Theoretical and experimental characterizations of gigahertz acoustic streaming in microscale fluids

The term acoustofluidics refers to a new field that combines acoustics with microfluidics by confining acoustic waves or energy within a microfluidic system to stimulate the micro/nanoscale motions of fluids and particles, and interactions between them.^1–3 In recent decades, researchers have developed different kinds of acoustofluidic strategies. From the acoustic wave form perspective, there are two basic wave types, i.e., standing waves and traveling waves. Generally, acoustic waves with frequencies ranging from kHz to several MHz are generated by a PZT plate, which is placed on the substrate of a microchannel chip.^4,5 Standing waves form in the microfluidic channel because the acoustic wavelengths at such frequencies are similar to the microchannel scale, i.e., from several hundred to tens of micrometers. The spatial patterns of acoustic antinodes or nodes provide a gradient physical field for particle trapping and operations.^6,7 Acoustic waves traveling on the substrate surface (typically a surface acoustic wave (SAW)) can push the particle or fluids away much like shooting pool. The above strategies utilize the acoustic radiation force. It is very easy perform microscale manipulations or even to manipulate millimeter-scale particles. For example, both standing waves and SAW-based traveling waves have been widely investigated for use in cell separations.^8,9 The basic idea of these applications is to push the bigger cells from the main flow. From the frequency perspective, the most commonly used frequencies range from kilohertz to tens of megahertz. The acoustic frequency is determined by the resonators used. For example, for PZT, the thickness vibration is related to the plane thickness.¹⁰ The frequency of a SAW is determined by the interdigital (IDT) periodic distance.^1,3 In other words, the reason that ultrahigh frequency (generally above 300 MHz) acoustofluidics has rarely been explored is due to the lack of high frequency resonators. GHz SAWs are fabricated for communication purposes, but IDT distances are too small to fabricate by the conventional fabrication process available to university researchers. On the other hand, GHz SAWs cannot withstand high power, which also limits their use in liquids.

Acoustic streaming is a simple yet practical means of effectively triggering fluid motion by directly introducing acoustic energy to a specific region. Microscale vortex streaming induced by acoustic-driven bubbles^11,12 and sharp edges^13,14 have served as convenient acoustofluidic tools for microfluidic mixing and particle manipulations. Construction and operation of these inserted components, however, remain a professional task, as does the difficulty of maintaining long-term stability. SAW-driven microfluidics has become a very useful fluid actuation method due to its ability to transfer a large amount of momentum into fluids. Using this approach, complex fluidic and particle operations have been realized in microfluidic systems.^3,15 The typical amplitudes of SAWs are on the order of nanometers or less, however, owing to the high frequencies used (10–100 MHz), the accelerations induced by these waves are enormous (over 10⁷ m/s²).² In addition, the attenuation length of high frequency SAWs is comparable with the scale of microfluidic systems, which enables the coupling of most SAW energies with fluids. Shilton et al. experimentally demonstrated the ability of SAWs with operating frequencies of up to 1.1 GHz with respect to refined nanoscale manipulation, thereby revealing the significance of the use of ultrahigh frequencies to effectively generate acoustofluidic streaming in microscale fluids.¹⁶ As well, Ye Ai et al. used focused ultrahigh frequency SAWs (193–636 MHz) to generate a micro-vortex, and then developed this technique as a versatile tool for performing continuous micro/nanoparticle manipulation.¹⁷ 

Recently, we demonstrated the use of a GHz-acoustic-wave resonator to generate a localized micro-vortex, which we applied to some exciting applications including microfluidic mixing,¹⁸ acoustofluidic tweezering,¹⁹ and cellar surgery.²⁰ However, at present, almost all of the developed high frequency acoustofluidic techniques are at their very earliest developmental stages, and their theoretical principles have yet to be established. In this work, we investigate and reveal the properties of GHz-acoustic-induced vortex streaming, including GHz acoustic device, streaming generation, and microscale streaming characterizations, and present a full picture of GHz acoustic streaming and its microfluidic applications. We develop an analysis model to quantitatively characterize vortex streaming, and offer a simple method for tracing and characterizing microfluidic streaming motion to replace the use of particle image velocimetry (PIV).

The solid mounted piezoelectric acoustic resonator (SMR) is a typical film bulk acoustic wave resonator. As shown in Fig. 1(a), the core structure of an SMR is essentially a multi-layer sandwich, with a piezoelectric film in the center sandwiched by two electrodes. When an electrical signal is applied to the electrodes, the electric fields trigger a mechanical vibration within the piezoelectric film by the piezoelectric effect. Behind the sandwich structure is a Bragg reflector, which blocks any leakage of acoustic energy into the substrate and confines the acoustic waves to within the piezoelectric layer. Fig. 1(b) shows the vibration mode of an SMR. The SMR works in the thickness extensional mode, which is excited in a vertically grown piezoelectric material film by coupling the vertical electric field through the d₃₃ piezoelectric coefficient. Both the wave velocity and resonant frequency of the TE mode are much higher than those of any other possible modes for a given piezoelectric film, and offers the highest energy transduction.

The frequency of an SMR can be estimated by the following equation:²¹ 

where d is the thickness of the piezoelectric film, and c, ρ are, respectively, the stiffness coefficient and density of the piezoelectric film material, i.e., alumina nitride here. We note that the thickness of the piezoelectric layer of an SMR can be precisely controlled to within from several nanometers to several micrometers during the film deposition process, which enables the accurate fabrication of acoustic devices with a frequency from hundreds of megahertz to tens of gigahertz.

The SMR is fabricated using a standard complementary metal–oxide–semiconductor (CMOS) process, as presented in our previous paper.²² This process is illustrated in Fig. 2 and can be described as follows. SMR devices are fabricated on 100-mm undoped Si wafers, beginning with the deposition of the Bragg reflector. AlN and SiO₂ layers are alternatively deposited through physical and chemical vapor deposition (PVD and CVD), respectively. Then, a sandwiched structure comprising a bottom electrode (BE), piezoelectric layer (AlN), and top electrode (TE) is deposited and patterned layer by layer: The BE of the acoustic device consists of 600-nm thick Mo deposited via PVD on top of the Bragg reflector, and the film is then patterned by photolithography and plasma etching into a pentagon. PVD is used again to deposit the piezoelectric layer—a 1000-nm thick AlN film—on top of the BE, with a crystal orientation along the c-axis. In the final step, the SMR is capped with a gold TE film, which is deposited using E-beam evaporation followed by a wet etch. The thicknesses of the Au electrodes and underlying Cr adhesive layer are 300 nm and 50 nm, respectively. We configured the electrode area to be 20,000 μm² such that the SMR had a characteristic impedance of 50 Ω to match the impedance of the external circuits. We then used a PDMS microchannel prepared with soft lithography to ensure microscale confinement of the liquid samples and acoustic waves. Fig. 2(b) shows a schematic of the prepared GHz acoustofluidic chip consisting of an SMR and a microchannel.

Fig. 3(a) shows a scanning electron microscope (SEM) image of a fabricated SMR device. The sandwich structure is pentagon-shaped and confines the resonating region of the SMR. We measured the performance of the SMR in air and water, respectively, with a network analyzer (Agilent, E5071C). As Fig. 3(b) shows, the quality value (Q-value) is dramatically decreased when the device is submerged in water, which is considered to be mainly caused by acoustic leakage into the liquid. Generally, the serial resonant frequency is used as the working frequency of the acoustofluidic chip, which is about 1560 MHz here.

As shown in Fig. 2(b), the SMR vibrates at a resonant frequency in the GHz range. The vibrating displacement (A) of the SMR surface can be described simply as follows: A = ξsin(ωt). The acceleration can be obtained by ∂²A/∂t². With an assumed magnitude of about 10 nm, the acceleration is greater than 10¹⁰ m/s², which is faster than any other known technique except that of particle accelerators. For this reason, it is possible to obtain extraordinary inertial behavior from fluids and particles down to the nanoscale. However, many other factors must be considered that can affect the final performances. When submerged in water, it would be interesting to explore what would occur. Prior to describing our acoustofluidic experiment, we introduce and discuss some critical concepts and parameters, including the Stokes boundary layer, acoustic decay length, and body force.

According to the classical Rayleigh–Schlichting streaming model,²³ the acoustic triggered fluid bulk can be divided into two parts, as shown in Fig. 4, in which the light blue region supports a horizontal sinusoidal pressure wave (magenta line) of wavelength λ in the horizontal direction parallel to the wall. The dark blue region is the viscous boundary layer of sub-micrometre thickness δ, wherein large shear stress appears to generate the boundary layer (Schlichting) streaming rolls (yellow arrow line), which then drive the bulk (Rayleigh) streaming rolls (red). In traditional standing wave systems at ordinary acoustic frequency, the streaming pattern is periodic in the horizontal direction with periodicity λ/2, and thus only the top and bottom walls are subject to the no-slip boundary condition. The energy within these two regions is attributed to acoustic dissipation. The expression for the viscous boundary layer thickness can be written as follows:²³ 

where μ, ρ_f0 are, respectively, the viscosity and density of the liquid, and ω is the acoustic frequency. In viscous acoustics, the length is about 0.01 μm for water at 2 GHz.

When the acoustic wave transfers into the liquid, it is subject to an acoustic damping effect and the acoustic energy is radiated into the liquid with an attenuation coefficient of β_l:¹⁸ 

where ρ_l and c_l are the density and sound speed in the liquid, respectively; μ and μ′ represent the dynamic and bulk viscosities of the flows, respectively; and the attenuation length of the TE-mode acoustic waves is defined as $βl−1$⁠, which is proportional to ω⁻². This high frequency will induce a short decay length, and enable rapid energy dissipation within a rather short propagation distance near the SMR–liquid interface. As shown in Fig. 5, we calculated the decay length of 1560-MHz acoustic waves in water to be 7.5 μm, which is much shorter than the channel height, thereby avoiding the formation of standing waves.

The analysis of the decay length of GHz acoustic waves reveals that most of the acoustic energy is dissipated within or near the thin viscous boundary layer. Considering that the thickness of the GHz acoustic triggered boundary layer is on the order of ∼10 nm, the energy is ultra-confined and would generate a great stress force in the liquid.

The attenuation of SMR-generated acoustic waves into liquid introduces a body force at the SMR–liquid interface, which is expressed as follows:¹⁸ 

where ξ is the maximum amplitude of the acoustic waves at the SMR–liquid interface. Eq. (4) indicates that the body force scales with ω⁴, which reveals the significance of applying ultrahigh frequency to generate greater momentum to actuate the microfluids. Fig. 5 shows the body-force distribution generated by the SMR with an initial value on the order of 10¹³ N/m³. Another critical issue is the localization or focus of the body force region. Because the resonant region of the SMR is defined by the pentagon-shaped sandwiched structure, the body force is naturally focused within the locally confined region.

To evaluate the microfluidic streaming triggered by GHz acoustic waves, we used COMSOL software to perform a finite-element simulation of the fluid motion in a spatially confined area with a height of 50 μm (as shown in Fig. 6(a)). Considering the fact that the interaction between such high frequency acoustics and fluids is as yet not clearly understood, we conducted a weak-coupled simulation and neglected the nonlinear effects. Investigations of GHz acoustic streaming in micro/nanoscale fluids are ongoing. The acoustic streaming response of the fluid is characterized using a second-order system of equations, which in turn is driven by first-order equations. The fluid response is governed by the standard Navier–Stokes equation for a linear, viscous compressible fluid. As discussed above, we introduced the GHz-acoustic-wave-induced body force into the Navier–Stokes equation by presetting a boundary condition, as follows:

where $V⇀$ is the velocity vector, P is the pressure, and ρ, μ denote the density and viscosity of fluid, respectively.

We considered the SMR to be the ideal device with a perfect match layer on the substrate, despite the fact that the fabricated device contains flaws that can provide various pathways for acoustic energy leakage into the substrate. Another factor is the heating effect caused by the acoustic energy dissipation. The heating ability of the SMR has been characterized within the microfluidic system.²⁴ Localized heat has been demonstrated to generate vortex streaming in various optofluidic systems at velocities on the order of μm/s.²⁵ Here, we studied the heat-streaming effect using a two-dimensional finite-element simulation, and we used parameters from the experimental data described in our previous paper.

The preset conditions of the heat-streaming simulation are shown in Fig. 6(b). The heat-streaming effect is expressed in the following:

where Q is the input heat flux, and C and k denote the heat capacity and thermal conductivity of the fluid, respectively. The input heat source is assumed to be at the liquid–solid interface. The profile of the heat flux is assumed to be Gaussian and focused in the center of the source. The fluid motion obeys the Navier-Stokes equation, and we set the external force term to be proportional to the temperature gradient.

The SMR is excited by a radio frequency (RF) signal generator (MXG Analog Signal Generator, Agilent, N5181A 100 kHz–3 GHz) and a power amplifier (Mini-Circuits, with 35 dBm enhancement of the original RF source power). Prior to the microfluidic mixing experiments, we cleaned the channels by flushing them with ultrapure (UP) water at a flow rate of 20 μL/min. We then introduced the UP water with and without fluorescent dye (FITC, 20 μg/mL) into the chip via two inlets using a syringe pump (New Era Pump Systems, Inc.). We maintained equal flow rates for both streaming experiments, and set their total flow rates Q to 5 μL/min, 10 μL/min, 20 μL/min, 40 μL/min, 60 μL/min, and 80 μL/min. We measured the operating frequency of the SMR by frequency sweeping and used the serial resonant value as the working frequency. All experiments were recorded using a florescent microscope (Olympus, BX53) integrated with a CCD camera (DP73), with the images captured at 25 frames per second.

As localized micro-streaming can generate laminar flows within microfluidic systems, different laminar flows can be mixed to reflect and characterize the strength of the acoustic streaming. We described the mixing effect of a GHz acoustofluidic chip in our previous paper,¹⁸ as well as detailing the characterization method. Briefly, the mixing performance is determined by examining a cross-sectional area of the microfluidic mixer perpendicular to the flow direction in terms of a mixing index (MI). In the experiment, we used an FITC solution and acquired the fluorescence intensity value of i-th pixel (I_i) in the region of interest (ROI) to characterize the concentrations,¹⁸ as follows:

where N is the number of pixels along the line of the ROI, I_i and $I¯$ are the intensity values of the i-th pixel and the average value of N pixels in the mixed region, respectively, and I′ represents the intensity value in the unmixed region.

To better understand the vortex mixing principles, we developed a dynamic model by analyzing the molecule transfer process at the interface of the vortex and flowing fluids. Fig. 7(a) shows the mass transfer of two laminar flows at the vortex edge, wherein the vortex velocity, V, equals the flow velocity, and V_f, defines the mixing length from the unmixed to the mixed region. The vortex area is confined by the edges of V/V_f = 1, and the influence of the flow rate on the vortex area is determined by normalizing the vortex velocity field with the flow velocity. Fig. 7(b) shows the values of V/V_f on the labeled line on the simulated vortex velocity field. The inner edge of the vortex is closer to the center of the device (x = 300 μm), and the vortex area is primarily tuned by adjusting its outside edges according to the experimental results.

Fig. 8(a) shows the maximum velocity of the vortex as a function of the applied power, which reveals a linear relationship between velocity and power. The insert in Fig. 8(a) shows the results of the experimental vortex generation in microflows, which demonstrate the formation of vortex streaming, and which fit well with the simulation results. Fig. 8(b) shows the heat-streaming effect simulated by a 2-D model, with the conditions preset as in Fig. 6(b). The results show that acoustic-dissipation-generated heat can induce a pair of vortices similar to the acoustic-streaming effect. We plotted and fitted the relationship between maximum velocity and temperature. Compared with the vortex induced by the acoustic fields, for which the velocity is on the order of m/s, the streaming generated by heat is much weaker, on the order of μm/s. Thus, the streaming induced by the acoustic-heating effect can be neglected, as the vortex is mainly induced by the acoustic-streaming effect.

As shown in Fig. 8(a), vortex streaming is effectively generated in the microfluids. We can clearly see that there are multiple vortices (those in the downstream are hidden by the well-mixed florescence flow) around the resonator device, which agrees well with the simulation results. The vortex can efficiently mix the laminar flows, thereby enabling a homogenous mixed flow in the downstream (i.e., mixed region). Fig. 9(a) and (b) show the streaming fields of the vortices for different power and flow-rate conditions. In the upstream, two vortices can be clearly observed by the border lines of the fluorescent dye. First, we evaluated the power effects on the formation of the micro-vortex. The simulation result shows that the power input of the device has a strong effect on the rotation speed of the micro-vortex, which is directly related to the fluid mixing efficiency in the microchannel. Experimentally, we studied this issue by analyzing the shape of the vortex formed at different input powers. Fig. 9(a) shows the streaming field induced by the SMR with applied power values of 100 mW, 300 mW, and 500 mW, respectively, at the same flow rate (5 μL/min). At a lower input power (100 mW), the vortex remains approximately symmetrical along the flow direction and the streaming area does not cover the full microchannel, which results in poor mixing. When the power is increased to 500 mW, the behavior of the vortex array becomes much more intense, and disturbs the fluids in a larger area until it is confined by the boundaries of the microchannel, thereby improving the mixing efficiency. This result confirms the simulation results, which indicated that a higher power input will induce faster vortex formation, and thus improve the fluid mixing efficiency. Next, we experimentally investigated the effect of the flow velocity (V_f) in the microchannel. We obtained the flow velocity by $dQdA$⁠, where Q is the flow rate and A is the cross-section area of the microchannel. Here, we use the average velocity (⁠$Vf¯$⁠) to represent the flow velocity field. While keeping the same input power (500 mW), we varied the flow rate (Q) at 10 μL/min, 40 μL/min, and 80 μL/min. As shown in Fig. 9(b), a higher flow rate reduces the vortex area and confines the shape, which is a similar result to the lower power case in Fig. 9(a), and therefore weakens the mixing effect. We can conclude that both the input power and the flow conditions confine the vortex, and the fluid mixing efficiency can be finely tuned by these parameters. To further quantify the influence of different input power and flow conditions, we carefully characterized the mixing efficiency using the mixing index presented in Eq. (7). As shown in Fig. 9(c), for a given flow rate, the mixing efficiency increases with increased power. In the low-power range, the mixing index has an approximately linear relationship to the applied power. Combined with the simulation results, this reveals that the mixing efficiency is proportional to the velocity of the vortex. The power applied to the SMR can be varied from several milliwatts to several watts to tune the mixing efficiency over a rather large range. Fig. 9(d) shows that for a given applied power, the mixing efficiency increases with decreases in the flow rate in most cases. In particular, in the low-power case, the mixing efficiency is greatly influenced by the flow rate. This is due to the fact that the vortex is confined by the flow, which limits the disturbance range inside the microchannel. The influence of the flow rate is less apparent in the high-power case, since when high power is applied, the SMR induces a much stronger vortex to offset the influence of the flowing fluids.

Based on the definition of the vortex edge, the vortex area can be obtained in both simulations and experiments by acquiring the curve ratio of the vortex area. The curves in Fig. 10(a) show the vortex edges at different flow rates, with the corresponding radii obtained shown in Fig. 10(b). As the vortex velocity on the edges is approximately equal to the flow velocity, the vortex velocity triggered by different power levels and the velocity distribution within the vortex can be directly measured using the flow tuning method. The above analysis highlights a new approach for measuring the streaming velocity field that can replace PIV methods. Fig. 10(c) shows the radius values obtained from Fig. 7(b), which show a similar functional relationship as those obtained in the experiment.

In conclusion, both our simulation and experimental results demonstrated the determinative role of GHz acoustics in streaming generation. To understand the GHz-acoustic-induced microscale vortex streaming, we introduced the classical Rayleigh–Schlichting model to explore the particular case of such high frequencies. Even though the theoretical principles can be illustrated rather reasonably, there remain many aspects of the acoustic-fluid interaction process that are unclear. In addition to a mixing index, we developed a micro-PIV method in which the vortex edges are defined, which enables a determination of the precise velocimetry within microscale and even nanoscale fluids. For the first time, in this work, we introduced a whole map of GHz acoustofluidics from its theoretical principles to experimental characterizations, which contribute to broadening the understanding of GHz-acoustic-fluid interactions.

The authors gratefully acknowledge financial support from the National Natural Science Foundation of China (Grant Nos. 91743110, 61674114, 21861132001), National Key R&D Program of China (Grant No. 2017YFF0204600), Tianjin Applied Basic Research and Advanced Technology (Grant No. 17JCJQJC43600), the Foundation for Talent Scientists of Nanchang Institute for Microtechnology of Tianjin University, and the 111 Project (Grant No. B07014).We also thank Prof.Mark Reed at Yale University for useful discussions.