Study on the size and spatial configuration of liquid metal droplets in conductive hydrogels induced by surface acoustic waves

Abstract

Conductive hydrogels based on liquid metal microdroplets are widely used as wearable electronic devices. Droplet uniformity affects sensor sensitivity for weak signals, such as heart rate and pulse rate. Surface acoustic waves at micrometer wavelengths allow precise control of a single droplet, and have the potential to make uniformly discrete liquid metal droplets and distribute them in hydrogels. But the control law of liquid metal droplet size and its spatial configuration by acoustic surface waves is not clear. The aim of this paper is to present an analysis of the acoustic regulation mechanism in the interfacial evolution of fluids with high interfacial tension coefficients, and to investigate the influence of microdroplet generation characteristics (size and spacing) on the conductive and mechanical properties of conductive hydrogels. The results showed that the combined action of acoustic radiation force, shear force and pressure difference force helped to overcome interfacial tension and speed up the interfacial necking process during the filling and squeezing stages. The use of acoustic surface waves serves to diminish the influence of droplet size on the two-phase flow rate. This provides an effective approach for achieving decoupled control of microdroplet size and spacing, alongside the formation of a homogenous array of liquid metal droplets. The acoustic surface wave effect makes the liquid metal microdroplets more uniform in size and spacing. As the liquid metal content relative to the hydrogel substrate solution increases, the liquid metal size decreases. The hydrogel's initial conductivity and conductivity after self-healing increase by 10% and 25%, respectively, which can realize the effective monitoring of ECG and EMG signals. This study helps to reveal the evolution mechanism of liquid-metal interfaces induced by acoustic surface waves, elucidate the effects of microdroplet size and spacing on the conductive and mechanical properties of hydrogels, and provide theoretical guidance for the high-precision preparation of wearable electronic devices.

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1 Introduction

Wearable electronics offer a valuable means of disease prevention, monitoring and treatment through the real-time monitoring of physiological signals, including heart rate, blood pressure, and blood glucose.^1,2 Liquid metals with fluidity and high electrical conductivity, combined with polymer materials with elasticity and good flexibility, form flexible sensors that have gained widespread attention in areas such as health detection and electronic skin.^3–6 When the liquid metal is in the form of microdroplets dispersed in the hydrogel, it can be deformed synergistically, thereby enhancing the toughness and deformability of the hydrogel.^7,8 Liquid metal conductive hydrogels are a common means of monitoring health data, including human movement, electrocardiogram (ECG) signals, and electromyogram (EMG) signals.^9–15 The uniform dispersion of small-sized liquid metal droplets in hydrogels has the potential to form a complete conductive network, which could significantly enhance the conductivity of hydrogels and the stability of electrical signal transmission. This is of paramount importance for the effective monitoring of weak physiological signals.

Conducting hydrogels are typically prepared through the random dispersion of liquid metals in a gel base solution via ultrasonic oscillation,^16–18 mechanical stirring,¹⁹ and rotational shearing.²⁰ Macroscopic ultrasonication is more suitable for micro- and nanoscale liquid metal droplet preparation. However, it is a time-consuming process to break the droplets,²¹ and there is a risk of damaging the container as a result of the accumulation of heat in high viscosity polymer solutions. In addition, the conductivity of the hydrogel strongly depends on high temperature or mechanical sintering and annealing technologies, which will form a random conductive path through the aggregation and fusion of liquid metal.²² In the process of mass production, the conductivity and stability of the device show high randomness. In order to improve the integrity and reliability of the conductive network in the hydrogel, the precise control of the size and spatial distribution of liquid metal droplets needs to be solved urgently.

Conventional passive microfluidic allows the adjustable modulation of bubble droplet configuration in hydrogels through the control of two-phase flow and fluid physical parameters, representing a novel solution for the stable preparation of hydrogels.²³ The high interfacial tension coefficient of liquid metal and its distinctive characteristics of non-hydrophilic and non-lipophilic properties present a significant challenge in controlling droplet size and homogeneity using traditional microfluidic technology.²⁴ Therefore, it is necessary to introduce an external force field into the two-phase flow system to improve the stability of the generation and manipulation of liquid metal droplets.^25,26

Surface acoustic waves possess the advantages of non-contact and energy concentration.^27–31 The acoustic radiation force exerted on the interface between two phases can directly deform the interface.³² Concurrently, the acoustic streaming effect within the fluid can alter the local channel pressure and two-phase flow.^33–35 Acoustofluidics enhances the precision and reproducibility of controlling liquid metal droplets.³⁶ It's an effective solution for stable, controlled production of high-performance hydrogels. However, the precise regulatory mechanism underlying the generation of liquid metal droplets by acoustic surface waves remains uncertain. Furthermore, the potential effects of droplet generation size and spacing on the conductivity and mechanical properties of hydrogels warrant additional investigation.

To fabricate high-performance hydrogels with liquid metal microdroplets as conductive functional materials, a comprehensive investigation of the physical mechanism underlying the necking and fracture process at the liquid metal interface under the influence of an acoustic field is imperative. To enable the customization of the size of metal microdroplets and ensure their precise spatial distribution within the hydrogel. This paper presents an in-depth investigation of the force state of the liquid metal interface induced by the traveling acoustic wave. Additionally, it analyzes the regulatory mechanism of the acoustic and flow conditions that influence the generation state of microdroplets. Furthermore, a prediction model for droplet size is derived, and the impact of droplet size and spacing on the conductivity and mechanical properties of the hydrogel is investigated. The findings of this study offer a theoretical foundation for the batch-controlled preparation of wearable electronic devices.

2 Research methodology and modeling

The controlled distribution of liquid metal droplets in hydrogels creates a stable, responsive network that responds to weak physiological signals. To address the issue of non-uniformity in liquid metal droplet size, this paper proposes utilizing acoustic surface waves in a two-phase flow system, as illustrated in Fig. 1. This study establishes a force model for the liquid metal interface by comparing the evolution law of the interface induced by the acoustic waves. The key parameters affecting the size and spacing of liquid metal droplets are determined. Subsequently, the mixed solution of PVA with discrete liquid metal droplets was gelated. The conductivity and mechanical properties of the hydrogels under different preparation processes were compared to determine the optimal reparation method.

Fig. 1 Schematic diagram of the experimental setup. (a) Geometric diagram of the channel for preparing liquid metal droplets. (b) Vertical cross-section diagram of the channel.

2.1 Experimental methods

(1) Liquid metal microdroplet preparation and observation methods. The uniformity of the distribution of liquid metal droplets in the PVA solution is contingent upon the stability of the microdroplet generation state and the sphericity of the droplets. Fig. 2 illustrates the surface acoustic wave-based liquid metal droplet formation device. In this study, a square cross-section with a depth-to-width ratio of 0.75 was employed to mitigate the asymmetric squeezing effect of the channel wall on the droplets and to facilitate the formation of liquid metal droplets with enhanced sphericity. T-channels with neck structure have been implemented, and localized contraction and expansion of the channel width is employed to enhance the shear and squeezing effects, thereby reducing the microdroplet size. Furthermore, the rapid release of microchannel pressure facilitates improved generation stability. The microchannels were manufactured using polydimethylsiloxane (PDMS) via the standard photolithography process. The substructure was constructed with a 20 μm thick rigid PDMS film to enable reusability of the channel and the SAW device (see details Note S1, ESI†).

Fig. 2 Preparation steps of the liquid metal droplet–PVA hydrogel.

The continuous phase adopts a 20 wt% PVA aqueous solution with a viscosity of 220.5 mPa s. The dispersed phase adopts eutectic gallium indium with a viscosity of 1.99 mPa s. The interfacial tension coefficient of the two-phase fluid is γ = 530 mN m⁻¹. To solve the problem of uneven distribution of interfacial tension coefficient caused by liquid metal oxidation, resulting in interface distortion and device insulation,³⁷ this paper reserves 2 mL of NaOH aqueous solution in a 10 mL dispersed phase needle tube. The flow rate range of continuous phase flow Q_c and dispersed phase flow Q_d is controlled between 10 and 80 μL min⁻¹.

The acoustic surface wave device consists of two parts: a piezoelectric substrate and a fork-finger transducer. The interdigital transducer (IDT) is fabricated on a 128°Y–X lithium niobate (LiNbO₃) piezoelectric substrate through a series of processes such as evaporation, coating, photolithography, and etching. In order to improve the conductivity of the electrode and the adhesion between the electrode and the piezoelectric substrate, a 10 nm thick chromium layer was deposited before depositing a 100 nm thick gold nanolayer. The focused IDT contains 24 pairs of fork-finger structures with a finger width and spacing of 48.75 μm, and the resonant frequency is 19.5 MHz. The experimental apparatus and data processing procedures are detailed in Note S2 of the ESI.†

(2) Conductive hydrogel preparation method. Liquid metal droplet conductive hydrogels are usually dispersed using ultrasonic oscillation, but it is difficult to control the size of the microdroplets. In this study, acoustofluidics was used to disperse the liquid metal in the form of droplets into a 20 wt% PVA aqueous solution. The generated liquid metal droplets were tightly aligned by self-assembly in the hydrogel mold. After evacuating treatment, borax solution spraying, freeze–thaw cycle treatment and dehydration treatment, hydrogels with good electrical conductivity and mechanical properties were formed. As shown in Fig. 2, the detailed steps of hydrogel preparation are described in ESI† S3.

PVA contains a large number of carboxyl groups, and the tetraborate ions in the borax solution will combine with the carboxyl groups on the PVA molecular chain to form borate bonds, forming the first layer of the chemical cross-linking network. At the same time after the hydrogel has been processed by freeze–thaw cycles, the hydrogen bonds between the carboxyl groups on the PVA molecular chain form crystalline regions, which in turn form a second layer of physically cross-linked network. The strength and stability of the hydrogels were improved under both crosslinked networks.

Conductive hydrogels prepared by traditional stirring or ultrasonic methods usually require high temperature or mechanical sintering and annealing to achieve droplet fusion and eliminate the insulation effect of the oxide layer due to the dispersed and random spatial distribution of liquid metal. However, the conductivity of the device depends on the aggregation degree of the droplets. It has been proposed to use gravity sedimentation to induce liquid metal to accumulate at the bottom of the gel to achieve self-sedimentation.⁹ Compared with traditional ultrasound and stirring methods, this study utilizes acoustofluidics to improve the uniformity of liquid metal droplet size. Under isotropic interaction forces, droplets self-assemble into a hexagonal tight arrangement, reducing the randomness of droplet spatial distribution and improving droplet aggregation density and compactness. After the freezing–thaw cycle, the hydrogel is dried and dehydrated for a long time, the volume of hydrogel is significantly reduced due to water loss, and the conductive path is formed between liquid metals through extrusion and fusion.

When the traditional droplet microfluidics is applied to the preparation of the hydrogel, the droplet size is adjusted by the two-phase flow ratio, and there is a coupling mechanism between the droplet size and spacing affected by the continuous phase flow rate, resulting in the large spacing of small droplets. As an auxiliary adjustment method, acoustofluidics can realize decoupling control of droplet size and spacing, which improves the problem of the proportion of the liquid metal to hydrogel matrix solution being difficult to control in traditional microfluidic technology.

2.2 Numerical modelling and method validation

Since it is difficult to accurately extract the distribution of the flow and pressure fields during the microdroplet generation process in the experiments, this paper adopts the same microchannel structure and two-phase flow parameters as in the experiments, and uses the COMSOL software to carry out a two-dimensional simulation of the liquid metal microdroplet generation process without acoustic influence. Laminar flow and phase field module models are selected for iterative calculations based on a pressure–velocity coupled solver. The inlet types of both continuous and dispersed phases are velocity inlet, the flow rate of the continuous phase is Q_c = 20 μl min⁻¹, and the flow rate of the dispersed phase is Q_d = 10 μl min⁻¹. The outlet pressure is standard atmospheric pressure. It is assumed that there is no wall slip and both fluids are incompressible. Non-wetted wall boundary conditions were used with a wall contact angle of 185° and a time step of 10⁻⁵ s.

3 Results and discussion

Unlike the traditional aqueous–oil system where there are multiple regimes of droplet generation, the liquid metal has a single regime of droplet generation in T-channels with a neck structure due to its high interfacial tension coefficient. As shown in Fig. 3, under different flow and acoustic conditions, the liquid metal completely blocks the neck structure, resulting in direct breakup in the squeezing regime and generating droplets in the area near the neck structure. When liquid metal droplets are applied to the preparation of flexible circuits, the circuit forming accuracy depends on the liquid metal droplet size. The circuit conductivity depends on the effective contact between the droplets, and the reduction of the spacing between the droplets helps to improve the circuit conductivity. In order to achieve effective control of droplet size and spacing, this section will undertake a detailed analysis of the evolutionary characteristics of the liquid-metal interface and further investigate the regulatory mechanism of the acoustic waves on droplet generation.

Fig. 3 Image of the droplet generation experiment and division of generation stages. (a) Experimental images of liquid metal droplet generation under different continuous phase flow rates and acoustic input powers. (b) Evolution curves of neck width at the generation stage under different flow rates. (b1–b5) Numerical simulation results of the phase interface during droplet generation at each critical moment.

3.1 Mechanical modelling

(1) Microdroplet generation stage. Liquid metal droplet generation in T-channels with a neck structure can be divided into three stages: filling, squeezing and breakup. The variation rule of dispersed-phase neck width l_b with time t can reflect the expansion and contraction state of the interface. We define the initial moment of droplet generation as t = 0 and the period of droplet generation as T_max, and use the ratio between the two to make the time dimensionless in order to cross-compare the time course t* = t/T_max. The numerical simulation results of liquid metal droplet generation without acoustic induction are shown in Fig. 3(b).

The conclusion of the dispersed-phase interface demonstrates a gradual expansion throughout the filling stage, accompanied by a corresponding increase in l_b/w_c, which reaches a maximum value at the end of the filling stage. When the tip of the dispersed phase starts to migrate towards the neck structure, the microdroplet generation enters the squeezing stage, in which the neck width l_b/w_c tends to decrease. When the contraction rate of the microdroplet neck undergoes an abrupt change and accelerates significantly, it corresponds to the breakup stage.

(2) Stress model. The two-phase interface induced by the acoustic waves is subjected to inertial force, shear forces, differential pressure, interfacial tension and acoustic radiation forces. In the state where the inlet flow is continuously passed through, the inertial force stretches the dispersed-phase interface downstream. In order to comparatively analyse the effects of different acoustic intensities on droplet generation, the dispersed-phase flow rate was kept unchanged at 10 μL min⁻¹ in this study to control the variables. The shear stress originates from the internal friction effect in viscous flow. Previous studies have found that the acoustic streaming effect is weaker than the acoustic radiation force effect in the process of acoustic surface wave-induced deformation of the two-phase interface.^28,31 According to Newton's law of internal friction, the dispersed-phase interface is subjected to shear force estimated by:

F_τ = μ_c(du/dy)A_τ (1)

Among them, μ_c is the viscosity of the continuous phase, du/dy is the velocity gradient near the two phase interface, and A_τ is the area affected by shear force. The velocity gradient is obtained through numerical simulation, and A_τ can be estimated by multiplying the channel height h by the length of the shear force application area l_τ:

A_τ = hl_τ (2)

In the equation, l_τ is the length of the shear force acting along the axial direction. The pressure difference originates from the pressure drop on both sides of the fluid interface. The pressure difference force F_R caused by the resistance of the dispersed phase tip interface to the continuous phase flow can be estimated by simulating the pressure difference ΔP between the upstream and downstream of the droplet:

F_R = ΔPbh (3)

ΔP is the pressure difference, and b is the width of the dispersed phase tip interface. The interfacial tension originates from the uneven van der Waals forces between molecules on both sides of the interface. The curvature of the two-phase interface leads to the product of the internal and external pressure difference and the projected area of the interface, which can be used to estimate the interfacial tension:

F_γ = γ(1/R_a + 1/R_r)A_R (4)

γ is the interfacial tension coefficient, R_a is the axial curvature radius of the three-dimensional interface, R_r is the radial curvature radius of the three-dimensional interface, and A_R is the area of interfacial tension. When a surface acoustic wave acts on the two-phase interface, the acoustic radiation force F_AR acting perpendicular to the direction of acoustic wave propagation can accelerate interface breakup. Its estimation equation can be written as:

Among them, E_c and E_d represent the energy density of plane asymptotic waves in the continuous and dispersed phases, respectively. ρ_c and ρ_d are the fluid densities of the continuous and dispersed phases. c_c and c_d correspond to the propagation velocities of acoustic waves in the continuous and dispersed phases. P₀ is the acoustic pressure intensity. The surface acoustic wave used in this paper corresponds to acoustic pressure P₀ in the range of 2–8 MPa at different input powers,²⁸ and the acoustic radiation force F_AR increases continuously with the increase of input power.

(2) Mechanisms of action of the acoustic waves. To analyse the acoustic mechanism, this section simulates the generation of liquid metal microdroplets to identify the dominant force. The two-phase flow and pressure fields for varying continuous-phase flow rates are presented in Fig. 4. In the squeezing stage, the liquid-metal interface will completely block the neck structure due to the high interfacial tension coefficient, as shown in Fig. 4(a1–a3), and there is an obvious reflux vortex in the flow field upstream of the neck structure, which indicates that the resistance to continuous-phase flow is increased. According to the velocity gradient, the velocity gradient near the interface in the filling stage is about 213.31 s⁻¹, and as the dispersed phase blocks the neck structure, the reflux flow leads to a increase in the velocity gradient, and the corresponding velocity gradients at the moments of t* = 0.5 and 0.847 are 431.56 and 918.93 s⁻¹, respectively. Therefore, the continuous phase in the squeezing stage not only exerts squeezing pressure on the interface by the stacking upstream, but also enhances the shear force on the interface.

Fig. 4 Cloud map of flow and pressure field at different stages of liquid metal droplet generation under different flow conditions. (a1–a3) Flow field. (b1–b3) Pressure field.

The pressure at the tip of the dispersed phase shows an evolutionary pattern of increasing and then decreasing during a microdroplet generation period. As shown in Fig. 4(b1–b3), the dispersed-phase interface continuously extends downstream of the neck structure during the squeezing stage, and the continuous-phase pressure tends to gradually increase until the continuous-phase pressure is instantaneously released after the breakup. As the continuous phase flow rate increases, the pressure at the tip of the dispersed phase gradually increases with the continuous phase flow rate, and at the same time, the continuous phase piled up to the upstream of the shrinkage region increases, and the pressure of the continuous phase also tends to gradually increase. As the continuous phase accumulates upstream of the shrinkage region, its pressure tends to increase gradually.

Substituting the simulation results into eqn (1)–(4) estimates the shear force, difference pressure force and interfacial tension at the tip of the dispersed phase. Table 1 shows the estimated results at different flow ratios (t* corresponds to 0.75, 0.566 and 0.426, respectively) at the moment when the tip of the dispersed phase is flushed on the right side of the neck structure. As the flow rate increases, the shear force, differential pressure force and interfacial tension gradually increased. The shear force is smaller than the differential pressure force, which is similar in magnitude to the interfacial tension. Without acoustic effects, the differential pressure force overcomes the interfacial tension to dominate the interface breakup.

Table 1 Estimation results of shear force, differential pressure force and interfacial tension under different flow ratios

Q d/Qc	t*	F τ	F R	F γ
0.5	0.750	8.18 × 10^−7	5.12 × 10^−5	3.04 × 10^−5
0.25	0.566	2.33 × 10^−6	6.35 × 10^−5	4.77 × 10^−5
0.125	0.426	4.14 × 10^−6	7.75 × 10^−5	5.11 × 10^−5

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To analyze the effect of acoustic radiation force on the generation of liquid metal droplets, the flow rates of the dispersed phase and continuous phase were 10 μL min⁻¹ and 20 μL min⁻¹, respectively. Fig. 5 (a and b) shows experimental images of liquid metal droplet generation and the variation curve of neck width l_b with time under different input powers. By comparing the evolution curves of neck width, it can be seen that the trend of neck width over time is basically the same when the acoustic force is turned on and off. As the input power increases, the growth rate of l_b in the filling stage significantly increases with the input power, and the decrease rate of l_b in the squeezing stage also significantly accelerates with the input power. The acoustic radiation force applied to the two-phase interface accelerates the contraction and breakup rate of the dispersed phase by squeezing the two-phase interface. Therefore, the acoustic radiation force adjusts the droplet size by changing the interface evolution rate.

Fig. 5 Experimental data and images of interface evolution, droplet size, and spacing of liquid metal under the influence of acoustic waves. (a) Evolution curve of dispersed phase neck width over time under different acoustic input powers. (a1–a3) Experimental images of droplet generation at critical moments. (b) Experimental images of liquid metal droplet generation with different acoustic input powers. (c) Evolution curve of liquid metal droplet size with acoustic and flow conditions. (d) Velocity and time distribution of droplet in different acoustic and flow conditions.

3.2 Droplet size

The characteristics of two-phase flow in microchannels mainly depend on the interaction of various forces. According to the force model proposed in sec. 3.1, under the action of acoustic waves, the acoustic radiation force, pressure difference force, and shear force jointly overcome the interface tension to regulate the interface deformation and droplet deformation state. The force state is determined by both flow and acoustic conditions. The dispersed phase flow rate is fixed at 10 μL min⁻¹. The evolution of droplet size under different continuous phase flow rates and acoustic input powers is shown in Fig. 5(c). Microdroplet size was dimensionless using the ratio l_d/w_c of the microdroplet length l_d to the microchannel width w_c. When the dispersed-phase flow rate was kept at 20 μL min⁻¹, the liquid-metal microdroplet size l_d/w_c decreased from 1 to 0.89 as the input power was reduced from −15 dBm to −30 dBm, shrinking the microdroplets by 11%.

We define the dimensionless ratio Ca_f = AP₀²w/γ of the acoustic radiation force F_AR to the interfacial tension coefficient γ, using continuous phase capillary number Ca characterisation to represent the relative magnitude of shear and interfacial tension, where μ_c is the continuous phase viscosity and v_c is the continuous phase flow rate. There is a power law relationship between the droplet size of the traditional water–oil system and the continuous phase capillary number, flow rate ratio and other parameters.³⁸ In this paper, based on the corresponding microdroplet size data obtained in experiments with different flow rate ratios, fluid properties and acoustic intensities, the indices in the prediction equation of the microdroplet size were obtained by using the multivariate nonlinear regression parameter fitting model and the final expression of the microdroplet size prediction equation can be expressed as:

The predicted values of microdroplets and the corresponding experimental measurements for different acoustic input power, flow ratios, and viscosity ratios are presented in Fig. S1, ESI.† The coefficient of determination R² = 0.98 verifies the accuracy of eqn (6). In summary, it can be seen that the two-phase flow conditions promote interfacial breakup by changing the shear force and differential pressure forces, while the acoustic input power changes the interfacial deformation rate by modulating the acoustic radiation force.

(2) Microdroplet spacing. The dimensions of the liquid metal microdroplets are a determining factor in the accuracy of circuit molding, while the effective contact between the microdroplets in the hydrogel is a crucial element in achieving high electrical conductivity. The experimental image in Fig. 5(b) clearly shows the trend of droplet spacing changing with input power. As the input power increases from −25 dBm to −15 dBm, the spacing between droplets decreases from 277 μm to 188 μm. To analyze this phenomenon, the evolution curve of droplet velocity over time after dispersed phase breakup was extracted in Fig. 5(d), and the color blocks at the bottom correspond to the generation stages. When the input power to the acoustic wave is −20 dBm, the continuous phase flow is 20 μL min⁻¹ and the dispersed phase flow is 10 μL min⁻¹, the corresponding working condition is designated as “S-20-10”.

After the breakup of the dispersed phase interface, the droplets move downstream under the drag force of the continuous phase. The velocity of microdroplet motion is affected by the continuous phase flow, showing a tendency of decreasing and then increasing. Under the squeezing stage, the dispersed phase completely blocks the neck structure, resulting in a blockage of the continuous phase flow downstream. The flow rate of the continuous phase downstream of the neck structure decreases, so the microdroplet movement velocity will be at its lowest point during the squeezing stage. Comparing the microdroplet generation period of “S-20-10” and “20-10”, it can be seen that the filling stage is reduced by 20.1%, the squeezing stage is reduced by 30%, and there is no significant change in the length of time of the breakup stage. Therefore, the acoustic radiation force mainly contributes to the interfacial deformation in the filling and squeezing stage, and shortens the microdroplet generation period. When the continuous phase flow rate was kept constant, the period of microdroplet generation was reduced, the volume of continuous phase filled between microdroplets was reduced, so the microdroplet spacing was significantly shortened.

3.3 Performance analysis of liquid metal-conducting hydrogels

In conventional droplet microfluidics, the droplet size is usually regulated by the two-phase flow rate ratio, and the droplet size decreases gradually with the increase of the continuous phase flow rate, which is usually accompanied by a large droplet spacing. Based on sec. 3.2, it has been found that microdroplet acoustofluidics provides an effective solution to realize the decoupled regulation of liquid metal droplet size and spacing. This section further analyzes the mechanism of regulating the mechanical and conductive properties of hydrogels when acoustofluidics is applied to the preparation of conductive hydrogels, in order to determine the optimal liquid metal droplet generation scheme for conductive hydrogel performance in practical applications.

(1) Conventional microfluidics applied to hydrogel preparation. Liquid metal droplet is added as a conductive functional material to the PVA matrix, and the relative content of liquid metal and PVA is a key factor affecting the mechanical and conductive properties. Traditional microfluidic technology depends on flow conditions to change the size of liquid metal droplets. The stress–strain curves of conductive hydrogels prepared under different continuous phase flow rates are shown in Fig. 6(a). As the droplet spacing increases with the continuous flow rate, as illustrated in Fig. 6(a2 and a3), the volume ratio between small-sized liquid metal droplets and PVA decreases significantly. Consequently, the tensile stress of the conductive hydrogel will gradually increase with the continuous flow rate. When traditional microfluidic technology is employed in the preparation of small-sized microdroplet hydrogel, due to the evident coupling relationship between the size and spacing of droplets, it will exhibit robust mechanical properties.

Fig. 6 Performance test of conductive hydrogel. (a) Stress–strain curves of hydrogels under different flow conditions. (a2 and a3) Experimental images of droplet generation. (b) Resistance–strain of hydrogels under different flow conditions. (b₁–b₅) Experimental images of the morphology of the droplet array and its connection state after freeze – thaw cycles. (c) Experimental images of droplet formation and corresponding gel resistance–strain curves under different acoustic and flow conditions. (c1–c4) Experimental images of droplet generation under different acoustic and flow conditions. (d) Conductivity comparison diagram of liquid metal droplet PVA hydrogels prepared under different acoustic and flow conditions. (Insets) The electrical conductivity of the hydrogel after self-healing.

Liquid metal droplets are conductive functional materials, and effective contact between droplets is a necessary prerequisite for achieving high conductivity of hydrogel. However, liquid metals have the characteristic of easy oxidation, and the oxide layer formed on the surface of droplets can cause insulation problems. Flexible conductive devices prepared by traditional ultrasonic or stirring methods require the introduction of additional thermal, laser, or mechanical sintering processes when fusing liquid droplets to form conductive pathways,²² or the use of capillary forces formed by solvents between droplets during evaporation to induce liquid metal agglomeration.^39,40 In this study, acoustofluidics is used to stably disperse the liquid metal into PVA, and the self-assembly characteristics between the droplets are used to form a uniformly distributed droplet array (Fig. 6(b₁–b₄)). After the freeze–thaw cycle, the hydrogel is exposed to a dry environment for a long time. The volume of the hydrogel is significantly reduced due to water loss, as shown in Fig. 6(b₅), and the liquid metal droplets can fuse in a large area to form a conductive path without additional heat treatment or mechanical pressure.

The improvement of mechanical performance will be accompanied by a weakening of electrical conductivity. The conductivity curves of hydrogels prepared under different flow conditions are measured in Fig. 6(b). At the continuous phase flow rate of 80 μL min⁻¹, the liquid metal content is low, and when the strain reaches 280%, the resistance increases sharply by 400% and the conductivity decreases dramatically. However better mechanical properties are observed in Fig. 6(a) for high PVA content gels with a maximum tensile strain of 760%. However, the liquid metal content is low, and the maximum strain of the hydrogel is only 280% while maintaining the electrical conductivity.

As the continuous phase flow rate decreases, the liquid metal content in the hydrogel gradually increases. When the continuous phase flow rate was less than 60 μL min⁻¹, abundant conductive pathways were formed in the hydrogel as shown in Fig. 6(b₁–b₃). The interaction force between the droplets after deposition is isotropic short-range force and when the droplet size is relatively uniform, the droplets will form a hexagonal array. At this point, for the conductive hydrogel after the freeze–thaw cycle, as shown in Fig. 6(b₅), a large area fusion to form a conductive pathway, until the gel is on the verge of fracture moment, can maintain a relatively low resistance. The maximum strains with the hydrogel maintaining conductivity are 600%, 640% and 680%, respectively. The contents of liquid metal and PVA determine the conductive and mechanical properties of the hydrogels, respectively, so the effective control of the size and spacing of the liquid metal microdroplets is a key factor in realizing the modulation of hydrogel properties.

(2) Acoustofluidics to hydrogel preparation. The regulation of the microdroplet condition by the flow rate gives rise to a correlation between microdroplet size and spacing, indicating that as the size of the microdroplets decreases, the spacing between them increases. Surface acoustic wave offers a novel approach for reducing the spacing of small-sized microdroplets. The conductivity of hydrogels fabricated under different flow and acoustic conditions are presented in Fig. 6(c). Comparison of the experimental images shows that the microdroplet spacing is significantly reduced under the action of the acoustic waves, and the content of liquid metal per unit volume is increased. Combined with the strain–resistance curves, it can be seen that the effect of acoustic waves on the ultimate tensile strain of the hydrogel is small and does not substantially reduce the stretchability of the hydrogel.

PVA reacts with borax to form a diol borate bond, which is a chemical bond that can be rapidly broken and reorganized, conferring rapid self-healing properties to the hydrogel, making it possible to achieve self-healing properties through simple contact after damage. The acoustic-induced decrease in microdroplet spacing and the increase in liquid metal content in the hydrogel also had an effect on the conductivity after self-healing. The conductivity statistics of the hydrogels prepared under different flow and acoustic conditions after three cycles of fracture and self-healing are compared in Fig. 6(d).

Acoustofluidics increases the content of liquid metal. Meanwhile, the regular arrangement of droplets enables the formation of conductive pathways over a large area. The initial conductivity of the hydrogel is increased from 4261 S m⁻¹ to 4687.5 S m⁻¹ after the acoustic force is turned on at a continuous phase flow rate of 20 μL min⁻¹, which is a 10% increase in conductivity. The conductivity increased from 3024 to 3348 S m⁻¹ after self-healing of the first fracture, and from 2180 to 2725 S m⁻¹ after self-healing of the second fracture. Acoustic-based liquid metal microdroplet generation can reduce the spacing between droplets and increase the liquid metal content per unit volume. It can effectively improve the initial conductivity of the circuit and the conductivity after self-healing. Acoustofluidics provides a new idea for the preparation of self-healing hydrogels with strong adaptability to extreme environments.

The conductive hydrogel prepared when the input power is −20 dBm, the continuous phase flow rate is 40 μL min⁻¹, and the dispersed phase flow rate is 10 μL min⁻¹ is used as the electrode unit. The triple conductor and hydrogel are pasted to the skin surface with medical tape. The ECG signal and EMG signal detection data are shown in Fig. 7. The high-quality ECG signals, QRS complex peaks, P wave, and T wave are well duplicated by the conductive hydrogel (Fig. 7(a)), which can be used for long-term monitoring of cardiac tissue movement. The conductive hydrogel can be monitored in real time during palm clenching and opening to detect EMG signals from the radial lateral wrist flexor muscles (Fig. 7(b)). Compared with traditional dry electrodes, the liquid metal conductive hydrogel can be highly adhered to the skin surface and has good biocompatibility, which can be used as an effective tool for long-term monitoring of bioelectrical signals.

Fig. 7 Application of hydrogel in biological signal monitoring. (a) Electrocardiogram monitoring data. (b) Monitoring data of biological electromyographic signals. (b1) EMG signal monitoring electrode.

4 Conclusion

Conventional ultrasonic methods for microdroplet generation are prone to size inhomogeneity. Surface acoustic waves control single microdroplets precisely, but the regulatory mechanism is unclear. Additionally, the influence of droplet size and space on the conductive hydrogel's electrical and mechanical properties is unknown. This article presents the preparation of conductive hydrogels utilising acoustofluidics. It investigates the impact of acoustic and flow conditions on droplet size and spacing, examines the deformation characteristics of the interface, establishes a force model within acoustic waves, performs a predictive analysis of droplet size, and conducts a comprehensive analysis of the influence of droplet size and spacing on the conductivity and mechanical properties of the hydrogel. The principal conclusions are as follows:

(1) The generation of liquid metal droplets in T-channels can be divided into three stages: filling, squeezing and breakup. During the filling stage, the interface is stretched and expanded by a combination of shear and inertial forces. The squeezing stage begins when the neck width reaches its maximum value. The tip of the dispersed phase obstructs the neck structure, impeding the downstream flow and causing the accumulation of upstream flow. Surface acoustic waves facilitate acoustic radiation force, which overcomes interfacial tension with shear and differential pressure forces. This accelerates two-phase interface deformation and reduces the generation period of liquid metal droplets.

(2) Flow and acoustic conditions influence the force state during droplet generation, thereby changing the size and spacing of droplets. The size of the droplets can be altered by changing the capillary number Ca, flow ratio Q_d/Q_c, and acoustic input power. The dimensionless number used to characterize the intensity of the acoustic wave is defined as Ca_f. An equation is established between the size of liquid metal droplets and various variables, l_d/w_c = 0.426 × Ca^−0.248 × (Q_d/Q_c)^0.09 × Ca_f^−0.031, with R² = 0.98. The size of the liquid metal droplets gradually decreases with an increase in the flow ratio and acoustic input power. The equation enables the effective prediction of the droplet size of liquid metal.

(3) The formation quality of the conductive network of the hydrogel is dependent upon the size and spacing of the liquid metal droplets. The flow conditions can simultaneously change the droplet size and spacing size. The surface acoustic wave can offer an effective approach for decoupling the control of droplet size and spacing. The application of acoustic force results in the intensification and reduction of the droplet, accompanied by an increase in the liquid metal content. The initial conductivity of the liquid metal droplet gel prepared with the assistance of acoustic force exhibited an increase of 10%, while the conductivity of the gel following fracture self-healing demonstrated a 25% enhancement.

This paper helps to reveal the regulation mechanism of acoustic surface waves on liquid metal microdroplet generation, determine the mechanism of the effect of microdroplet size and spacing on the conductive and mechanical properties of hydrogels, and realise the preparation of self-healing high-performance liquid metal microdroplet hydrogels.

Data availability

All data needed to evaluate the conclusions are present in the paper.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The authors are grateful for the support of the National Natural Science Foundation of China (12172017, 12202020, 12272016, and 12202021) and Beijing Natural Science Foundation (L241076, 1232003, 2254086).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4lc00935e

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