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Sci Rep
Sci Rep
Scientific Reports
2045-2322
Nature Publishing Group UK London

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72089
10.1038/s41598-024-72089-5
Article
Resonant oscillation of droplets under an alternating electric field to enhance solute diffusion
Bono Shinji bono@fc.ritsumei.ac.jp

123
Kinugasa Hiroki 4
Kajita Hiroki 4
Konishi Satoshi 1234
1 https://ror.org/0197nmd03 grid.262576.2 0000 0000 8863 9909 Research Organization of Science and Technology, Ritsumeikan University, Shiga, 525-8577 Japan
2 Ritsumeikan Advanced Research Academy, Kyoto, 604-8502 Japan
3 https://ror.org/0197nmd03 grid.262576.2 0000 0000 8863 9909 Ritsumeikan Global Innovation Research Organization, Ritsumeikan University, Shiga, 525-8577 Japan
4 https://ror.org/0197nmd03 grid.262576.2 0000 0000 8863 9909 Graduate Course of Science and Engineering, Ritsumeikan University, Shiga, 525-8577 Japan
12 9 2024
12 9 2024
2024
14 2132616 5 2024
3 9 2024
© The Author(s) 2024
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
This study investigates a novel microfluidic mixing technique that uses the resonant oscillation of coalescent droplets. During the vertical contact-separation process, solutes are initially separated as a result of the combined effects of diffusion and gravity. We show that the application of alternating current (AC) voltage to microelectrodes below the droplets causes a resonant oscillation, which enhances the even distribution of the solute. The difference in concentration between the top and bottom droplets exhibits frequency dependence and indicates the existence of a particular AC frequency that results in a homogeneous concentration. This frequency corresponds to the resonance frequency of the droplet oscillation that is determined using particle tracking velocimetry. To understand the mixing process, a phenomenological model based on the equilibrium between surface tension, viscosity, and electrostatic force was developed. This model accurately predicted the resonance frequency of droplet flow and was consistent with the experimental results. These results suggest that the resonant oscillation of droplets driven by AC voltage significantly enhances the diffusion of solutes, which is an effective approach to microfluid mixing.

Keywords

Digital microfluidics
Droplet
Electro-wetting on dielectric
Vertical contact-separation process
Particle tracking velocimetry
Wetting pattern
Subject terms

Fluidics
Electronic devices
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pmcIntroduction

Understanding the dependence of concentration is crucial to investigating the impact of reagents on biochemical applications, such as the development of novel drugs and the evaluation of physical properties1,2. Nevertheless, conventional techniques require the preparation of many samples having different concentrations, which results in the waste of materials and the introduction of operational complexity. The application of digital microfluidics (DMF) enables us to manipulate discrete fluids individually. In particular, DMF dealing with droplets decreases reagent volume and simultaneously realizes multiple experimental systems on a chip. In other words, DMF presents a promising approach to conducting high-throughput tests3,4 by modifying liquid samples in the form of droplets5. DMF reduces reaction time and reagent consumption6.

The combination of the wetting pattern (WP) technique and DMF enables the control of single liquid droplets without the need for a binary, incompatible liquid7. A chip with hydrophilic regions arranged in an array and surrounded by hydrophobic material forms a stable array of water droplets8. Droplet-array sandwiching technology (DAST) utilizes opposing droplet arrays to enable a vertical contact-separation process (VCSP), which facilitates target transport. When the WP technique is used, water droplets in an array are independent of each other; thus, they can be regarded as an ideal independent experimental system that is free of contamination from incompatible liquid1,9.

Previous studies have shown that during VCSP, it is possible to transport target particles that are denser than water8,10. This allows for the simultaneous dispensing of solutes into many droplets and supports the use of hanging droplet cell culturing systems. Thus, VCSP is an attractive method for biochemical applications, as it can manage droplets separately, thereby providing a contamination-free experimental environment and making operations such as solute dispensing and cell culturing more efficient11,12.

The force of gravity presents a challenge in transporting solutes upward within the droplets10. If the solutions containing solutes are denser than pure water, the force of gravity causes the solutes to precipitate, which makes it difficult to transport the solutes to the top droplets. Previous studies have investigated the use of a rotational magnetic field to enhance the transport of a solute against gravity13. An external magnetic field induces flow through a micro-rotor, which facilitates viscosity dissipation and improves solute diffusion. However, this method leads to the introduction of impurities and presents difficulties in the consistent application of the magnetic field to all droplets in an array13. Thus, an additional mechanism for designing the appropriate distribution of the magnetic field is needed14.

To address these challenges, electrowetting-on-dielectric (EWOD) was used to enhance the diffusion of solute within the droplets. The control of droplet wettability can be achieved by applying a direct current (DC) voltage to microfabricated electrodes coated with a dielectric material. The incorporation of arrayed electrodes onto a semiconductor is made possible by microelectromechanical systems, which enable the expansion of DC-EWOD into a droplet array15–17.

Previous research effectively transported droplets two-dimensionally using DC-EWOD. It was observed that the resulting flow in a plane achieved a uniform distribution of solute18. The present study modified DC voltage to alternating current (AC) voltage and propose the application of AC-EWOD to prevent VCSP of droplets, which enabled three-dimensional dispersion of solutes. The primary objective was to use AC voltage to periodically modulate the shape of the droplet, induce flow within the droplets and improve dispersion using the oscillatory flow as a mixer. Thus, this study focuses on using AC-EWOD to enhance solute diffusion in droplets, investigating the impact of AC frequency on the extent of diffusion enhancement. Then, we carried out a quantitative analysis of the frequency response of the flow created within the droplets and the concentration difference between the solutes in the top and bottom droplets. The objective of this analysis was to elucidate the role of AC-EWOD in facilitating the movement of solutes against the force of gravity.

Results

We investigated the impact of droplet oscillation on solute diffusion in coalescent droplets using AC-EWOD. Figure 1a depicts solute diffusion during the VCSP of droplets. We formed droplets consisting of 4 μL of water on the topmost WP substrates. The hydrophilic region R has a circular shape and a radius of 1.24 mm. A split-patterned electrode was integrated into the WP substrates; this was followed by the fabrication of AC-EWOD substrates. A water solution was prepared from 4 μL of a solution containing a solute (Rhodamine B) with an initial condition of 0.0125 wt.%. Thin Cr/Au films were used to fabricate the split-patterned electrodes. However, due to the high specific gravity of the solute solution relative to pure water, precipitation occurred quite often13.Fig. 1 Solute diffusion of droplets during VCSP and oscillation of the AC-EWOD-driven coalescent droplet. (a) Schematics of the VCSP of droplets. During contact, the coalescent droplet was oscillated by applying AC voltage to the AC-EWOD substrate. (b) A perspective image of the coalescent droplet between the WP and the AC-EWOD substrates with AC voltage (Supplementary Video 1).

A z-axis stage was used to secure the WP substrate, and the WP and AC-EWOD substrates were positioned such that the droplets at the top and bottom were opposite each other. Next, the distance between the top and bottom substrates (D) brought the top and bottom droplets in contact with each other. When D decreased to less than the diameter of droplet 2R, the top droplet came into contact with the bottom droplet. Subsequently, D was shortened to ∼43R∼1.65mm so that the shape of the coalescent droplet became approximately cylindrical. AC voltage was applied to the microfabricated electrodes for 30 s immediately subsequent to contact. The amplitude and the waveshape of the AC voltage were 80 V and sinusoidal, respectively. A visual representation of the coalescent droplet under AC voltage is presented in Fig. 1b, demonstrating that the droplet oscillates at the same frequency as the applied voltage. The Supplementary Video 1(a) and Supplementary Video 1(b), show behavior of the coalescent droplet when subjected to AC voltage at 1 Hz and 50 Hz, respectively. This result indicates the ability of the AC-EWOD to induce fluid motion within the coalescent droplet.

The coalescent droplet was isolated by raising the top WP substrate. A circular hydrophilic material (fibronectin) with a radius of ~ 1 mm was patterned to prevent droplet oscillation and to maintain a droplet on the bottom of the AC-EWOD substrate after VCSP. It was verified that red droplets remained on both the WP and AC-EWOD substrates after VCSP, which suggested that solutes initially introduced in the bottom droplet diffused upward against gravity.

As an indicator for evaluating the solute diffusion, we focused on comparing the concentration in the top and bottom droplets after VCSP. Uniform solute distribution indicates effective diffusion, whereas gravity tends toward heterogeneity. Thus, if gravity is dominant, the solute concentration in the top droplets should be less than that in the bottom droplets.

To quantitatively evaluate the concentration solute, droplets remaining on the top and bottom substrates after VCSP were collected, and their absorbance was analyzed using a spectrophotometer to estimate the solute concentration based on the Beer–Lambert law19,20. Figure 2 shows the relationship between the frequency (f) of the AC voltage and the solute concentration after VCSP. The solute concentrations in the top and bottom droplets are denoted as Ct and Cb, respectively.Fig. 2 Frequency response of the solute concentration in the top and the bottom droplets.

Ct is much less than Cb in the low f range (< 10 Hz), despite the presence of solutes in the top droplet. The solutes precipitate downward, which suggests that gravity dominates over solute diffusion. However, at ~ 50 Hz, the solute concentration in the top droplet is almost equal to that in the bottom droplet (Ct ~ Cb). This result suggests that the concentration distribution of the solutes in the coalescent droplet becomes uniform because of the AC-EWOD-enhanced diffusion. Furthermore, a higher frequency increases the difference in concentration (Ct < Cb). This suggests that the increase in diffusion is due to the inadequate flow generated by AC-EWOD, which fails achieve a uniform distribution of solute concentration. This is because the droplets are unable to adhere to AC-EWOD at the higher frequency (~ 500 Hz). Thus, the gravity effect again becomes the dominant in the solute diffusion, which causes the solutes to precipitate.

It was reported that the mechanism of AC-EWOD at high frequency; AC-EWOD at 10–1000 kHz generates Joule heat and serves as a heater21. In L-DEP, hydrodynamic flow is generated owing to the coupling between heat and flow. In this study, we used the AC-EWOD technique to modulate droplet shape, rather than heating. Thus, we exclude any discussion on high frequency region and establish a maximum limit of 500 Hz.

Next, we investigated the droplet flow mechanism using particle tracking velocimetry (PTV) to determine the optimal solute diffusion at a specific f22–27. Figure 3a presents the experimental setup, which included introducing 4-μm silica colloids to water droplets for visualization. Subsequently, colloidal positions were monitored using an optical microscope while applying an AC voltage to split-patterned electrodes. The focus and observation area of the microscope were adjusted to 0.1 mm above the bottom AC-EWOD substrate and in close proximity to the center of the split-patterned electrodes, respectively. AC-EWOD during PTV did not require a fibronectin film, hence separating the coalescent droplets in not necessary.Fig. 3 Optical microscopic observation of colloidal dispersion in the coalescent droplets for PTV. (a) Schematic representation of experimental systems. (b) Micrographs of colloids in the coalescent droplet. Red circles mark the positions of colloids in the absence of voltage (V ~ 0 V). Yellow circles highlight the positions of colloids with positive or negative voltages. The displacements of colloids from their initial positions are denoted by white arrows.

Figure 3b shows the results for f = 1 Hz (Supplementary Video 2). The position of the colloids in the central image, as denoted by the red circles, corresponds to the absence of applied voltage. The images on the left and right show the results for positive and negative voltages, respectively. The white arrows originating from the red and yellow circles show that the colloids disperse and oscillate when AC voltage is applied, indicating flow creation by AC-EWOD, the frequency of colloidal oscillation is proportional to f.

The time evolution of the colloidal position is crucial for evaluating flow. However, the speed of colloids is too fast to track the positions of the colloids at any given time, particularly at high-f region. The amplitude of the colloidal oscillation (A) was used to quantitatively evaluate flow. A higher A value indicates that AC-EWOD generates a greater flow in droplets. In this investigation, A was utilized as an indication to quantify flow.

Figure 4 displays the frequency response of A to colloidal oscillation within the coalescent droplet. The upper limit of f was set to 200 Hz due to constraints on the resolution of the optical microscope; when f increases from 1 Hz, A decreases. A exhibit a local peak at ~ 50 Hz, which converges to zero as f increases; this suggests that the resonant behavior in the oscillation of the coalescent droplet is driven by AC-EWOD.Fig. 4 Frequency response of A to colloidal oscillation in the coalescent droplet. The dashed line is a uniform curve that serves to guide the eye.

Discussion

The resonant behavior of the coalescent droplet under AC-EWOD is examined, beginning with the equation of motion (EOM). The geometry of our theoretical model is presented in Fig. 5. The total mass of the top and bottom droplets is expressed as m=ρ2V0=43πρR3, where V0 and ρ are the initial volume of a droplet (~ 4 μL) and the water density, respectively. The EOM of the horizontal displacement of the center of gravity of the coalescent droplet x is shown in Eq. (1).1 mx¨=Fa-l+Fvis+FE,

where Fa−l, Fvis, and FE represent the surface tension at the air–liquid interface, the viscous force, and the electrostatic force, respectively.Fig. 5 Geometry of our phenomenological model of droplets driven by AC-EWOD.

In deriving Fa-l, the surface area of the air–liquid interface is first examined11,12. The deformation of the droplet shape leads to an increase in the surface area at the air–liquid interface, ΔS= 2πRD2+ 4x2tD, as shown in Fig. 5. Thus, the increase in surface energy due to the deformation is written as γ∆S = 2πγR{D + 2x2/D−O(x4)}, where x is an infinitesimal quantity, and the fourth and higher terms are disregarded. Fa- l=-∂∂xγΔS=-6πγx is proportional to x; therefore, the surface tension can be regarded as a linear spring that induces deformation in the droplet.

Next, let us consider the velocity gradient in the coalescent droplet in determining Fvis. When the velocity of x˙ is small, a linear flow with a gradient of 2x˙/D is generated in the coalescent droplet. As the viscous force is proportional to the gradient, Fvis=-μ2x˙DπR2=-32πμRx˙, where μ is the viscosity of water, Fvis is proportional to x˙ and can be regarded as a dashpot for droplet deformation.

On AC-EWOD electrodes, a periodic electrostatic force having an angular frequency of ω = 2πf is applied to the coalescent droplet. In this model, FE is phenomenologically defined as FE=F0cosωt, where the parameter F0 depends on the physical properties of the insulating layer and the ionic impurities.

Substituting Fa-l, Fvis, and FE into Eq. (1), the EOM of x can be calculated as follows:2 x¨+μ¯x˙+ω02x=f0cos(ωt),

where we denote μ¯=316μρR2, ω0=32γρR3, and f0=38πF0ρR3. The oscillation of the coalescent droplet under AC voltage is comparable to an oscillation induced by a force in a viscous solvent. The solution to Eq. (2) can be calculated independently of an initial condition, assuming a steady state. Using the phase delay φ, we obtain the steady state solution of Eq. (2) x = A cos(ωt−φ), where A is given as3 A=f0ω02tω22+μ¯2ω2.

A has a local maximum at ωM=ω02μ¯2. By substituting water-related material parameters (ρ = 997 kg m−3, γ = 72.75 mN m−1, and μ = 1.0 mPa s), it was found that ωM ~ 400 rad s−1, which corresponds to the resonance frequency fM ~ 60 Hz28. Thus, the proposed theoretical model predicts the resonant oscillation of the coalescent droplet due to AC-EWOD.

This section examines the correlation between the theoretical value of A, the experimental value of A, and the difference in concentration. The process of transporting solutes with high specific gravity upwards to achieve uniform concentration distribution increases the potential energy U and mixing entropy Smix. In the absence of the flow in the droplet, the solutes disperse such that the contribution of gravity to free energy in the system is (U − TSmix, where T is temperature) is balanced by the mixing. However, the presence of a velocity gradient along the z-axis induces mixing entropy, which enhances uniform distribution of the solutes. Previously, we generated rotating flow in-plane using a microrotor inserted within a droplet and reported faster rotational flow, for diffusion enhancement13. In this study, AC-EWOD was used to generate oscillatory flow in droplets. Based on previous analogy, we observed that a larger A creates a larger velocity gradient along the z-axis, resulting increased mixing entropy. Thus, the velocity amplitude Af (∝ Aω) is crucial for solute diffusion in droplet.

In Fig. 6, a summary of the Af values observed theoretically and experimentally is presented. In theory, f0 was considered to be a fitting parameter (f0 = 8.7 × 102 mm s−2). As shown in Eq. (3), the resonance frequency is not dependent on f0; both the experimental and theoretical Af values display resonant behavior, and their resonance frequencies are in agreement (fM ~ 50 Hz).Fig. 6 Frequency response by Af obtained from both experimental and theoretical models. We superimposed the dependence of ∆C on f.

To compare the frequency responses of Af and ∆C =Ct  – Cb, we superimposed the experimental result for ∆C on Fig. 6. A ∆C ~ 0 wt.% corresponds to the uniform distribution of solutes in the coalescent droplet. A decrease in ∆C results in an increase in solute heterogeneity. The frequency response of ∆C exhibits a local maximum with a frequency that aligns with the resonance frequency of Af. These results suggest that the flow is efficiently driven by the resonant oscillation of the droplet, which enhances the diffusion of solutes and ultimately leads to the uniform distribution of solutes.

Materials and methods

Integration of wetting pattern substrates and split-patterned electrodes

Figure 7a,b show the top view of the AC-EWOD electrodes and the α−α’ cross section of the AC-EWOD substrates. First, the Cr and Au layers, with thicknesses of 50 and 200 nm, respectively, were deposited on a glass substrate using a thermal evaporation process. Subsequently, a photoresist (OFPR-800LB, Tokyo Ohka Kogyo Co.) is spin-coated onto a Cr/Au thin film and patterned using photolithography. Using the wet-etching technique, a section of the Cr/Au thin film was partially removed. The diameter of the circular electrodes and the distance between the electrodes were set to 5 mm and 100 μm, respectively. This study involved the simultaneous patterning of six pairs of electrodes on a substrate for application to a droplet array. Afterward, the photoresist was removed with acetone. To create an insulating film (Parylene-C, Specialty Coating Systems™) with a thickness of 1.5 μm, chemical vapor deposition was employed. The insulation film was spin-coated with hydrophobic material (CYTOP™, AGC) and the substrate was annealed at 200 °C for 60 min. Hydrophilic regions were created by applying a 1 μL fibronectin water solution containing 30 μg mL−1 to the substrate and leaving it in an incubator for 180 min to ensure complete drying. After it was washed to remove residual solution, the dried fibronectin film presented a diameter of 1 mm and was finally annealed at 110 °C for 60 min.Fig. 7 The AC-EWOD substrate and the WP substrate. (a) Top-view image and (b) schematic α−α’ cross section of the AC-EWOD substrate. (c) Schematic cross section of the WP substrate.

Transparent WP substrates were fabricated according to a previous report11. Figure 7c shows a schematic cross section of the WP substrate. On this substrate, TiO2 and CYTOP™ were used as the hydrophilic and hydrophobic materials, respectively. Circular hydrophilic regions having a radius of 1.24 mm were generated, which enabled the spontaneous formation of a hemispherical droplet when 4 μL of water was added to the hydrophilic region.

Spectroscopy for measurement of solute concentration

To determine the solute concentration, a microvolume UV–Vis microphotometer (Nano Drop One, Thermo Fisher Scientific Inc.) was used. Red dye (Rhodamine B, TCI) was employed as the “solute” in the study. Prior to measurement, a calibration curve was established by analyzing the correlation between the absorbance and the concentration of the bulk water solution containing Rhodamine B. Through this calibration, we confirmed the linear relation between the solute concentration and the absorbance. The coefficient for the proportion of absorbance to solute concentration at a wavelength of 400 nm was 5.7 × 10 wt.%−1.

Optical microscopy for PTV

A connection between AC-EWOD electrodes and a waveform generator (33210A, Keysight) was established using a high-speed bipolar amplifier (HSA4052, NF). To visualize the flow within the droplets, silica colloids (Micropearl SP-204, Sekisui Chemical Co., Ltd.) having a diameter of 4 μm were added to the droplets. The substrates were positioned on the microscope (MX9430, Meiji Techno) and a charge coupled device camera (DFK23UP031, The Imaging Source) was used to capture the motion.

Conclusion

In this study, AC-EWOD was used to induce resonant oscillation in coalescent droplets, which resulted in enhanced solute diffusion against gravity. The frequency response of ∆C was investigated to quantitatively evaluate the diffusion. The results showed that the oscillation of the coalescent droplet enhanced the solute diffusion, and the degree of enhancement varied with the frequency of the AC voltage. In particular, the specific frequency at which the solute showed uniform distribution in a droplet was determined. The experimental analysis of coalescent droplet flow using PTV validated the presence of resonant characteristics, as the resonance frequency was in agreement with the theoretical prediction. Our phenomenological model provides a qualitative prediction of the concentration difference between the top and bottom droplets. Previously, simulation techniques for calculating hydrodynamic flow in related fields were reported21,29. In future research, applying the previous technique to our system technique could facilitate the accurate prediction of the difference in concentration between the top and bottom droplets.

Furthermore, the alignment of the frequency at which ∆C ~ 0 wt.% occurs signified that a uniform distribution of solutes in the coalescent droplet could be achieved by droplet oscillation efficiently driven by AC-EWOD.

In this study, we proposed the dynamic control, using the AC voltage frequency, of solute amounts transported upward. The use of arrayed electrodes enables the expansion of the VCSP mechanism to DAST. Therefore, the precise modulation of the concentration of solutes within a droplet array is also possible via the selective control of the AC voltage frequency across a pair of electrodes. The use of AC-EWOD in the proposed concentration control method exhibits potential for accurately dispensing solutions in the droplet arrays, thereby presenting viable opportunities for implantation in high-throughput biochemical assays.

Supplementary Information

Supplementary Video 1.

Supplementary Video 2.

Supplementary Video 3.

Supplementary Information 1.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-024-72089-5.

Acknowledgements

This work was partially supported by Ritsumeikan Advanced Research Academy (RARA) and Ritsumeikan Global Innovation Research Organization (R-GIRO).

Author contributions

S.B., H.K., and S.K. conceived of direction of this research. All the authors conducted the experimental results. All the authors approved the final manuscript.

Data availability

All data analyzed during this study are included in this published article and its supplementary files.

Competing interests

The authors declare no competing interests.

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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