Methods

SAW microfluidic chip

This study employs standing surface acoustic waves (SAWs) to transform aqueous sessile droplets with varied volumes into a jet. Two focused interdigital transducers (FIDTs) generate counter-propagating SAWs with the same amplitude on the substrate where the sessile droplet is located. Interdigital transducers are structured on a 4" single-side polished lithium niobate wafer substrate with X-propagation direction (128∘YX LiNbO3), subsequently diced into single SAW jetting chips (8 × 14 mm2). In the current chip layout, two focused interdigital transducers (IDT) (60 μm wavelength, 30 degree focusing angle and matched to 50 Ω impedance) are opposing each other with a distance of 4 mm for SAW excitation based on the superposition of two counter-propagating traveling SAWs. For detailed fabrication and configuration of the SAW chip, see Section X of the Supplementary Information. The fabrication procedure follows established methods described in refs. 61,62. A signal generator (BSG F20, BelektroniG, Freital, Germany) was employed to drive the IDT with an excitation frequency of 64.4 MHz. During the experiments, the applied electrical input power was maintained at approximately 4 W, with 2 W delivered to each IDT. To increase the static contact angle between the sessile drop and the substrate surface, SAW wafers were coated with a monolayer of 1H,1H,2H,2H-perfluorodecyltriethoxysilane (PFDTES) utilizing molecular self-assembly, using the protocol described by Sablowski et al.63. A microscopic image of a microfluidic SAW jetting chip with its components is shown in Fig. 1b.

Electrical and acoustical characterization

The electrical radio-frequency (RF) behavior of the standing SAW chips was studied in the form of their complex scattering (S)-parameters in a frequency range close to the Rayleigh-SAW excitation frequency. At the ideal working frequencies (∣Sxx∣ minimum) and within a narrow bandwidth, i.e., 64.4 ± 1 MHz, the focusing IDTs manufactured are ideally matched to 50 Ω impedance with a reflection coefficient of power of ∣S__x__x∣2 < 2% and very low electric losses, characterized by an almost ideal baseline at∣_S_11∣ > 0.95. The SAW chips were placed in the chip holder and connected to an Agilent Technologies 5070B network analyzer via SMA cables and custom 50 Ω-matched PCBs with electric waveguides and gold-coated spring pins. The network analyzer cables were calibrated up to the point where their male SMA connector met the PCBs female SMA connector. Since the acoustic wave field is the dominant boundary condition for the SAW-liquid interaction, the wave field of a focused IDT structured on a SAW chip was measured around the jetting zone and for various frequencies close to the Rayleigh-SAW excitation frequency using a UHF 120 laser Doppler vibrometer (Polytec GmbH, Germany), mechanically and thermally stabilized for long-term measurements. Based on the results of traveling SAW wavefield measurements, the distance between the IDTs was carefully chosen to ensure that the center point of the sessile droplets, i.e. the intended jetting zone, corresponds to a defined SAW focal region.

Sessile droplets

The aqueous sessile droplets with volumes ranging from 1 to 10 μ__l, were positioned on the SAW chip for jetting. The aqueous droplets contain PNIPAM microgels at varying concentrations (0.01 wt%, 0.1 wt%, and 1 wt%). The PNIPAM microgels were synthesized by surfactant-free precipitation polymerization64 with different cross-linker contents: 1 mol%, 5 mol%, and 10 mol%, labeled as MG1, MG5, and MG10, respectively. It is noteworthy that microgels with lower cross-linker content exhibit greater softness65, allowing them to stretch more at the interface. To support our experiments, we used surfactant(C14TAB)solutions at two concentrations: 0.01 mM (0.00035 wt%), 1 mM (0.035 wt%), 3.33 mM (0.117 wt%) and 30.33 mM (1.117 wt%) corresponding to about 0.01 CMC, 0.3 CMC, 1 CMC and 10 CMC, respectively.

Microgel characterization

Surface tension measurements (Fig. S2) were performed using a drop-shape analyzer OCA 20 (DataPhysics Instruments, Filderstadt, Germany). The dynamic viscosity of the microgel dispersions as a function of shear rate, as well as interfacial shear rheology, was measured with a rheometer (MCR702, Anton Paar). The results are shown in Fig. S3. The microgel sizes were measured with Dynamic Light Scattering (DLS) from LS Instruments (Switzerland) to obtain the hydrodynamic radius at different temperatures (Fig. S4). We used the Langmuir-Blodgett method (please see ref. 66.) to transfer microgels onto a silicon wafer at a certain surface pressure. The microgel distribution on the interface as well as indentation measurements, were then carried out using Atomic Force Microscopy (Cypher AFM system, Asylum Research, Santa Barbara, CA, USA). The corresponding results are presented in Fig. 3.

Optical imaging setup

Two high-speed, one at TU Darmstadt (UX50 mini, FASTCAM, Photron, Japan) and one at SAWLab-Saxony (Phantom VEO 410, Vision Research Inc.), together with illumination systems were used to monitor the jet formation and development. The filming speed is 4 kfps.

Computer simulations

To investigate the molecular-scale behavior of microgels at the air–water interface, we developed a coarse-grained dissipative particle dynamics (DPD) framework67,68. In this hybrid polymer-solvent model, each microgel is represented as a cross-linked polymer network composed of monomer and cross-linker beads. All beads interact via the Weeks–Chandler–Andersen (WCA) potential69 to enforce excluded volume, where ϵ = k_B_T sets the energy scale and r is the bead separation. Covalent bonds within the network are modeled by the finitely extensible nonlinear elastic (FENE) potential70, with _k_F = 15 and _R_0 = 1.5, ensuring structural integrity while allowing finite extensibility.

2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${V}_{{{{\rm{WCA}}}}}(r)=\left\{\begin{array}{ll}4\epsilon \left[{\left(\frac{\sigma }{r}\right)}^{12}-{\left(\frac{\sigma }{r}\right)}^{6}\right]+\epsilon,\quad &r\le {2}^{1/6}\sigma,\\ 0,\hfill \quad &\,{\mbox{otherwise}}\,,\end{array}\right.$$\end{document}VWCA(r)=4ϵσr12−σr6+ϵ,r≤21/6σ,0,otherwise,

3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${V}_{{{{\rm{FENE}}}}}(r)=-\epsilon {k}_{{{{\rm{F}}}}}{R}_{0}^{2}\ln \left[1-{\left(\frac{r}{{R}_{0}\sigma }\right)}^{2}\right],\quad r < {R}_{0}\sigma,$$\end{document}VFENE(r)=−ϵkFR02ln1−rR0σ2,r<R0σ,

Following ref. 52, the microgel network is generated using patchy particles: monomers carry two patches and cross-linkers carry four, otherwise behaving identically. This yields coarse-grained analogs of PNIPAM microgels. We simulate microgels with cross-linker concentrations c = 2%, 5%, 10% to match experimental conditions, with N ≈ 14,000 monomers per microgel.

The surrounding water and air phases are represented by mesoscopic DPD beads interacting via conservative, dissipative, and random forces: where Here a__i__j is the conservative interaction amplitude, λ is the friction coefficient, Ξ is the noise amplitude satisfying Ξ2 = 4_λ__k_B_T_, w(r) = 1 − r__i__j/R__c is the weight function, θ__i__j is a Gaussian random variable of zero mean and unit variance, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\hat{r}}{ij}$$\end{document}r^ij is the unit separation vector, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbf{v}}}{ij}$$\end{document}vij is the relative velocity.

4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbf{F}}}_{ij}={{\mathbf{F}}}_{ij}^{C}+{{\mathbf{F}}}_{ij}^{D}+{{\mathbf{F}}}_{ij}^{R},$$\end{document}Fij=FijC+FijD+FijR,

5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbf{F}}}_{ij}^{C}={a}_{ij}\left(1-\frac{{r}_{ij}}{{R}_{c}}\right){\hat{r}}_{ij},$$\end{document}FijC=aij1−rijRcr^ij,

6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbf{F}}}_{ij}^{D}=-\lambda {w}^{2}({r}_{ij})({{\mathbf{v}}}_{ij}\cdot {\hat{r}}_{ij}){\hat{r}}_{ij},$$\end{document}FijD=−λw2(rij)(vij⋅r^ij)r^ij,

7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbf{F}}}_{ij}^{R}={\Xi }\,w({r}_{ij})\,{\theta }_{ij}\,{\hat{r}}_{ij}.$$\end{document}FijR=Ξw(rij)θijr^ij.

In the hybrid polymer-solvent model, water beads (w) and air beads (a) interact with microgel monomers (m) via DPD forces. The polymer-solvent parameter a__m__s controls solvent quality and thus the microgel swelling behavior71. To capture interfacial properties, we use a Flory-Huggins-based parameterization: a__w__w = a__a__a = 8.8 k_B_T/σ for water-water and air-air interactions, a__m__w = 4.5 k_B_T/σ for polymer-water interactions, a__m__a = 5.0 k_B_T/σ for polymer-air interactions, R__c = 1.9 σ, and a dimensionless DPD bead density \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rho }{{{{\rm{DPD}}}}}=\rho {R}{c}^{3}=4.5$$\end{document}ρDPD=ρRc3=4.550. The molecular volumes of water and air are approximately 30 _Å_3 and 120 _Å_3, respectively68. To ensure equal effective DPD bead volumes, each DPD water bead represents two water molecules ( ≈ 60 _Å_3), while each air molecule is mapped onto two DPD beads. This mapping yields an average DPD bead volume of 60 _Å_3 and the interaction range R__c = 6.46 Å. In the absence of microgels, these parameters yield an air–water surface tension γ ≈ 70 mN/m, consistent with experiment. Upon placing a microgel at the interface, we observe the characteristic fried-egg conformation.

To assemble interfacial monolayers, two microgels are placed at the air–water interface in a rectangular box with periodic boundaries. The system is equilibrated in explicit solvent, allowing microgels to adopt their interfacial morphology72. Due to periodicity, two air–water interfaces are present; we analyze the one occupied by the microgels by computing the virial pressure within − 40_σ_ < z < 40_σ_. The interfacial tension is obtained from the pressure anisotropy: where P__z__z is the normal pressure, P__x__x and P__y__y are the lateral pressures, and L__z is the sub-volume height.

8\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma={L}_{z}\left({P}_{zz}-\frac{1}{2}({P}_{xx}+{P}_{yy})\right),$$\end{document}γ=LzPzz−12(Pxx+Pyy),

All simulations are performed with LAMMPS73. Units are given in σ (length), m (mass), k_B_T (energy), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\tau }{0}=\sqrt{m{\sigma }^{2}/{k}{{{{\rm{B}}}}}T}\approx 1.3\times 1{0}^{-12},{{{\rm{s}}}}$$\end{document}τ0=mσ2/kBT≈1.3×10−12s (time), and k_B_T/_σ_2 (surface tension).