the introduction of micropumps can make it to realize continuous fluid supply. Shiokawa and Matsui⁷⁵ first proposed a micropump in the SAW streaming system to produce a stable water ejection application. The fluid ejection system included three parts, which are SAW device, plate glass, and cover glass. The SAW device contained IDTs (a frequency of 50 MHz, 25 pairs of electrodes, and an aperture width of 1 mm) and 128° Y-cut X-propagation LiNbO₃ piezoelectric substrates. A glass plate of 1 mm thick was used for supporting the SAW device. A glass cover of 0.15 mm thick with a slit width of 0.2 mm was attached at the end of the SAW device and overhang 0.25 mm from the SAW device surface, which acted as an effective capillary wall. The experimental results have shown that the streaming jet rate, pumping height, and streaming jet angle were all proportional to the driving voltage.

Castro et al.¹¹⁴ engineered a capillary-driven self-replenishing liquid delivery system platform that consists of a 3D printed liquid reservoir and chip holder with the SPUDT SAWs device with a frequency of 30 MHz, shown in Fig. 10. The reservoir was placed outside of the SAW propagation pathway to avoid the energy damping of the acoustic wave. A 1 mm diameter circular hydrophilic barrier region was formed by coating approximately 100 μm thick layer of photoresist followed by vaporing deposition of an octadecylsilane on the substrate. A parent sessile droplet on the chip was formed through a 150 μm inner diameter capillary tube adjoined at the end of the circular hydrophilic region. Then, single or multiple liquid droplets with the diameter from 60 to 500 μm were generated by pulsed excitation of the FSAWs device. The ejected droplet size could be flexibly tuned by simply adjusting the pulse width duration; therefore, this versatile jetting method could jet and print cells onto the substrate for applications of cell encapsulation, dispending, and 3D bioprinting.

FIG. 10.

Continuous sessile droplet jetting induced by two opposing FSAWs. (a) Schematic illustration used for jetting a single drop from a piezoelectric substrate based on two opposing SAWs. (b) Sessile drop elongation and jetting for leaking acoustic energy at the Rayleigh angle θ_R into the drop. (c) Schematic depiction and (d) images of experimental device. Reproduced with permission from Castro et al., Soft Matter. 14, 5721–5727 (2018). Copyright 2018, The Royal Society of Chemistry.

Chen et al.¹¹⁵ applied a sample reservoir on the top surface of a 37.61 MHz FSAW device with a circular interdigital transducer (CIDT) to jet picoliter digital microfluidic. The maximum height and the volume of the ejected droplet depended on the surface tension of the sample liquid. As the surface tension increased from 22.1 mN m⁻¹ to 72 mN m⁻¹, the jetting rising height dropped from 2.82 mm to 1.48 mm. However, the ejected droplet volume linearly increased with the surface tension of the sample liquid. When the ethanol and water mixture with surface tension varied from 22.1 mN m⁻¹ to 72 mN m⁻¹, the ejected droplet volume increased from 5 nl to 28 nl. Most importantly, the ejected droplet volume could be tuned by adjusting the pulse width and amplitude of the input RF voltage. For ethanol and water mixture with a surface tension of 25.9 mN m⁻¹, the ejected droplet volume increased from 0.08 nl to 21.9 nl as the pulse width increased from 130 μs to 1560 μs and reached a plateau by increasing the pulse width above 1170 μs. The exact regulation degree of droplet volume with four different pulse widths of 780 μs, 520 μs, 260 μs, and 208 μs shows that the droplet volumes were 11.2 nl, 5.8 nl, 4.1 nl, and 1.9 nl, respectively. Moreover, some biological materials, such as cells, DNA, and photoresist, could be encapsulated into droplets and ejected simultaneously.

In fact, dating back to 2005, Demirci^116,117 has presented an acoustically actuated 4 × 4 two-dimensional micromachined ejector array for picoliter droplets ejection with CIDTs, shown in Fig. 11(a). The unit cell of the acoustically actuated microdroplet ejector is an interdigital ring transducer with an operation frequency of 34.7 MHz on the piezoelectric substrate. In particular, a top spacer with 200-μm-thick and 300-μm-wide was bonded to a bottom spacer with 350-μm-thick and 1.5 mm-wide by fabricating silicon substrates to form a microfluidic channel that stabilizes the fluid surface at a focal point with 550 μm height above the CIDTs as shown in Fig. 11(b). As the SAWs generated by the CIDTs and leak into the fluid to form a focus just at the fluid surface, enough force excited by the acoustic radiation at the focal point overcomes the surface tension force of the fluid that a droplet can be ejected. The droplet ejection can be in all directions because the focus location is not affected by the tilt of the device with the designed microfluidic channel spacers. The droplet ejection rate can be achieved from 1 kHz to 0.1 MHz by varying the input tone burst signal repetition rate. Photoresist, water, isopropanol, ethylalcohol, methanol, and acetone were tested and ejected from the 2D micromachined ejector array. The smaller the acoustic wavelength in fluid or the smaller the acoustic speed in fluid, the smaller the diameter of the ejected droplet. As shown in Fig. 11(c), 21 μm diameter photoresist solvent droplets were ejected downward through a 100 μm wide fluid spacer opening with an individual ejector. Furthermore, three ejection modes can be realized through the designed two-dimensional micromachined ejector array: single droplets of photoresist in drop-on-demand, overlapping many droplets resulted in photoresist lines, repeating or printing many photoresist lines simultaneously for covering wafer surface, as shown in Fig. 11(d). A spinless photoresist coating of a 4 in. wafer was realized at a line speed of 2 cm/s and 1 kHz ejection rate, with a thin film thickness of 2.4 μm, thickness uniformity varying from ±0.02 μm to ±0.3 μm, surface roughness varying from 68 to 600 A. This acoustic picoliter droplets generation system shows great potential in semiconductor applications of coating or dispensing, and biotechnology applications of drug testing and delivery, cells and DNA writing.

FIG. 11.

Two-dimensional micromachined ejector array for picoliter droplets ejection with CIDTs. (a) 4 × 4 two-dimensional micromachined ejector array. (b) Schematic of the physical operation of an unit ejector. (c) Images of ejected 21 μm diameter photoresist droplets from a 100 μm wide spacer. (d) The diagram of photoresist deposition on 4 in. wafer. Reproduced with permission from Demirci, Rev. Sci. Instrum.. 76, 065103 (2005). Copyright 2005, AIP Publishing LLC.

If the liquid is directly placed on the upper surface of the IDTs, the driving capacity for the liquid would be greatly reduced. Shiokawa et al.⁶⁸ made an experiment putting the water on the IDTs, in which the water could not separate but just remained a steady state after moving toward propagation direction a few seconds. The reason explained that the streaming force of the left and right direction balanced with each other. Also, the reason may be that the mass effect of the liquid on the IDT dramatically reduces the SAW amplitude. A SAW-microfluidic jetting system with a vertical capillary tube was designed by Lei et al.⁹⁹ for microliter droplet generation, shown in Fig. 12. In particular, the aperture of the IDTs was only 0.5 mm, and there is no glass adhesive between the vertical capillary tube and the SAW device with the aperture area. For 10 μl de-ionized water in the vertical capillary tube, only an applied RF power of 2.6 W was required to generate a single stable droplet at a frequency of 29.4 MHz. The jetting threshold RF power gradually decreased as the liquid level increases, while the ejected droplet dimension decreased as the liquid level increases in the vertical capillary tube. Nonetheless, the ejected droplet dimension was almost not affected by the SAW resonance frequency but determined by the initial characteristics of the liquid in the vertical capillary tube. In order to obtain a single droplet ejection with good quality, four necessary conditions should be satisfied. The first condition is that the fundamental liquid level must be uniform. The second condition is that the inner diameter of the vertical capillary tube should be moderate as two to four times the SAW attenuation length. The third condition is that the optimal liquid level in the vertical capillary tube may be higher than h = D/2 tan θ_R and lower than the capillary pressure burst threshold, where θ_R is the jetting inclination angle and D is the inner diameter of the capillary. The last condition is that the input RF power happens to be the jetting threshold power value. In general, the introduction of a micropump in the SAW-driven microfluidic system solves the problem of continuous liquid supply and also provides the possibility of further achieving drop-on-demand jetting.

FIG. 12.

A group of snapshots for the droplet jetting phenomenon in a vertical capillary tube induced by SASE SAWs. The figure in the dashed box is a schematic diagram of the interaction principle mechanism between traveling SAW and fluid. Panels (a)–(h) in the bottom are the evolution of single droplet jetting and pinching-off. Lei et al., Actuators 9, 5 (2020). Copyright 2020 Author(s) licensed under a Creative Commons Attribution 4.0 License (http://creativecommons.org/licenses/by/4.0/).

Rezk et al.¹¹¹ demonstrated a novel platform that ejects droplets without the contact of the piezoelectric substrate. As shown in Fig. 13(a), the IDTs were patterned on the underside of the double-sided polished 128° Y-cut X-propagation LiNbO₃ piezoelectric substrate with a thickness of 500 μm that generates hybrid surface and bulk waves, which was defined as surface reflected bulk waves (SRBWs), with a resonant frequency of 10 MHz. The SRBWs were generated on the IDTs but propagated through the thickness of the piezoelectric substrate to the top surface, where they interface with the fluid couplant and transmit into the fluid unit. Here, the electrical signal was introduced by pin pairs soldered on the printed circuit board (PCB) to the IDTs of the device mounted in a 3D printed housing. Figure 13(b) shows a liquid jet process from the formation, elongation to subsequent pinch-off based on the SRBWs actuating platform. The conclusion also has been drawn that the ejected droplet size can be tuned by varying the input RF power applied to the IDTs. The most significant advantage of this new platform in manipulating fluid is that the liquid does not directly contact the IDTs and even the piezoelectric substrate surface, which can protect the electrode and the device well. In addition, single droplet ejection from single or multiple units can be carried out simultaneously by selectively triggering fluid unit array.

FIG. 13.

The surface reflected bulk waves (SRBWs)-actuated platform in manipulating fluid. (a) Schematic illustrations of the SRBWs device. (b) A liquid jet formation images based on the SRBWs device with an initial liquid volume of 200 μl and a pulse duration of 7 ms. Reproduced with permission from Rezk et al., Lab Chip 18, 406–411 (2017). Copyright 2017, The Royal Society of Chemistry.

H. Drop-on-demand for multiphase fluid ejection

SAWs have been introduced to produce and modulate the size of droplets in real time in a two-immiscible-fluid-phase system with flow-focusing and T-junction geometries, as shown in Fig. 14. In the absence of SAW, the main generated drop size is a function of flow rates and flow rate ratios of the two fluid phases. The drop size, velocity, and production frequency increase approximately linear with the flow rate ratios of the dispersed fluid phase to the continuous fluid phase.^118–123 When the SAW is introduced, some changes will occur in the parameter control. Figure 14(a) shows water ejection that the SAW device with a working frequency of 161–171 MHz located at the flow-focusing PDMS junction with 30 μm in width and 30 μm in height. A flow rate of dispersed aqueous is Q_d= 100 μ h⁻¹, and a flow rate of the continuous oil phase is Q_c= 50 μl h⁻¹ and Q_c= 100 μl h⁻¹, the generated droplets are at a length of 230 μm and 130 μm and at a rate of 210 m s⁻¹ and 370 m s⁻¹, respectively. The length of the droplets decreased to 37% for the application of the SAW power from 200 mW to 800 mW.¹²⁴ When the SAW actuates the continuous fluid in T-junction with a working frequency of 160 MHz in Figs. 14(b) and 14(c), a reduction in droplet size was observed with the SAW power increased. A similar phenomenon for the reduction in droplet size will be realized if the inlet pressure of the continuous liquid is increased, which means that the SAW generated a volume force on the continuous liquid in the wave propagation direction.¹²⁵ To further enhance the droplet ejection effect, one kind of circular focused interdigital transducer (CFIDT) was employed to T-junction geometry in Figs. 14(d)–14(f).^126,127 About 70 nm layer of SiO₂ was evaporated on the surface of CFIDTs, and then the polydimethylsiloxane (PDMS) microchannel was bounded partly or entirely on the CFIDTs area. The SAW energy was focused on a narrowing line on the oil–water interface that helps to push the water into the oil phase to droplet production. The droplet volume and ejected droplet numbers were determined by the SAW power and pulse duration. The SAW device allows for electric control of droplet size in real time by adjusting PF power, acting only on the continuous or dispersed fluid. Compared with the method of directly adjusting the flow rate, the response time of the SAW device is much faster. Furthermore, the SAW system offers the advantage of the implementation of several drop-makers on the same device that can be controlled independently. The reliable pico- and femtolitre on-demand droplet production also holds potential applications in high-throughput screening and bioprinting.

FIG. 14.

On-demand droplet production in a two-fluid-phase microfluidic device by applying SAW. (a) Water ejection that the SAW device with a working frequency of 161–171 MHz located at the flow-focusing PDMS junction with 30 μm in width and 30 μm in height. [(b) and (c)] SAW actuates the continuous fluid in T-junction with a working frequency of 160 MHz. Reproduced with permission from Schmid and Franke, Appl. Phys. Lett. 104, 133501 (2014). Copyright 2014, AIP Publishing LLC. (d)–(f) Droplet ejection effect with one kind of circular focused interdigital transducer (CFIDT) employed to the T-junction geometry. Reproduced with permission from Schmid and Franke, Lab Chip 13, 1691–1694 (2013). Copyright 2013, The Royal Society of Chemistry and Brenker et al., Lab Chip 16, 1675–1683 (2016). Copyright 2016, The Royal Society of Chemistry.

I. Heat effect

The SAW-microfluidic driving process is accompanied by heat generation, which is mainly derived from two possible heating mechanisms, namely, the heat generated by the piezoelectric substrate and the heat generated by acoustic wave radiation in the liquid. During the SAW generation process, the part of the electrical energy is converted into mechanical energy in the form of an acoustic wave, and the remaining portion of the energy is lost into heat within the structure due to mechanical loss and dielectric loss in the piezoelectric material.¹²⁸ Dielectric loss is caused by the polarization phenomenon in a piezoelectric material placed in an alternating electric field. The power density by dielectric loss is given by

$$P_d={\displaystyle \frac{1}{2}\omega E^2\epsilon {\eta }_e,}$$ (30)

where ω = 2πf is the angular excitation frequency, E is the electric field amplitude vector, ɛ is the relative permittivity vector, and η_e is the dielectric loss factor. The power density by mechanical loss in the piezoelectric material such as viscoelastic effect is given by

$$P_{\mathrm{m}}={\displaystyle \frac{1}{2}\omega {\eta }_m\mathrm{Re}al[\epsilon Conj(D\epsilon )],}$$ (31)

where ω = 2πf is the angular excitation frequency, η_m is the mechanical loss factor, ɛ is the strain vector, and D is the elasticity tensor. For piezoelectric materials, temperature increasing can shift the resonant frequency of SAW devices, slightly change the surface contact angle of a droplet on the piezoelectric substrate, and vary the SAW transmission amplitude that ultimately makes the SAW device not working in the optimal state and reduces the driving ability for the liquid. Du et al.¹²⁹ found that the surface temperature of the ZnO piezoelectric film increases with an increase in the voltage and duration of the applied RF signal. The temperature rises rapidly in the first 20 s, and the maximum temperature can be up to 140 °C at a 60 V input RF voltage. Surprisingly, the heat induced by piezoelectric material can be significantly reduced by loading pulse signals on a standard RF signal. Guo et al.¹³⁰ applied ZnO/Si SAW device attached on the top of the bulk aluminum holder to test the acoustic heating effect. As a result, the acoustic heating effect was characterized as insignificant in the temperature of SAW devices due to the high thermal conductivity and fracture strength of the Si substrate and the metallic holder. Lee et al.¹³¹ evaluated the thermal stability of the FSAW device in air and water environments. They demonstrated that the maximum temperature was 129 °C in air and about 28.5 °C in water under an input RF power of 13 W, so the maximum temperature increase of the FSAW device in water was one-twentieth of that in the water, owing to the higher convective heat transfer coefficient of water.

The liquid heating effect is caused by longitudinal acoustic radiation into a liquid accompanied by the SAW streaming phenomenon that the temperature of the liquid increases. Kondoh et al.¹³² tested the heating characteristics of a thin liquid layer in filter paper on a piezoelectric substrate during SAW generation. As a result, the temperature of the liquid is a function of the SAW amplitude. The SAW amplitude is determined by the power of the carrier signal, which is linearly related to the square of the applied voltage. In addition, the temperature of filter paper with water is about two times higher than without water under the same driving conditions. Later, Kondoh et al.¹³³ further studied liquid droplet-heating characteristics by varying the applied voltage, duty factor, liquid viscosity, and liquid volume. In addition to verifying that the liquid temperature was proportional to the applied voltage, it also concluded that the temperature was proportional to the modulation pulse signal's duty factor and the liquid viscosity; however, the liquid volume has a relatively weak effect on the temperature. Similarly, Zhang et al.¹³⁴ also studied microdroplets (purified and mineral oil) heating by using intermittent surface acoustic waves. The conclusions were drawn that the temperature growth of the microdroplet heated by the intermittent surface acoustic wave was proportional to the increment of the power of carrier signal and the reduction of the modulation frequency and the volume of the microdroplet. Moreover, the carrier signal power does a more significant effect on the temperature variation of the microdroplet than the modulation frequency and the microdroplet volume. Then, Bao and Dong¹³⁵ studied the heating characteristics of pure water droplets encapsulated by paraffin oil droplets on a piezoelectric substrate. They concluded that the temperature variation tendency of a water droplet encapsulated by a paraffin oil droplet was similar to that of water or oil alone for increasing with the applied power. The temperature value of a water droplet encapsulated by a paraffin oil droplet was located between that of the individual water droplet and that of the individual paraffin oil droplet. Shilton et al.¹³⁶ used a temperature-controlled aluminum heat sink placed under the SAW device to remove heat from IDTs. Eventually, the temperature changes reached a highly stable steady-state value in 3 ms, and a maximum temperature change was about 10 °C in 1 μl water droplets and 40 °C in 100% glycerol droplets for the direct acoustic heating effect in SAW driven with frequency from 50 MHz to 900 MHz and applied power below 23.5 dBm. The Joule heat of the electric field ignored by other researchers was considered by Zheng et al.,¹³⁷ and the experimental results have shown that the heating induced by the electric field is more significant than that induced by acoustothermal effects. So far, although some conclusions have been obtained through experiments, the theoretical understanding of the acoustothermal effect is still unclear. Until 2019, Das et al.¹³⁸ presented a multiple time scale perturbation model, which focuses on the fluid domain only to try to understand the acoustothermal heating in SSAW-driven microchannel fluid. The simulation results have shown that significant acoustothermal heating was caused by the transformation from acoustic energy to the internal energy in liquid, and the corresponding temperature change characteristics are not only related to the applied RF power and frequency, but also related to the ratio of the microchannel.

IV. PERSPECTIVES AND FUTURE DIRECTIONS

SAW device consists of the piezoelectric substrate material and finger-cross shaped metal IDTs coating on the surface of the substrate. When the metal electrode is loaded with an alternating power source of the same frequency as the SAW device, the SAWs will be generated and transmitted along the surface of the piezoelectric substrate. Although different boundary conditions and propagation medium conditions can excite different modes of SAWs, only several kinds of SAWs (Rayleigh SAW, Lamb SAW, and Sezawa SAW) have been successfully applied to manipulate microfluidic. In general, there are currently three types of alternating excitation signals that are commonly used, which are sine waves, square waves, and pulse wave signals. The research studies on SAW-microfluidic jetting are basically based on the sessile parent drop placed statically on the surface of the piezoelectric substrate the same or opposite as the direction of gravity. In the case of the pendant drop, the drop stretching is mainly induced by stationary effects of gravity and radiation pressure that both act in the same direction, while drop stretching is mainly induced by nonlinear dynamical effects for gravity and radiation pressure act in the opposite direction in sessile drops. Even for relatively small droplets, gravity strongly affects the drop dynamics. Contact angle, exciting frequency, and input power all affect the jetting process of the drop. For the SAW microfluidic ejection, the larger the droplet contact angle of the same liquid, the more likely the ejection phenomenon occurs. With the increase in the contact angle, the contact area decreases, thus the energy required to drive the droplet ejection is correspondingly reduced. On the other hand, the number of satellite droplets is also considerably reduced by increasing the surface contact angle. Furthermore, the ejection is more directional with hydrophobic treatment than without treatment. Finally, the droplet–substrate contact area on different surface wettability would affect the droplet's expansion and detachment time. The jetting angle significantly depends on the liquid droplet size, RF power, hydrophobic surface treatment, and IDT configuration, but merely the jetting angle decreases as the frequency increases. Further, increasing the RF frequency of the SAW device resulted in an increased power threshold for the jetting phenomenon. As the resonant frequency increases, the length of the droplet jetting column beam and droplet pinch-off time are all become shorter. A special kind of non-piezoelectric material can be placed in contact with the LiNbO₃ substrate to scatter acoustic waves into the superstrate and to transform the Rayleigh wave into Lamb waves for jetting fluid drop. Micropumps are trying to be used in the SAW-microfluidic jetting system for continuous liquid supply as well as continuous droplet ejection. It can even realize drop-on-demand for multiphase fluid ejection when combined with flow-focusing and T-junction geometries of micropumps. Unfortunately, one of the factors involved in incompatibility is the temperature changes caused by the thermal effect accompanied by droplet ejections. The thermal effect mainly comes from two aspects, one is the dielectric loss of the piezoelectric material, and the other is the viscous dissipation of the longitudinal pressure wave in the liquid. In general, four key parameters would affect the heat effect in the liquid, which are the power of the carrier signal, the frequency of modulation signal, the volume of the microdroplet, and liquid viscosity.

As presented in this article, SAWs have demonstrated tremendous capability in microfluidic jetting. However, despite an extensive literature on the use of SAW for droplet jetting actuation, a clear understanding of the underlying physics is still missing in these systems. One of the reasons is that the nonlinear coupling between the acoustic waves and the liquid response involves time and length scales that differ by several orders of magnitude, along with nonlinear effects, which render the analysis and simulation of these behaviors extremely difficult. The current theoretical research is based on the analysis of ignoring the second-order nonlinear term with small amplitude sound waves in slow streaming, which is inconsistent with the finite-amplitude sound waves that some nonlinear terms cannot be ignored in fast streaming. On the other hand, the current literature only researched the effect of increasing contact angle by transforming the piezoelectric substrate surface into a hydrophobic surface; however, the energy dissipation and distribution caused by the hydrophobic film and the contact angle changes due to the fluid characteristics (i.e., surface tension) are all not be analyzed. There is a preliminary conclusion that the exciting signal's pulse width affects the acoustothermal phenomenon and the ejecting droplet size, but the reasons are all unknown. Although the micropump structure has begun to be used in SAW-microfluidic jetting, continuous and controllable droplet ejection also cannot be achieved with many uncertainties. The incongruity thermal effect would increase the temperature of the piezoelectric substrate surface and the liquid, the current studies are basically limited to the case of low RF signal power driving, and the case of high RF signal power driving needs to be further studied. Current research is basically droplet ejection with low viscosity, such as de-ionized water, and higher viscosity droplet ejection is more worth exploring. Although it has been found that the Sezawa wave has much higher acoustic velocity and larger signal amplitude than those of Rayleigh SAW, using the Sezawa wave to achieve droplet jetting is still missing. Therefore, mathematical modeling of droplet ejection, simulation method, the influence of exciting signal on the jetting phenomenon, protection method for SAW device and electrode, energy attenuation caused by coating layers of SiO₂ or photoresist, overall structure design for continuous droplet ejection, relationships between the objected jetting droplets (i.e., diameter, velocity) and input parameters (i.e., resonance frequency, input power, characteristics of fluid), comprehensive coupled thermal effect analysis, and applications field of SAW-microfluidic jetting are all needed to be further characterized in the future.

DATA AVAILABILITY

The data that support the findings of this study are available within the article.