Mixing enhancement in T-junction microchannel with acoustic streaming induced by triangular structure

Abstract

The T-shaped microchannel system is used to mix similar or different fluids, and the laminar flow nature makes the mixing at the entrance junction region a challenging task. Acoustic streaming is a steady vortical flow phenomenon that can be produced in the microchannel by oscillating acoustic transducer around the sharp edge tip structure. In this study, the acoustic streaming is produced using a triangular structure with tip angles of 22.62°, 33.4°, and 61.91°, which is placed at the entrance junction region and mixes the inlets flow from two directions. The acoustic streaming flow patterns were investigated using micro-particle image velocimetry (μPIV) in various tip edge angles, flow rate, oscillation frequency, and amplitude. The velocity and vorticity profiles show that a pair of counter-rotating streaming vortices were created around the sharp triangle structure and raised the Z vorticity up to 10 times more than the case without acoustic streaming. The mixing experiments were performed by using fluorescent green dye solution and de-ionized water and evaluated its performance with the degree of mixing (M) at different amplitudes, flow rates, frequencies, and tip edge angles using the grayscale value of pixel intensity. The degree of mixing characterized was found significantly improved to 0.769 with acoustic streaming from 0.4017 without acoustic streaming, in the case of 0.008 μl/min flow rate and 38 V oscillation amplitude at y = 2.15 mm. The results suggested that the creation of acoustic streaming around the entrance junction region promotes the mixing of two fluids inside the microchannel, which is restricted by the laminar flow conditions.

I. INTRODUCTION

Mixing is an operating process involving the combination of different materials in microfluidic systems. Micromixers are one of the main components of the microfluidic system. It is mainly used in the processing industries, biological analysis processes, chemical synthesis, and polymerization processes. Micromixers are mainly categorized as passive and active. Passive micromixers work with the applied fluid pressure difference to move the fluid, while active micromixers use additional input power to achieve mixing within the micro-fluidic system. Oscillation driven by piezoelectric material at ultrasound frequencies to mix two different fluids¹ and a magneto hydro micromixer generated by an electric and magnetic field produced around electrodes to create flow field² are examples of active micromixers techniques.

A microchannel is usually referred to as a channel that has a hydraulic diameter of less than 1 mm dimension. In microchannel, microscale fluid flows are mainly pressure-driven and can be developing or fully developed. Compared to macroscale flow devices, microchannels are advantageous in heat transfer equipment to increase heat transfer surface area, reduce weight and size. Therefore, it can be found in many applications in flow control and heat transfer systems.³ T-junction is one of the microchannel configurations often used in microfluidics, which may have different cross section geometries, such as square, circular, rectangular, and triangular. Its operational region also depends on the fluid’s flow rates, viscosity, and dimensions of the channels.^4,5 The fluid flow is usually characterized by the Reynolds number and the T-junction microchannel plays a vital role in the mixing of the two sides of the fluid flow.⁶ In most situations, due to its small geometry, the flow is laminar or a very low Reynold number.⁷ As a result, viscous force plays a very significant role than inertial force in many microfluidic systems. Also, the uniform concentration within the two sides fluids mixing channel section appears when the fluid flows at a high Reynold number.⁸ The T-shaped microchannel deliberately rises the vortex structure throughout its flow length and this vorticity can improve the mixing quality even at low Reynolds numbers.^9,10

Acoustic streaming is a steady flow phenomenon due to the time-averaged nonlinear dynamics of the fluid-solid interaction in a viscous flow.^11–13 Fluid elements are forced to oscillate in the direction of wave propagation, during a continuous acoustic wave propagating in the fluid. Also, it is capable of generating hydrodynamic forces that are used to move fluids inside the microchannel.^13–15 Acoustic streaming has the ability also to generate a 3D flow phenomenon inside the microchannel due to the force applied from acoustic radiation force and the acoustic streaming-induced drag-force.¹⁶, and can be generated from any solid surface in or around the incident acoustic pressure field to cause the second-order time-averaged flow patterns.¹⁷ Due to the small dimensions of the microchannel, flow is mostly not turbulent, and it is, therefore, become a challenge to promotes effective fluid mixing by disturbing the flow pattern in microscale flows. One way to achieve this goal is to create a small vortical flow pattern by inducing acoustic streaming and further enhances the vertical flow that exists in the channel. The sharp edge of solid bodies that oscillates in the flow channel is used as the origin of acoustic streaming. It creates centrifugal forces around the sharp edge. Sharp tip edge oscillations generate a large Reynold body force when compared to their non-sharp counterparts.¹⁸ The triangular microstructure can generate acoustic streaming within the microchannel but depends on parameters such as applied voltage, oscillation frequency, top angle, flow rates, etc. The strength of streaming is directly related to an applied voltage and is also strong enough near to top vertex at a small top angle.¹⁹ It is also found that the induced flow pattern is stronger at low Reynold number than high Reynold number flows.²⁰

Acoustic streaming has been investigated for mixing and other purposes in different areas, such as the effect of near sharp edges of solid bodies,²¹ the placement of transducers outside the cylindrical water vessel to create an acoustic field and circulating water for mixing, as well as three-dimensional flow pattern generation.²² Adding the triangular sharp-edge geometry structure to the Y-microchannel sidewall was also done by recirculating and inducing acoustic streaming near to sharp-edge for mixing of two fluids.^23,24 The application of acoustic waves for micromixing has also been investigated in a dome-shaped chamber device.²⁵ It has so far been used in chemical, biomedical, and material synthesis study areas such as the generation of chemical gradients,²⁶ cell lysis using surface acoustic wave oscillation,²⁷ synthesis of organic nanoparticles,²⁸ synthesize of hierarchically porous metal-organic framework crystals with micro and macropores,²⁹ to fabricate hollow nanocrystals in microfluidics³⁰ and the enhancement of DNA hybridization.³¹ It is also applied to convective heat transfer in an open-ended channel up to a temperature drop of 40 °C with a vibration amplitude of 25 μm at 28.4 kHz.³² In general, the mixing quality is a common problem in microchannel because the flow of fluid is laminar and depends on the effective length of the microchannel mixing section. The T-microchannel mixing performance is enhanced by inducing different geometries such as obstacles and zigzag in the mixing channel section^33,34 and by increasing the mixing section length of the microchannel.³⁵ Since the T-shape microchannel has two inlets and one common outlet to the mixing section, the previous studies were, therefore, mostly far away from the T-junction area. Subsequently, it is exposed to material saving and manufacturing problems, which means that the cost of making the microchannel is higher.

The purpose of this study is, therefore, to propose a new configuration to apply acoustic streaming to assist mixing in a T-junction channel. By placing triangular geometry at the junction of two inlet and middle sections of the outlet channel, as shown in Fig. 1, the performance and flow patterns of mixing with acoustic streaming on the T-junction microchannel are investigated, and different parameters are tested, including triangle geometry (top angle, width, height), oscillation amplitude and fluid flow rates. The paper is organized in the following order: methods and experimental setup are presented in Sec. II, following by the results in Sec. III and discussion in Sec. IV. Finally, the important findings and future works are concluded in Sec. V.

FIG. 1.

Experimental setup.

II. MATERIALS AND METHODS

A T-microchannel mold is produced with a standard manufacturing process of a microfluidic device.³⁶ A 200 μm negative T-shaped microchannel cast is produced by the micro-milling process to minimize the manufacturing costs. Similarly, another 2 mm polymethyl methacrylate (PMMA) is openly cut. Polydimethylsiloxane (PDMS) was mixed with a mass of 10% and gas removed in a vacuum chamber, then spilled onto negative T-shaped PMMA to form the positive microchannel structure on the PDMS mixture plate and placed all inside an oven for 1 h at $80{}^{°}\mathrm{C}$. The product edge is then attached to 2 mm open polymethyl methacrylate (PMMA) by a double-sided tape. Again, the final negative PDMS T-shaped microchannel is produced in the same as above. Then, the final PDMS is attached to a standard microscopic sliding glass (26 × 76 × 1 mm³) after both sides oxygen plasma treatment to withstand the fluid from leakage. Finally, a 200 μm height T-microchannel is formed between the sliding glass and PDMS. Microchannel geometrical configuration and basic dimension are as shown in Fig. 1. The triangular geometrical structure is located at two inlet junctions and the middle axis of the outlet channel section. It has different tips, i.e., ${22.62}^{°},{33.4}^{°},{61.91}^{°}$ with widths of 92, 138, and 276 μm, respectively. All cases of microchannel tips were independently manufactured and sealed to a glass slide.

The experimental setup layout for acoustic streaming and mixing is shown in Fig. 1. Microchannel and 12.7 mm diameter piezo disc (T216-A4NO-273X, Piezo System) are connected by an ultrasound hydrogel (XY-35, Taiwan Stanch Co. Ltd) to generate acoustic streaming. The piezo disc is driven with sinusoidal waveform at various 3–13 kHz frequencies by a signal generator (HDG2022B, Hantek) and the amplitude voltages vary from 9 to 44 V, which is magnified with an amplifier (HSA 4012, NF Corp.). The amplitude of a sinusoidal voltage is its peak or half of its peak-to-peak voltage measurement. The signal is monitored by a digital storage oscilloscope (TDS 2002B, Tektronix), which is connected to the amplifier.

A Double syringe pump (NE-4000, New Era Pump Systems Inc.) delivers an equal fluid flow rate through the two inlets of the microchannel. Yellow fluorescent particles (Fluorescent Pigment Yellow 27, Emperor Chemical Co. Ltd) is seeded with liquid water to visualize and study acoustic streaming. Likewise, for the mixing performance study, one inlet is de-ionized water and the other is de-ionized water with a fluorescent green dye (Fluorescein Sodium Salt, Sigma Aldrich) has the maximum spectrum properties of 460 nm of excitation and 515 nm emission.

For acoustic streaming and mixing performance test, a high-speed camera (i-speed 3, Olympus) is mounted on a microscope (Eclipse Ts2R, Nikon) illuminated with a continuous 460 nm LED light source. The camera has a resolution of 1280 × 1024 pixels. The 10× and 20× magnification objective lenses were installed on the microscope for mixing performance and PIV experiments, respectively.

Flow videos result are recorded on a 16GB card with 75 fps (frame per second) frame rate at 13.33 ms exposure time for micro-PIV, and 200 fps frame rate with 4.998 ms exposure time for mixing experiments, respectively. 400 images are extracted from hsv file format for one experimental run with the i-speed camera software. The velocity field is determined by the relative acoustic streaming displacements of the particles with consecutive image pairs of ensemble correlation using the open-source PIVlab toolbox in MATLAB environment.³⁷ The image pairs are first processed by setting in the image preprocessing section with the contrast-limited adaptive histogram equalization (CLAHE) and set the processing window size to 20 pixels. The velocity field is then analyzed with a $64\times 64$ pixel² interrogation window size with a 50% overlap ratio, eventually down to $32\times 32$ pixel² in four passes. Finally, the vortices are determined by the successive visualization of trajectories and interpolation of the velocity field.

The triangular geometry structure has constant height h and different width w based on the tip-edge dimensions. Table I shows the experimental test matrix values and triangle geometry parameters with height h (base to tip) of 230 μm.

TABLE I.

Test matrix for acoustic streaming and mixing performance.

Top angle (αo)	22.62	33.4	61.91
Width w (μm)	92	138	276
Height h (μm)	230
Frequency (kHz)	3, 9, 13
Amplitude (V)	9, 19, 28, 38,44
Total flow rate (μl/min)	0.008, 0.012, 0.016, 0.02, 0.032, 0.2

III. RESULTS

A. Flow visualization and acoustic streaming

Acoustic streaming is induced by the oscillation of the flow when the piezo disc transduces the power to the solid PDMS and then to the flowing fluid in the microchannel. As shown in Table I, the tip-edge height dimension is less than 1 mm, which means that the characteristics flow dimension is much lower than the acoustic wavelength (${\lambda }_{\mathrm{c}}$ = $\mathrm{c}/\mathrm{f}$), where c is the speed of sound in water (at 25 °C, c = 1490 m/s) and f is the oscillation frequency. Microchannel geometrical dimensions are therefore less important than the acoustic wavelength, and the flow can also be treated as incompressible properties. Liquid water has low viscosity and also the oscillation frequency in kHz, the solid–liquid interface is exposed to viscous friction and occurred at low viscous boundary layer ($\delta =\sqrt{2\mathrm{v}/\omega }$),¹⁸ where v is the kinematic viscosity of water, ω represents the angular frequency in which $\omega =2\pi \mathrm{f}$, and f is the oscillation frequency.

Figure 2 shows the particle stream trajectories at 0.012 μl/min flow rate, oscillation frequency 13 kHz, and 28 V amplitude. The fluorescent particle mixture flows from the two side inlets and the acoustic streaming flows originates from the triangle structure tip edge and create two large counter-rotating vortices than other microchannel regions. These revolving streaming vortices extended to both sides of the microchannel entrance up to outlet microchannel bends, and dragging back to the triangular tip edge, then started the flow forward to the outlet area of the T-microchannel. The T-microchannel geometry can naturally generate vortices during the flow of fluid. In the same way, vortices along the z-direction can generate with acoustic streaming and determine from plane velocity vector component x and y-direction using Eq. (1),

$${\omega }_z={\displaystyle \frac{\mathrm{\partial }V}{\mathrm{\partial }X}-{\displaystyle \frac{\mathrm{\partial }U}{\mathrm{\partial }Y}.}}$$ (1)

FIG. 2.

Acoustic streaming flow visualization.

Figures 3(a) and 3(b) demonstrate the influence comparison of vector and contour layer of Z vorticity with acoustic streaming at 0.012 μl/min flow rate, 38 V amplitude, and 13 kHz frequency. The acoustic streaming is generated highly at the microchannel entrance junction region as shown in Fig. 3(b). High vorticity delivered around the entrance junction and outlet of the microchannel bend region. It then reached a peak value before y = 0.6 mm and gradually decreased its magnitude value, then tried to follow its almost uniform Z vorticity through the microchannel outlet flow length.

FIG. 3.

Effect of acoustic streaming at flow at flow rates of 0.012 μl/min; (a) vector and contour layer of Z vorticity plot without piezo disc; (b) vector and contour layer of the Z vorticity plot at 38 V, 13 kHz; (c) comparison of the line Z vorticity profile plot along the flow direction.

Figure 3(c) shows the Z vorticity distribution along the y-direction at the sides of the triangle structure extracted from the vector and contour layer plots shown in Figs. 3(a) and 3(b). There is a high Z vorticity structure on both sides with acoustic streaming. It has shown that more than 60(1/s) of the peak vorticity structure around the entrance T-junction region. This indicated that the maximum improvement is also more than ten times between y = 0.2 and 0.6 mm with the acoustic streaming application. After y = 0.7 mm of the microchannel flow length, both cases have an equivalent z vorticity between almost −2 and 2 (1/s).

Generally, it is clear that the mixture of the particles flows from two inlets to the common microchannel junction zone and runs to one microchannel outlet section. The flow rotates due to the oscillation energy transmitted from the piezoelectric plate before entering the common outlet microchannel area. The generated acoustic streaming velocity is found to be greater than the total fluid flow outlet velocity. Oscillation amplitude, inlet volume flow rate, oscillation frequency, and triangle geometry dimension parameters influence the generation of acoustic streaming around the sharp edge. This means that the performance of the current microchannel also depends on these factors as well. The effects of these factors are presented in the following sections.

1. Effect of volume flow rate and oscillation frequency

The microchannel has two side inlet directions and a high Z vorticity develops with acoustic streaming due to the transducer power to the flowing fluid. However, when the total flow rate has increased, the acoustic stream flow back to the tip edge and the radial dimension coverage from the tip edge of the triangle is reduced. This leads the flow to the outlet area of the microchannel between the bent edges of the T-microchannel and acoustic flow, which rotates around the ${22.62}^{°}$ angle of the tip edge. Figures 4(a) and 4(b) show the impact of flow rate on acoustic streaming vortices generation. The rotating vortices around the triangle tip and entrance region decrease at a high volume flow rate due to the impact of the piezo disc decrease based on the momentum statement. The transducer power is more effective at 0.012 μl/min flow rate than 0.2 μl/min flow rate between y = 0.2 to 0.6 mm at x = 0.6 mm and x = 0.8 mm left and right of the triangle tip edge as shown in Fig. 4.

FIG. 4.

Effect of volume flow rate on acoustic streaming at 38 V, 13 kHz; (a) Z vorticity profile extracted at line x = 0.6 mm; (b) Z vorticity profile extracted at line x = 0.8 mm.

The frequency of the oscillation refers to the sinusoidal wave function of periodic motion. Figure 5 presents a comparative study of the Z vorticity distribution along the y-direction at the sides of the triangle structure at different sinusoidal waves in volume flow rate of 0.016 μl/min and oscillation of $22{.62}^{°}$ tip edge triangle geometry. The result suggested that the oscillation frequency 13 kHz has good performance. This frequency is selected for all experimental work to evaluate the remaining parameters.

FIG. 5.

Effect of oscillation frequency.

2. Effect of oscillation amplitude and geometry

Oscillation amplitude refers to the peak applied voltage toward the piezo disc device. Figures 6(a) and 6(b) show a comparison of the vector and contour plot using ${22.62}^{\mathrm{o}}$ angle at 19 V and 44 V oscillation amplitude, respectively. It has also a great impact on the creation of acoustic streaming. It was monitored with an oscilloscope equipment. The near-triangular tip is exposed to higher acoustic amplitudes than the other inside of the microchannel. The particle mixture flows back to the tip of the triangle with more radial distance at high oscillation amplitudes and produces higher Z vorticity as shown in Fig. 6(b). Similarly, Figs. 6(c) and 6(d) illustrate the vortices generation profile at a line x = 0.6 mm and x = 0.8 mm oscillation amplitude in 19 V to 44 V at 0.016 μl/min and 13 kHz frequency. There is a high peak vortices structure generation from y = 0.1 to 0.6 mm along the flow direction. The results show that oscillation amplitude is directly related to the acoustic streaming vortices. At high 44 V oscillation, amplitude transferred more transducer power to the fluid flow component.

FIG. 6.

Effect of amplitude on acoustic streaming at volume flow rate of 0.016 μl/min and oscillation frequency 13 kHz; (a) vector and contour layer Z vorticity plot at 19 V; (b) vector and contour layer Z vorticity plot at 44 V; (c) Z vorticity profile along x = 0.6 mm at different amplitudes; (d) Z vorticity profile along x = 0.8 mm at different amplitudes.

The geometric dimension variation means the change of the triangle tip edge angle with respect to other dimensions of the triangle structure dimensions, i.e., height or width. The current T-microchannel inlet width is a small dimension and difficult to vary the geometrical factor with height. Therefore, the tip edge angle varied only by changing the width (w) of the triangle dimension. Figure 7 shows the Z-vorticity distribution along the y-direction at the sides of the triangle structure. The acoustic streaming vortices are influenced by the geometrical dimension of the triangle. The two side streaming vorticity depends on the geometry of the tip edge angle. The ${22.62}^{°}$ sharp edge angle has better effectiveness than ${33.4}^{°}$ and ${61.91}^{°}$ angles. The space gap between each side and the microchannel each corresponding bend edges is also changed at the entrance junction region, i.e., 310 μm (${22.62}^{°}$), 300 μm (${33.4}^{°}$), and 290 μm (${61.91}^{°}$). This decrease in entrance junction width leads to a decrease in the acoustic streaming back to the tip triangle edge.

FIG. 7.

Acoustic streaming Z vorticity distribution at different geometries.

B. Mixing performance

As seen in Sec. III A at a high oscillation amplitude and a minimum flow rate, acoustic streaming results in enhanced disturbance within the microchannel entrance junction region. The mixing experiment is done by using two miscible fluids, i.e.one inlet fluorescent green dye solution and another inlet is de-ionized water. The concentration of the dye across the T-microchannel outlet width and along the flow direction dimension is decreased due to mixing with water. Mixing without and with acoustic streaming has been primarily assessed and compared with similar flow conditions. In addition, the experiments are performed in different scenarios, but both sides have similar inlet flow rates.

Figure 8 shows the flow visualization results of mixing two fluids in the T-microchannel with a triangular tip edge geometry. Fluorescent dye solution and de-ionized water microscopic images have different pixel intensity information. Therefore, it can indicate the mixing of the two fluids, which means that if the mixing is perfect, the whole pixel has a similar intensity value.

FIG. 8.

Mixing visualization; (a) At 0.006 μl/min, 38 V and 13 kHz acoustic streaming and without piezo disc; (b) At 0.02 μl/min, 38 V and 13 kHz acoustic streaming and without piezo disc.

Acoustic streaming caused more disturbance during fluid mixing than non-acoustic streaming flow. Figures 8(a) and 8(b) show the mixing action of acoustic streaming at different volume flow rates without a piezo disc or at t = 0 s and with a piezo disc or after t = 10 s. Its acoustic stream has been more visible at 0.006 μl/min than 0.02 μl/min volume flow rate in the entrance junction region.

The mixing performance is quantified by the degree of mixing³⁸ at each width cross section of the microchannel outlet area,

$$M=1-{\displaystyle \frac{\sigma }{{\sigma }_o},}$$ (2)

where M is the degree of mixing range [0,1], σ is the standard deviation of the intensity distribution across the width of microchannel section,

$${\sigma }^2={\displaystyle \frac{1}{n}\sum _{i=1}^n{(I_i-I_m)}^2.}$$ (3)

σ_o is the maximum standard deviation at the beginning of the mixing process, n is the number of pixels in the cross section, I_i is the grayscale value of pixel intensity, I_m is the mean of the grayscale value of pixel intensity of n pixel.

The microscopic image has pixel grayscale intensity values from 0 to 1. Typically, 0 and 1 are taken to black and white images, respectively. The low and high pixel intensity standard deviations indicate the mixing performance of the microchannel along its flow length direction. It is a function of the microchannel flow dimension along the flow direction. On the other hand, the pixel intensity varies with the width of the microchannel. Therefore, the standard deviation is determined across the width of the microchannel, and the mixing performance is evaluated along the flow outlet direction.

The degree of mixing is also evaluated in similar ways like vorticity generation at three kHz levels operating frequency and applying the best frequency for future mixing performance studies. The main purpose of selecting at low kHz level operating frequency is to the viscous friction force at low boundary thickness and minimizing the power dissipation from the piezo disc to the microchannel chips.

As shown in Fig. 9, acoustic streaming performed much better mixing at 13 kHz operating oscillation frequency.

FIG. 9.

Degree of mixing at different oscillation frequencies with 0.016 μl/min and 38 V.

Figure 10 illustrated the mixing performance of the T-microchannel supported by acoustic streaming around the entrance junction area. The vortices induced by the acoustic streaming result in an improved degree of mixing from 0.4017 to 0.769 at a 0.008 μl/min flow rate, as shown in Fig. 10(a). Figure 10(b) demonstrates the degree of mixing with acoustic streaming as a function of total volume flow rate. When the inlet volume flow rate increased from 0.012 to 0.2 μl/min, the degree of mixing decreased from 0.629 to 0.368 at y = 2.15 mm. Similarly, Fig. 10(c) indicated the effect of oscillation amplitude on mixing quality and 0.652° of mixing at 44 V amplitude and 0.394 at 9 V amplitude due to the difference in acoustic streaming vortices structure. The sharper edge triangle also had a better degree of mixing in the measurement regions along the y-direction as shown in Fig. 10(d).

FIG. 10.

Mixing performance; (a) with and without acoustic streaming at 38 V amplitude, 13 kHz oscillation frequency; (b) in different flow rates at 38 V and 13 kHz oscillation frequency; (c) in different amplitudes at 0.016 μl/min and 13 kHz oscillation frequency; (d) in different tip angles at 13 kHz, 0.016 μl/min, and 38 V.

IV. DISCUSSION

Acoustic streaming is a 3D physical phenomenon, especially so at high operating frequencies. In this study, a low frequency oscillation at kHz level are utilized to generate the desired acoustic streaming. The oscillations at the sharp tip have a large Reynold body force when compared to their non-sharp counterparts.¹⁸ As a result, the 3D phenomenon of acoustic streaming is expected to be stronger around the sharp tip edge, and the highly rotational streaming flow is most likely to be produced around both sides of the tip. The mixing performance, on the other hand, is investigated away from the tee junction of the microchannel at the mixing regions at various microchannel lengths along the y-direction. After the two counter-rotating vortical flow regions, the mixed fluids were moving forward as in a bulk flow phenomenon toward the outlet region of the common mixing region. Therefore, the 3D flow region is confined near the tip region and the mixing performance is not expected to have a major difference along the microchannel height. To validate this argument, additional experiments were performed and at six focal planes with microchannel heights ranging from 30 to 170 μm were observed between PDMS and the glass slide. Figure 11 shows the results in term of the degree of mixing along flow length. All data lines are close to each other, and the difference of the degree of mixing between the maximum and minimum values at y = 2.15 mm is 0.027, which is quite small compared to its mean values. Therefore, the authors concludes that there is no significant 3D physical phenomenon effect at the mixing region.

FIG. 11.

Degree of mixing at different microchannel heights with 13 kHz, 0.016 μl/min, and 38 V.

The acoustic streaming can be generated from any solid surface in or around the incident acoustic pressure field to cause the second-order time-averaged flow patterns. The operating frequency in this study is in the kHz regime, which is significantly lower than those studies utilizing MHz level oscillations. Ovchinnikov's study also shows that the oscillatory sharp tip edges cause higher Reynold body forces and stronger microstreams than their non-sharp counterparts.¹⁸ The result of these factors on the current study is that acoustic streaming was expected to be more widespread around the triangle's sharp tip edge than in other regions. The kHz oscillation frequency also does not invoke the other parts of the microchannel to oscillate at the same level as the triangular tip, as observed in the studies that utilize MHz oscillation frequency. Therefore, the 3D acoustic streaming flow patterns is limited to only the near field of the triangular tip.

There are many types of active micromixers available based on different external energy sources to disturb the fluids and increase the contact area to enhance the mixing effect. The main external sources of energy are electrical, pressure, magnetic, and sound fields. Sound field energy sources are mostly induced by sharp-edges inside the microchannels.²³ In this experimental study, the triangle structure was induced in the T-microchannel entrance junction region to enhance the mixing of two different fluids with acoustic streaming.

A thermal analysis of the piezoelectric device was also performed to estimate the power consumption and heat dissipation during the experiments. In this study, the flow of the fluid was continuous from two side-inlets to the single outlet, and the maximum duration was also less than 1 min for a single experiment run. In practice, a piezo disc has electrical resistance that generates heat when the current passes through it. The power dissipation in the piezo disc is estimated using the following equation:

$$P=2\pi \times f\times C\times \tan (\delta )\times V_{rms}^2={\displaystyle \frac{\pi }{4}\times f\times C\times \tan (\delta )\times V_{PP}^2,}$$ (4)

where P is the power dissipated in the piezo disc, f is the operating frequency in Hz, C is the capacitance in F, $V_{PP}$ is the peak-to-peak driving voltage, $V_{rms}$ is the root mean square voltage, i.e., $V_{rms}=V_{PP}/2\sqrt{2}$, and $\tan (\delta )$ is the dielectric dissipation factor. The dielectric dissipation factor is defined as the ratio of equivalent series resistance of the capacitor (ESP) to the capacitive reactance $(X_C)$, i.e., $\tan (\delta )=\frac{ESP}{X_C}$.³⁹ According to the specifications of the piezo disc used in this study, the dielectric dissipation factor and capacitance of the piezo disc are 0.02 and 4 nF, respectively. In the current experimental cases of minimum and maximum applied voltages, the power consumption is estimated to be 0.0003 and 0.0063 W, respectively. The dissipation power in the piezo disc is highly dependent on operating frequency and applied peak-to-peak voltage of the sinusoidal voltage value. The kHz level frequency has less dissipation power than the MHz level frequency. Similarly, at lower peak-to-peak voltages, there is also an expectation of less power dissipation than at higher voltage conditions. Lower power dissipation in the piezo disc means less energy has been converted to heat as an electric field is applied in the piezo disc materials and due to mechanical loss. Furthermore, the fluid flow was continuous based on the flow rate setting from both inlets to the single outlet storage by the syringe pump. The overall piezo disc run time for recording the video for one experiment case was less than 1 min. No noticeable temperature change can be recorded at this experimental condition. Considering that mixing can be done in some application scenarios for long time by continuously running the device, a test is performed by using a thermocouple to measure the surface temperature of both the piezo disc and the microchannel during continuously running the piezo disc for 10 min. The maximum temperature recorded was 25.9 °C, which is almost similar to the maximum surface temperature of 25.8 °C recorded before experiment run, and both are within the variation of the ambient temperature in the room. Theoretically speaking, if the thermal boundary layer is relatively thick, the viscous dissipation should be considered in calculating the temperature of the wall. The Stokes boundary layer has the length scale $\delta \sim \sqrt{2\nu /\omega }$, where $\nu$ is the kinematic viscosity of water, $\omega =2\pi \mathrm{f}$ and f is the operating frequency at the kHz level. This defines the boundary layer thickness of the acoustic streaming. In this study, the boundary layer thickness is estimated to be around 11.72 μm at 13 kHz operating frequency. Compared to the mm-scale thickness of the microfluidic device, the boundary layer thickness is small and the viscous dissipation rate is relatively fast. The result of this is that the heat generated from the oscillation of piezo disc is quickly dissipated out of the boundary layer, and further transferred out of the device through convection. This provides a theoretical explanation of why in this study the viscosity dissipation can be negligible and heating is not a major challenge in this experimental design.

In this study, the flow from both inlets are provided continuously so the mixing is designed to be in steady-state instead of transient action. The average time to reach a steady-state was around 10 s. All mixing data was collected after this time period. Due to the hardware limitation of the microscopic optics in the authors' laboratory, the characteristic time scale of mixing is not directly observable. On the other hand, the bulk behavior of the mixing can be observed by inspecting the video recordings of the start-up of the acoustic streaming. The flow mixing enhancement by acoustic streaming takes place quickly once the piezo disc is turned on and reach a steady-state in 10 s. The mixing performance of the acoustic streaming was evaluated both by running piezo disc and without piezo disc, then comparing the results with and without acoustic streaming. Figures 8(a) and 8(b) show the temporal frame of the mixing action of the acoustic streaming at t = 0 s (=without piezo disc) and after t = 10 s (=with piezo disc). There was a decrease in the standard deviation of grayscale pixel intensity across the width of the microchannel in the measurement region after t = 10 s compared to t = 0 s. Therefore, the continuous vorticity obtained through acoustic streaming action improved the mixing event.

There are significant differences in the flow patterns near the tee junction region with and without the application of acoustic streaming. The T-microchannel produced almost no Z vorticity within the entire microchannel section and distributed in values between [−2 to 2 (1/s)], and only a small amount of Z vorticity is generated around the two tee microchannel bends and the edges of the microchannel without acoustic streaming. These vortices have been greatly improved by acoustic streaming created around the sharp tip of the triangle, as the velocity components around the entrance junction region increased with oscillation energy compared to other inlets and outlet section of the microchannel. The two side vortices are gradually increased until the triangle tip regions reach its peaks and, then began to fall when forwarded to the microchannel outlet region as seen in Fig. 3. There was a vorticity structure generation up to 60(1/s) peaks due to the application of acoustic streaming at 38 V amplitude and 13 kHz oscillation frequency.

The microchannel entrance region dimension is very small in comparison to the piezo disc diameter (12.7 mm), which is connected to the PDMS microchannel surface. Similarly, there was no fillet on the two bend edge of the microchannel. This resulted in a small revolving stream around the two edges at high amplitudes, as seen in Fig. 6(b), which influenced the creation of exact symmetrical main acoustic streaming vortices around the triangle sharp tip edge region. The parameters such as volume flow rate, oscillation amplitude, operating oscillation frequency, and geometry of the triangle structure as shown in figure Figs. 4, 6, 7, and 9–11 all have an effect on vorticity generation and mixing performance.

The difference between the flow velocity around the tip of the triangular obstruction in the tee-junction region and the flow velocity near the outlet region of the microchannel can be compared by converting to a local Reynolds number defined as

$$R{e}_{tip}={\displaystyle \frac{V\left({\displaystyle \frac{h}{w}}\right)d_h}{v},}$$ (5)

where $d_h$ is the hydraulic diameter, ${\mathrm{d}}_{\mathrm{h}}=4\mathrm{A}/\mathrm{P}$, A is the area, P is the perimeter, V is the local stream velocity magnitude, and v is the kinematic viscosity. The geometrical effect of the triangular obstruction is included by inserting the triangle's height-to-width ratio, $\frac{h}{w}$. The authors adopts this specific definition of characteristic length instead of the tip radius suggested by the reviewer because there is no observable fillet at the tip, and the radius is small and not measurable. Thus, the local Reynold number was defined and estimated using the hydraulic diameter of the microchannel, as well as comparing the geometrical effect by the triangle height-to-width ratio. $R{e}_{tip}\approx 1.77$ at a sharp tip angle of ${22.62}^{°}$, 0.016 μl/min flow rate, and with a oscillation of 13 kHz frequency and 38 V amplitude. Similarly, $R{e}_{tip}\approx 0.36$ along the outlet microchannel in y-direction. As a result, $R{e}_{tip}$ is higher as shown in Fig. 12. This is due to the higher generation of acoustic streaming strength around the triangle edge tip and tee-junction.

FIG. 12.

Velocity estimation around the triangle tip and outlet microchannel in terms of Re.

Acoustic streaming performed much better mixing at 13 kHz operating oscillation frequency and it can be concluded that the increase of volume flow rate and triangle tip edge angle decreased both the acoustic streaming vortices and degree of mixing. On the other hand, the oscillation amplitude has a direct relationship to some of the physical properties, i.e., Z vorticity and degree of mixing. The effect of these parameters have also been reported similarly in another type of microchannel design (Y-shaped) study.²² There was a degree of mixing of 0.62 with their acoustic streaming design input parameter and experimental setup apparatus specifications. In this study, there was a record of the degree of mixing up to 0.769 at a low flow rate. At high flow rates and low oscillation amplitudes, both sides of inlet fluids do not rotate fully at the junction region, due to the fluids passes through near to the tee bend edges. This reduced the Z vorticity generation at the tee junction and also decrease the degree of mixing performance.

V. CONCLUSIONS

In this study, the mixing performance of the T-microchannel was successfully improved by inducing vortices around the tee junction region. The generation of vortices and two side fluids mixing performance in terms of the degree of mixing (M) were characterized by different experimental conditions (with and without acoustic streaming, tip edge angle, oscillation amplitude, and total volume flow rate). Therefore, the following are the main conclusions.

First, regarding the impact of acoustic streaming generation around the entrance tee junction, our study confirms that it is possible to induce vortices and improved the degree of mixing. The Z vorticity is improved above ten times and the degree mixing (M) is improved from M = 0.4017 to 0.769 with 0.008 μl/min flow rate and 38 V amplitude applied at y = 2.15 mm. This indicates the impact of inducing acoustic streaming at the junction region.

Second, acoustic streaming and mixing performance are influenced by different parameters such as flow rate, oscillation amplitude. Higher oscillation amplitudes and low flow rates provided better streaming and effective mixing. In this test conditions, the minimum and maximum amplitude were 9 and 44 V, respectively. The degree of mixing at 0.016 μl/min was also increased from M = 0.394 to M = 0.652 at y = 2.15 mm. When the flow rate increased from 0.008 to 0.2 μl/min at 38 V amplitude the degree of mixing decreased from M = 0.769 to 0.368 at y = 2.15 mm.

Finally, in the case of triangle geometry parameters, the $22{.62}^{°}$ sharp-edge tip generated high Z vorticity and enhanced the degree of mixing M = 0.530 with oscillation amplitude of 38 V and flow rate of 0.016 μl/min at y = 2.15 mm. However, the degree of mixing decreased to M = 0.31 when the sharp-edge increased to ${61.91}^{°}$ with other similar parameters.

To further improve the mixing performance, it might be helpful to increase the width of the microchannel, height of the triangle tip, and making the two edge bends with radial fillets. A complete sweeping of the geometrical parameters along with the height of the triangle would be the next step to further improve the mixing performance supported by acoustic streaming around the entrance junction region, where the impact of the edge bends and fillets are significant on acoustic streaming and mixing results.

DATA AVAILABILITY

The data that support the findings of this study are available from the corresponding author upon reasonable request.