Results

Controlled jetting using surface acoustic waves

The SAW device comprises slowness-curve-adjusted interdigital transducers (IDTs)42 arranged in a delay-line configuration to generate a strong standing wave at the chip center. This geometry focuses the acoustic energy into a well-defined interaction zone, only 1.6_λ_SAW (FWHM) wide and approximately 25_λ_SAW (FWHM) long, ensuring highly localized coupling between the SAW field and the fluid above. A representative microscopic image of the chip layout, overlaid with laser Doppler vibrometry (LDV) measurements of the amplitude distribution at the optimal driving frequency together with the magnitude of reflection coefficients are shown in Fig. 1b.

Fig. 1: SAW-driven jetting of microgel dispersions.a An aqueous droplet containing microgels of varying concentration and stiffness (cross-linker density) is gently placed at the center of a SAW chip between two opposing interdigital transducers (IDTs). After allowing microgels to adsorb and equilibrate at the interface, a focused SAW field drives jet formation with diameter h and length L, recorded via high-speed imaging; jet performance is quantified as L/R, where R is the initial droplet baseline. b Top view of the interdigital transducer (IDT) and laser Doppler vibrometry (LDV) measurement showing the acoustic wave field profile superimposed on microscope images of the SAW chip. The standing surface acoustic wave (SAW) is generated at a wavelength of 60 μm and an excitation frequency of 64.4 MHz according to electrical characterization of the standing surface acoustic wave chip in terms of its reflection coefficient magnitude (∣S11∣). c In the early stages of jet formation, surface destabilization of the droplet (here water) occurs at two symmetric locations due to oppositely traveling surface acoustic waves (SAWs) of equal energy, leading to the formation of a vertical jet. A similar process is observed in microgel dispersions. d The maximum jet length of water and 1 wt% microgel dispersions at different cross-linker (BIS) contents (MG1: 1 mol%, MG5: 5 mol% and MG10: 10 mol%). e Schematic representation of a possible scenario of how soft vs stiff microgels behave at the interface during their extension. Microgel elements adapted from ref. 46. and modified.

We investigate the effect of microgel softness on SAW-driven jet formation by preparing droplets of varying volumes from microgel dispersions of three stiffness levels with 1%, 5% and 10% of nominal cross-linker concentrations (MG1, MG5, and MG10, with MG1 being the softest) at dispersion concentrations of 0.01, 0.1, and 1 wt%. These droplets are dispensed using a pipette [see Fig. 1a] and placed at the center of SAW chip. The dispensed droplet is equilibrated for 2–3 minutes prior to IDT activation. It is known that microgels adsorb at the air–water interface43 (prior to jetting), and that lower cross-linker density creates softer microgels, while higher cross-linker density produces stiffer ones44 [see Fig. 1a]. This classification as “soft" or “stiff" is based on their elastic modulus, which can be measured using atomic force microscopy (AFM) indentation of individual PNIPAM microgels in water, deposited on a silicon substrate. The elastic modulus profile reveals a systematic increase in stiffness with higher cross-linker concentrations. In all cases, the modulus is highest at the core of the microgel and gradually decreases toward the periphery, consistent with the well-established core-shell structure of PNIPAM microgels [see Fig. S1]. Quantitatively, microgels with 10% cross-linker (MG10) exhibit the highest elastic modulus across the particle, followed by MG5, while microgels with 1% cross-linker (MG1) show the lowest modulus values throughout the particle. This establishes a clear and physically meaningful distinction between stiff (MG10), intermediate (MG5), and soft (MG1) microgels. Upon activating the transducers at a combined input power of 4 W, SAWs induce jetting, and the jet length (L) relative to the initial droplet baseline (R), as shown in Fig. 1a, is recorded using a high-speed camera.

During the early stages of jet formation, which takes less than 3 ms [see Fig. 1c], the counter-propagating SAWs transfer energy into the sessile droplet, destabilizing the surface at two symmetric locations, in agreement with theoretical predictions15. This instability arises from two equal streaming forces generated by high acoustic pressure, known as _caustics_45, whose superposition leads to the formation of a single jet ejected perpendicularly to the substrate. During the jet formation, satellite droplets may form and disintegrate, but they are excluded from the analysis. The jet initially ejects when the inertial forces overcome capillary stresses at the interface, launching with a certain velocity14. It subsequently undergoes a classical Rayleigh-Plateau instability in which surface tension drives breakup of the jet into multiple droplets.

Softness-induced jet stability

Jet stability is governed by the balance of inertial, viscous, surface tension, and gravitational forces. By fixing the input IDT power at 4 W for all samples (jet velocity of about 1 m/s), we hold inertial forces constant, enabling direct comparison of remaining forces (viscous, surface tension, and gravitational). At this velocity, we estimate the gravitational length, the characteristic scale at which gravity balances inertial acceleration, by equating convective inertia and gravitational acceleration: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$| {{{\bf{v}}}}\cdot \nabla {{{\bf{v}}}}| \sim {u}{0}^{2}/{\ell }{g} \sim g$$\end{document}∣v⋅∇v∣u02/ℓgg. This yields a gravitational length \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\ell }{g}={u}{0}^{2}/g\approx 10$$\end{document}ℓg=u02/g≈10 cm, which far exceeds the maximum jet lengths observed in our experiments. Furthermore, we estimate the capillary length, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\ell }_{c}=\sqrt{\gamma /(\rho g)}$$\end{document}ℓc=γ/(ρg), which defines the length scale at which surface tension balances gravity. For our system, ℓ__c ranges from approximately 2.1 mm in microgel dispersions [see Fig. S2] to 2.7 mm in pure water, values that are significantly larger than the jet radius ( ≈ 100 μm). Viscous effects are also comparable across the samples [see Fig. S3]. Therefore, we conclude that capillary forces, rather than gravitational or viscous forces, dominate the interfacial dynamics that govern jet stability and breakup in our system.

We observe that introducing PNIPAM microgels into aqueous droplets enhances jet stability, as evidenced by increased jet length compared to pure water [see Fig. 1d]. For example, the jet from a 10 μl droplet containing soft microgels (MG1) at 1 wt% concentration reaches a maximum length of 15.59 ± 0.14 mm at 18 ms and breaks up at 18.25 ms [see Fig. S6]. A pronounced dependence of jet behavior on microgel softness is observed, with soft microgels (e.g., MG1) markedly suppressing droplet breakup relative to their stiffer counterparts (e.g., MG10), leading to longer jets. We hypothesize that the extensive deformability of soft microgels at the jet surface facilitates the formation of a cohesive interfacial layer, delaying exposure to the bare air–water interface [see Fig. 1e, Movies Supplementary Movie 1.avi and Supplementary Movie 2.avi]. To quantify this effect, we measure the maximum jet length L, normalized by the droplet base-line diameter R (denoted L/R), across a range of dispersion concentrations. Even at low concentrations (0.01 wt%), microgels increase L/R relative to pure water [Fig. 2], with the enhancement becoming more pronounced as both softness and concentration increase. At 1 wt%, soft microgels (MG1) extend the jet length by approximately 44% compared to water. At lower concentrations, the stabilizing effect diminishes, likely due to insufficient interfacial coverage prior to breakup. This concentration-dependent enhancement suggests that sufficient interfacial coverage by soft microgels is critical to achieving maximal jet stability.

Fig. 2: Effect of concentration and interfacial stabilizer type on normalized jet length.Maximum jet length normalized by the droplet’s initial baseline (L/R) as a function of liquid concentration. Data are shown for pure water (concentration = 0, also shown with the dashed line), C14TAB solutions at four different concentrations of about 0.01, 0.3, 1 and 10 CMC, and microgel dispersions with varying stiffness (different cross-linker densities): MG1, MG5, and MG10, across their respective aqueous concentrations.

To understand why softer microgels generate longer jets and delay breakup, we investigate their interfacial organization using Langmuir–Blodgett deposition (see methods) under a fixed lateral pressure of 5 mN/m, selected to reproduce the interfacial conditions expected during jet elongation. As shown in Fig. 3, softer microgels form flatter, more extended monolayers that efficiently cover larger interfacial areas with fewer particles than their stiffer counterparts. Although the dangling polymer chains of the microgels are not resolved in our AFM measurements, it is known that microgels interact through their outer, loosely cross-linked coronas43, which likely remain in contact at the interface. This efficient packing facilitates faster interfacial coverage and allows surface tension to reach a reduced value more rapidly compared to stiffer microgels46, as confirmed by pendant drop measurements [see Fig. S2]. While direct measurement of surface tension during jet elongation remains experimentally challenging, our molecular dynamics simulations support this scenario, showing that soft microgels remain entangled and connected under rapid interfacial extension (see Modeling section).

Fig. 3: Ex-situ AFM characterization of microgel arrangements at the air–water interface.The structure of the microgel particles at constant lateral pressure through the AFM at 5 μm2 scan. The layers were transferred to a silicon wafer using a Langmuir trough method at a lateral pressure of 5 mN/m for a MG1 b MG5 c MG10, The scales differ because the height of each scan varies significantly.

To demonstrate that conventional surfactants are less effective than microgels under identical jetting conditions (same speed _u_0 and droplet size R), we tested C14TAB at sub-critical (0.01 CMC), near-CMC (0.3 and 1 CMC) and high (10 CMC) concentrations. We find that at low concentrations, C14TAB provides a modest improvement ( ~ 4%) in jet length compared to pure water. We anticipate that it occurs due to Marangoni flows that transiently resist breakup [see Fig. 4a]. However, as concentration increases toward 1 CMC, jet length decreases slightly—suggesting that excess surfactant suppresses Marangoni flows, leading to faster destabilization and earlier breakup [see Fig. 4b]. Even at higher concentrations (10 CMC), we observe a moderate improvement ( ≈ 11%) in jet length compared to pure water. This behavior is also consistent with recent findings in air-blast jetting16. In contrast, microgels—particularly soft ones—form cohesive, stretchable interfacial networks that sustain reduced surface tension during rapid deformation, leading to a 44% increase in jet length compared to pure water.

Fig. 4: Schematic representation of jet from surfactant solutions and microgel dispersion.a At low surfactant concentration (sub-CMC), interfacial extension generates gradients in surfactant coverage, driving Marangoni flows that transiently counteract breakup and extend jet length. b At concentrations close to 1 CMC, the interface is more uniformly distributed, eliminating surface tension gradients and suppressing Marangoni flows, which leads to reduced jet stability and shorter jets. c At surfactant concentrations well above the CMC, the interface is saturated and the equilibrium surface tension—and corresponding Laplace pressure—are reduced. However, the surfactant layer remains molecular and lacks the ability to form a mechanically resilient interfacial network, limiting stabilization under strong extensional deformation. d In contrast, microgel dispersions form deformable, polymer-rich interfacial layers that can stretch, rearrange, and maintain a low effective surface tension during rapid jet elongation, leading to significantly enhanced jet stability.

Furthermore, _C_14TAB is a cationic surfactant and is therefore expected to exhibit relatively fast adsorption kinetics compared to neutral or anionic surfactants47. The fact that even such a fast-adsorbing surfactant fails to achieve stabilization comparable to that of microgels strongly supports our central conclusion: polymer-based interfacial stabilizers perform better under the rapid, high-strain interfacial dynamics relevant to jet formation [see Fig. S7].

This raises the question of whether jet stability is controlled by the viscoelastic properties48,49 of microgel-laden air–water interfaces, which are influenced by the softness of individual microgels. Additional interfacial rheology measurements, including interfacial shear [see Fig. S8] and dilatational experiments [see Fig. S9], show that interfaces stabilized by softer microgels exhibit higher dilatational elastic and shear storage moduli and sustain larger strains before yielding, indicating the formation of more resilient interfacial networks. However, these measurements probe the linear viscoelastic regime, typically at strains below 10%, whereas SAW-driven jetting subjects the interface to extreme extensional deformations exceeding 200%. Under such large, rapid extensions, the interfacial layer is driven far beyond the regime where small-strain elastic moduli remain well-defined. Consequently, jet stability in our system is governed primarily by the interface’s ability to maintain a low effective surface tension during rapid elongation rather than by its small-strain viscoelastic moduli.

Modeling the stretching of the air–water interface

To complement our experimental investigation of jet stabilization by microgels under SAW actuation, we developed a coarse-grained simulation framework to probe the molecular-scale mechanisms governing microgel behavior at dynamically deformed air–water interfaces. Our model mimics the stretching of a fluid jet by placing two microgels at an initially equilibrated interface and imposing lateral elongation at a constant velocity of 1 m/s (see Methods), consistent with experimental jet elongation rates captured via high-speed imaging.

Microgels are constructed from a self-assembled network of monomer and cross-linker beads, enabling systematic variation in cross-linker density. We focus on two representative cases: soft microgels (MG2, 2% cross-linker) and stiff microgels (MG10, 10% cross-linker). Due to the slow equilibration of the 1% cross-linked network system, MG2 was chosen as the softest microgel to complement experiments. The surrounding medium consists of a binary DPD fluid, representing water (blue) and air (yellow) phases. Following established approaches50, the microgels are first equilibrated at the interface. As expected, MG2 microgels exhibit extended, diffuse coronas with numerous dangling polymer chains, whereas MG10 microgels form compact, spherical structures with minimal surface flexibility [Fig. 5a, c].

Fig. 5: Simulation snapshots of soft and stiff microgels at the air–water interface.Representative configurations of soft (a,b) and stiff (c,d) microgels (red beads) adsorbed at the air water interface. Initially, two microgels are positioned in close lateral contact (a, c). The simulation box is then stretched laterally at constant volume to mimic interfacial extension during jetting, resulting in pronounced deformation and persistent connectivity for soft microgels (b), in contrast to the rapid disentanglement observed for stiff microgels (d).

Under imposed interfacial stretching, the two microgel types exhibit strikingly different responses. MG10 microgels quickly disentangle from one another, showing minimal resistance to separation. In contrast, MG2 microgels remain interconnected throughout the deformation process, facilitated by extensive chain interpenetration and high deformability [Fig. 5b, d]. This persistent adhesion allows soft microgels to maintain a contiguous interfacial layer even under dynamic strain [see Movie Supplementary Movie 3.mp4].

This mechanical distinction has direct implications for interfacial properties. Prior to stretching, all systems, MG2, MG5, and MG10, exhibit comparable surface tension values of approximately 40 mN m−1, consistent with experimental observations [see Fig. 6 and see also Fig. S2]. Upon initiating lateral deformation, the surface tension increases linearly with time as the microgels respond to interfacial strain, ultimately reaching a steady-state plateau. Notably, the temporal evolution of surface tension reveals stark contrasts between soft and stiff microgels: while MG10 systems rapidly recover toward the bare air–water tension of ∼ 65 mN m−1 within t/_τ_0 ≈ 20,000, the softest microgels (MG2) maintain a substantially reduced surface tension, remaining below 50 mN m−1 up to t/_τ_0 ≈ 80,000 [Fig. 6]. We have also prepared microgels with a 1% cross-linker density and repeated our simulations to investigate the effects of lower cross-linker concentrations. We find that while the 1% cross-linker concentration results in a slight reduction in surface tension compared to the 2% cross-linker concentration [see Fig. 6], the overall trend and our conclusions remain valid.

Fig. 6: Simulated surface tension dynamics.Dynamic surface tension as a function of time for microgels with different cross-linker densities. The plot illustrates how varying the cross-linker concentration influences the rate at which the surface tension evolves, highlighting the distinct behaviors of soft (low cross-linker density) and stiff (high cross-linker density) microgels during interfacial stretching.

Our simulations further reveal that the disentanglement of stiff microgels (MG10) during interfacial extension leads to pronounced inhomogeneities in the interfacial flow field [see Fig. 7a, c, e]. In regions where microgels separate and expose the bare air–water interface, the inward z-component of the velocity becomes significantly enhanced (two-times), generating a non-uniform velocity profile along the interface. In contrast, soft microgels (MG1) remain entangled under extension, maintaining a homogeneous velocity profile [see Fig. 7b, d, f]. We therefore conclude that a uniform extensional flow field (MG1) allows the jet to maintain its cylindrical shape, whereas a strongly non-uniform z-velocity (MG10) amplifies Rayleigh-Plateau-like instabilities and accelerates jet breakup [see also Fig. S10].

Fig. 7: Flow profiles of stiff (MG10) and soft (MG1) microgels during stretching of the interface.a,b Representative snapshots of stiff (MG10) and soft (MG1) microgels at the air-water interface during stretching at t/τ0 = 46,000. At this stage, stiff microgels (MG10) disentangle, exposing the central region of the interface to the bare air-water surface. In contrast, soft microgels (MG1) remain entangled and fully cover the interface. e,f Variation of the z-component velocity of water in the xz-plane. The lines represent regions of constant velocity, where the velocity magnitude remains the same between consecutive lines. The velocity anisotropy along the stretching axis is pronounced near the interface for stiff microgels (MG10) and diminishes with increasing distance from the interface. In contrast, for soft microgels (MG1), the z-component velocity remains position-independent along the stretching axis. The magnitude of the z-component velocity is indicated by the color code. c,d Spatial variation of the z-component water velocity along the stretching axis, immediately adjacent to the interface (at z=0). For MG10, the velocity at the center (where water is exposed to air) is approximately twice as large as in regions where the microgels remain attached to the interface. For MG1, the z-component velocity remains uniform across the interface due to the complete coverage by the soft microgels. Consequently, a uniform negative z-velocity (MG1) allows the expanding jets to roughly keep their cylindrical shape, whereas a strongly nonuniform z-velocity (MG10) provokes Rayleigh-Plateau-like instabilities and jet breaking. Simulation Parameters: The flow profile is obtained by time-averaging over 5000 DPD time steps, starting from t/τ0 = 46,000, followed by 500 independent simulation runs.

Scaling analysis: conversion of kinetic energy to surface energy

To rationalize our experimental observations, we analyze the conversion of a millimeter-sized droplet of initial diameter R into a high-speed, collimated jet of diameter h and length L under SAW excitation [see Fig. 1a]. In this nozzle-free and reservoir-free system, jet formation does not rely on continuous fluid supply; rather, it emerges solely from acoustic energy injected locally by the SAW. This energy is concentrated beneath the droplet, generating inertial streaming flows that drive fluid momentum toward the droplet’s free surface. When the flow inertia overcomes the stabilizing influence of surface tension, the liquid interface deforms and extrudes into a slender jet extending several centimeters–achieved without conventional nozzles or orifices.

Dimensional analysis6,14 suggests that viscous and gravitational effects are negligible in this regime: the Capillary number, Ca = _μ__u_0/γ ∼ 0.01, represents the ratio of viscous stress (μ__u_0/h) to capillary stress (γ/h) and indicates that viscous dissipation is weak; similarly, the Bond number, Bo = ρ__g__h_2/γ ∼ 0.001, compares gravitational stress (ρ__g__h) to capillary stress (γ/h) and indicates that gravity has minimal influence. Under these conditions, jet dynamics are governed primarily by a balance between inertia and surface tension. Hence, the entire kinetic energy imparted by the SAW to the droplet, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${E}{{{{\rm{kin}}}}} \sim \rho \pi {R}^{3}{u}{0}^{2}/6$$\end{document}Ekin~ρπR3u02/6, is converted into the surface energy needed to form a cylindrical jet of diameter h and length L, given by _E_surf ∼ γ__π__h__L. Equating these two energy scales (_E_kin _E_surf) yields the scaling relation which predicts that, for fixed ρ, _u_0, h, and R, a reduction of the surface tension γ produces longer jets.

1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{L}{R} \sim \frac{\rho {u}_{0}^{2}{R}^{2}}{6\gamma h},$$\end{document}LR~ρu02R26γh,

In our DPD simulations, soft microgel dispersions (e.g., MG2) lower the effective surface tension from ∼ 70 mN m−1 (pure water) to ∼ 50 mN m−1. This leads to a predicted jet elongation of about 40%, in excellent agreement with our experimental observations. Most importantly, using our experimental parameters (ρ ≈ 1000 kg/m3, u_0 ≈ 1 m/s, γ ≈ 70 mN/m, R ≈ 1 mm, and h ≈ 0.2 mm), the scaling relation predicts jet lengths on the order of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{\mathcal{O}}}}(1,{{{\rm{cm}}}})$$\end{document}O(1cm), in agreement with our experimental data. This is two orders of magnitude greater than the breakup length from the Rayleigh–Plateau instability13, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L}{{{{\rm{RP}}}}} \sim {u}_{0}{\left(\rho {h}^{3}/8\gamma \right)}^{1/2} \sim {{{\mathcal{O}}}}(0.1,{{{\rm{mm}}}})$$\end{document}LRPu0ρh3/8γ1/2O(0.1mm), demonstrating that our jets are not instability-limited. Instead, their length is set by the energy-balance scaling in Eq. (1) as the governing mechanism for SAW-driven jetting.