The UIH is a micro-heating method based on the energy conversion from acoustic energy to thermal energy due to viscoelastic damping of ultrasonic SAWs propagating in a viscoelastic material [19]. As shown in Figure 1A, the UIH device is composed of an interdigital transducer (IDT) deposited on a piezoelectric lithium niobate (LiNbO₃) substrate and an ultrasound absorbing layer made of viscoelastic polydimethylsiloxane (PDMS). When an alternating current (AC) signal with the IDT resonant frequency is applied, SAWs are produced from the IDT by the inverse piezoelectric effect and immediately refract into the wave absorbing layer in the form of longitudinal and shear bulk waves. Due to high viscoelastic characteristics of PDMS, the high-frequency mechanical oscillations experience stress-strain hysteresis, causing the wave energy dissipation in the form of heat (thermal energy) [20]. As found in our earlier studies [18, 19, 21, 22] the ultrasound-induced micro-heating method offers rapid, energy-efficient, volumetric heating and 2D spatiotemporal temperature gradient control on the microscale.

In UIH, heat is generated in the viscoelastic layer as the waves are attenuated by viscoelastic damping. In the present study, we further improve the energy efficiency of the UIH by enhancing ultrasound absorption based on a nature-inspired fibrous network embedded in the ultrasound absorbing layer. Moths are one of the main prey of bats which detect their prey or obstacles using ultrasound. The moth has a hairy structure on its wings to hide from the bat’s ultrasound echolocation since the microscale hairs on the moth wings serve as an ultrasound absorber [18, 23]. In analogy to the hairy structure on the moth wing, we have developed an improved UIH method based on a fiber network-embedded viscoelastic wave absorbing layer, as shown in Figure 1A. A thin PDMS membrane was first fabricated by spin-coating of uncured PDMS precursor solution, and then silver nanowires (AgNWs) (Flexiowire2040c, SG Flexio) suspended in isopropanol (IPA) were deposited on the oxygen plasma-treated PDMS membrane by air-brushing to form an AgNW-PDMS composite in a layer-by-layer process (Figure 1C). The AgNWs have 43 ± 5 nm in diameter and 19 ± 5 μm in length. Due to the acoustic impedance mismatch between PDMS and AgNWs, the AgNW fibrous network in PDMS serve as an ultrasound wave scatterer. As a result, the effective wave attenuation length in PDMS is increased due to random wave scattering, and the amount of heat produced in the wave absorbing layer is increased accordingly. The temperature increase (ΔT) in the UIH device heavily depends on the electrical power (P) applied to the IDT to produce SAWs. We measured the temperature increase in the wave absorbing layers made of plain PDMS and the AgNW-PDMS composite using an infrared thermal camera, as shown in Figure 1B. The IDT used in this study had a resonant frequency of 29 MHz for energy-efficient heating [21] and a wave-producing area of 3.1 × 2.6 mm². For the UIH device, the ultrasound absorbing layer made of the AgNW-PDMS composite was found to have a 61.09% improvement in the temperature increase on average at room temperature of 20°C, compared to that made of plain PDMS. Therefore, we confirmed that the nature-inspired ultrasound-absorbing layer made of the AgNW-PDMS composite can improve the energy efficiency of the conventional UIH method.

In sessile droplet-based microfluidics, the surface tension effect is significant. The Marangoni effect can be induced due to the surface tension gradient along with the droplet interface that can be caused by temperature gradient [19] surfactant [24] or solutes [25]. The vapor-mediated solutal Marangoni effect has been widely studied for translocating [26], splitting [27], and mixing [3] sessile droplets. Figure 2A shows a schematic diagram of the vapor-mediated solutal Marangoni effect. A spherical cap-shaped sessile droplet is placed near a capillary tube-based microchannel with one end open toward the droplet. A volatile liquid having a lower surface tension than the sessile droplet liquid, water in this study, flowing in the microchannel is vaporized at the capillary tip and radially diffuses in the direction toward the sessile droplet. As a consequence, the local surface tension gradient is induced along the droplet interface, and this imbalanced surface tension results in Marangoni flows inside of the droplet with a pair of Marangoni vortices. Especially for sessile droplet mixing, the vapor-mediated solutal Marangoni effect has attained much attention since it can be used to control flows inside sessile droplets without temperature increase and chemical contamination of the droplets.

In the present study, we apply the improved UIH heating to accelerate vaporization of volatile liquid used to induce the enhanced solutal Marangoni effect. From the simplified, steady-state Poisson diffusion equation in the spherical coordinates, assuming that the volatile vapor continuously diffuses in the radial direction with the negligible viscous boundary layer effect, the concentration profile of volatile vapor in the air (c _air ) can be expressed as [3, 12, 28], c a i r ( x , y ) = 1 2 c 0 × ( 2 r 0 ) ( d + R − x ) 2 + y 2 (1) where c ₀ is the initial concentration at the microchannel, r ₀ is the radius of a microchannel, d is the distance between microchannel and sessile droplet, and R is the sessile droplet radius. We placed the volatile liquid on one side of the droplet so that the volatile vapor effect region was defined as 0 < x < R and z is 0 attributed to the low-contact angle droplet (h/R < 1, where h is height of the droplet). By rapid solvation at the air-droplet interface, the volatile vapor concentration at the droplet interface was assumed to be the same as the concentration in the air [28]. The concentration profile along with the droplet interface can be estimated as the volatile vapor concentration as, Δ c d r o p l e t = c 0 r 0 ( 1 d − 1 ( d + R ) 2 + R 2 ) (2) where we assumed that the surface tension varied linearly in the low mass fraction regime under the 5% mass fraction [12, 29].

With heating of the volatile liquid, modified vapor concentration (c _0,modified ) as a function of temperature can be theoretically estimated from Dalton’s law and the Antoine equation as, c 0 , m o d i f i e d ( T ) = P v a p P a t m × M V m o l = [ 10 A − B / ( C + T ) / P a t m ] × M V m o l (3) where P _vap is the vapor pressure which is estimated from 10 ^A−B/(C+T), where A, B, and C are component-specific constants of the Antoine equation [3, 30]. P _atm is the atmosphere pressure, M is molecular weight of substance, and V _mol is molar volume. For volatile liquids (ethanol, acetone, and IPA) used in this study, the three constants of the Antoine equation are summarized with their molecular weight in Table 1 [30–32]. The local surface tension difference is consequently estimated as [3], Δ Υ = β Δ c d r o p l e t = β c 0 , m o d i f i e d ( T ) r 0 ( 1 d − 1 ( d + R ) 2 + R 2 ) (4) where β is the proportionality constant of the volatile liquids available in the literature [29, 33]. From this theoretical estimation, we can hypothesize that the surface tension gradient is proportional to the temperature-dependent c _0,modified of the volatile liquid and that the vapor-mediated solutal Marangoni flows can be controlled by the UIH.

Figure 2B indicates the initial vapor concentration at the microchannel (c _0,modified ) as a function of the temperature (T) for three volatile liquids used in this study (acetone, IPA, and ethanol). The theoretical calculation demonstrates that the volatile vapor concentration increases with temperature. Since the increased local vapor concentration is closely related to the increase in the local surface tension gradient along the droplet interface, the vapor-mediated solutal Marangoni flows can be significantly enhanced in the proposed method. For experimental validation, Figure 2C shows the stacked image of 1 μm-diameter particle-laden droplets exposed to the 50°C acetone vapor at the right-most end of the droplet, where symmetrical Marangoni vertical flows can be clearly observed, as predicted. A detailed discussion on the quantitative experimental flow investigation will be provided in the subsequent section.

We conducted quantitative analysis on the heating-mediated enhanced solutal Marangoni effect through theoretical and experimental investigation with PIV. Figure 4 shows the 2D velocity fields of the 2 ± 0.2 μL sessile drop of water/glycerol solution (R = 1.25 mm, h = 0.625 mm, and μ = 1.98 mPa s) locally exposed to vaporized acetone at varying temperature T = 20–60°C with the distance d = 2 mm. The acetone temperature in the 0.5 mm radius microchannel was controlled by UIH. A pair of the solutal Marangoni vortices was observed in all cases, and the solutal Marangoni flow velocity was measured to increase as the temperature of the volatile liquid increased. It was attributed that the increased vapor concentration induced by the increased temperature of the volatile liquid led to the enhanced vapor-mediated solutal Marangoni effect driven by increased local surface tension gradient along the droplet interface.

At a low Reynolds number (Re < 1), the Marangoni force per unit volume is mainly balanced by the viscous force per unit volume in the sessile droplet. The solutal Marangoni flow velocity can be theoretically estimated as [3], V ≈ Δ γ h μ R = β c 0 , m o d i f i e d r 0 h μ R ( 1 d − 1 ( d + R ) 2 + R 2 ) (5)

For investigation on the volatile liquid temperature effect on the solutal Marangoni effect, we performed five repeated experiments at varying volatile liquid temperatures of T = 20, 30, 40, 50, and 60°C for acetone, IPA, and ethanol as volatile liquids for water sessile droplets, while all other parameters (R, h, d, r ₀, and μ) remained the same. Figure 5A shows the maximum solutal Marangoni velocity (V _max) as a function of the temperature of three volatile liquids of acetone (black), IPA (red), and ethanol (blue), which was estimated by the PIV experiments (symbols) and theoretical estimation (solid lines). The error bar represents the standard deviation of the measured values from the repeated experiments. The theoretical estimation was conducted by applying the experimental conditions. Despite the discrepancy between the experimental and theoretical values for V _max, the maximum Marangoni flow velocity was confirmed to monotonically increase by accelerating the vaporization of the volatile liquid with increasing temperature in both all cases. The theoretically estimated V _max slightly deviated from the measured V _max from the PIV experiments can be attributed to the linear surface tension profile assumption, inaccurate measurement of the experimental conditions, and 3D Marangoni vortical flow structure [3, 12, 29].

For quantification of the droplet mixing, we introduced a mixing index defined as [36], M i = 1 C ″ ∑ ( C j − C c ) 2 N (6) where C″ is the mean grey value for the unmixed condition, C _c is the mean grey value for the completely mixed condition, C _j is the grey value in each pixel, and N is the total number of pixels. The normalized mixing index to indicate the index ranging from 0 (unmixed) to 1 (completely mixed) was then expressed as, M i , n o r = 1 − M i − M f M 0 − M f (7) where M ₀ is the mixing index for the initial unmixed case and M _f is the mixing index for the completely mixed case. Figure 5B shows the time (t _m ) required for complete droplet mixing of pure DI water (μ = 1.00 mPa s) in which M _i,nor = 1, driven by the vapor-mediated solutal Marangoni effect at varying the acetone temperature at T = 20–64°C. We used the erioglaucine disodium salt solution in DI water for visualization of the droplet mixing. As shown in Figure 5B, the time required for complete droplet mixing is significantly reduced with increasing temperature of the acetone. Especially at T = 60°C above the acetone boiling temperature, immediate droplet mixing was observed within a second whereas the solutal Marangoni flow-based mixing at room temperature of T = 20°C required more than 47 s for complete mixing. The error bar represents the standard deviation of the measured t _m from the ten repeated experiments, mainly due to somewhat inconsistent injecting location of the dye solution on the sessile droplets.

The time-sequential bright-field images of the droplet mixing of the pure DI water and erioglaucine disodium salt solution in DI water by acetone-mediated solutal Marangoni flow-induced mixing at room temperature (Figure 6A) and at T = 52°C (Figure 6B) were presented. As clearly shown in the figures, the heating-mediated solutal Marangoni flows can significantly enhance the digital microfluidic mixing efficiency. Figure 6C represents the normalized mixing index as a function of time for varying temperatures of T = 20–64°C. In accordance with the theoretical model and experimental data shown in Figure 6B, the time rate of change of the normalized mixing index increased with increasing acetone temperature. From the experiments, we confirmed that the heating-mediated increase in the local vaporized volatile liquid concentration induced enhanced solutal Marangoni effect for rapid digital microfluidic mixing of sessile droplets.

As in Eq. 5, the vapor-mediated solutal Marangoni flow velocity is inversely proportional to the dynamic viscosity of the droplet liquid. As the droplet viscosity is increased, the contribution of the viscous dissipation becomes significant, thereby disturbing the volatile vapor-mediated Marangoni flows formed inside the sessile droplets. Figure 7A shows the 2D velocity fields of the 2 ± 0.2 μL sessile droplet of water/glycerol solution (R = 1.25 mm, h = 0.625 mm, and μ = 3.7 mPa s) locally exposed to vaporized acetone at T = 20°C (left) and 60°C (right) with the distance d = 2 mm. As predicted from the theoretical estimation, the conventional vapor-mediated solutal Marangoni flow-induced mixing method cannot be utilized for the viscous liquid droplets, causing the application of the passive method to be strictly limited to the low-viscosity liquid drop mixing. On the other hand, the heating-mediated enhanced solutal Marangoni flow at T = 60°C can induce the Marangoni flow velocity of higher than 10 mm/s, which was enough to mix the viscous liquid droplets. Various liquids used in sessile droplet-based microfluidics have higher dynamic viscosity such as blood with μ ∼ 3.5 mPa s [37].

For further quantitative analysis, we performed the repeated experiments with varying the dynamic viscosity of μ = 1.78–6.00 mPa s by changing the mixing ratio of the water and glycerol mixture solution [38, 39], as shown in Figure 7B. The solutal Marangoni flow without heating (blue) at room temperature of 20°C, the droplet mixing can be achieved for low-viscosity droplets with μ < 2.5 mPa s. However, this passive method required a comparably long time of approximately 1 min for the complete mixing with M _i,nor = 1 to be used for practical application. Further, for high-viscosity liquid droplets with μ > 3.5 mPa s, the droplet mixing was not achievable by the room-temperature solutal Marangoni effect. On the contrary, the heating-mediated enhanced solutal Marangoni flow can be applied to rapid mixing with t _m < 10 s for low-viscosity droplets with μ < 2.5 mPa s. Even for high-viscosity droplets with μ > 3.5 mPa s, the enhanced solutal Marangoni flow-induced droplet mixing was clearly observed with a relatively increased time required for complete mixing. These results demonstrate the proposed active Marangoni flow-based droplet mixing method outperforms the previous passive method in terms of improved applicability for various kinds of liquids.

As discussed in the theoretical modeling (Eqs. 2, 4, 5), the distance between the sessile droplet and microchannel tip (d) also plays an important role in the vapor-mediated solutal Marangoni flow. Since the vapor concentration profile, surface tension gradient, and the solutal Marangoni flow velocity are heavily dependent on d, we conducted droplet mixing experiments with varying d = 2–6 mm. Figure 8A shows the 2D Marangoni flow velocity fields of the 2 ± 0.2 μL sessile droplet of pure DI water (R = 1.25 mm, h = 0.625 mm, and μ = 1.0 mPa s) locally exposed to vaporized acetone at T = 20°C (left) and 60°C (right) with the distance d = 4 mm. From the theoretical model (Eqs. 2, 4, 5), we could predict that volatile vapor concentration would be decreased as increasing distance d so that the flow velocity also would decrease, leading to increased requiring time for complete droplet mixing. At room temperature, the acetone vapor-mediated solutal Marangoni effect was observed to be negligible, and the droplet mixing was not achieved. On the other hand, at an increased temperature of T = 60°C by UIH, the acetone vapor-mediated solutal Marangoni flow velocity was measured to exceed 10 mm/s, and the complete droplet mixing was achieved within 10 s.

Figure 8B shows the time required for complete droplet mixing (t _m ) with varying d = 2, 3, 4, 5, and 6 mm at T = 20°C (blue) without heating and 60°C (black) by UIH. In compliance with the theoretical prediction, the droplet mixing time required for M _i,nor = 1 increased with increasing d in all cases. For the conditions with d ≤ 3 mm, room-temperature solutal Marangoni effect could be applicable for droplet mixing with t _m < 1 min; however, the droplet mixing cannot be achieved when the sessile droplet was placed far from the volatile liquid with d ≥ 4 mm, the droplet mixing cannot be achieved by the passive solutal Marangoni effect. On the other hand, at increased acetone temperate of T = 60°C with the help of the UIH method, the enhanced solutal Marangoni effect enabled rapid droplet mixing with t _m < 3 s for d ≤ 3 mm. Even with d ≥ 4 mm, the droplet mixing was achieved with t _m < 20 s by the heating-mediated solutal Marangoni effect, which was impossible in the passive method. These results imply that the enhanced solutal Marangoni flow-based mixing method can operate under less strict conditions for the location of the sessile droplets and the volatile liquid vaporization, preventing potential direct contact of the liquids for cross-contamination and improving the stability of the working conditions.