Drop impact printing

The study addresses the challenge of dispensing small, satellite-free microdroplets for diverse applications (electronics, biomedical, rapid prototyping) where conventional nozzle-based inkjet systems suffer from satellite drop formation and nozzle clogging, especially with high mass-loading inks and large particles. Existing alternatives (acoustic, electrohydrodynamic, laser-assisted, microfluidic) often require complex and costly setups. The authors propose a new drop-on-demand approach that replaces the nozzle with a superhydrophobic sieve. The research investigates whether cavity collapse during droplet recoil on such a sieve can enable satellite-free single-droplet ejection over a broad range of liquid properties, particle sizes, and mass loadings, and explores its suitability for practical printing applications.

The paper situates the work within microdroplet printing technologies that typically use nozzle-based dispensing with integrated actuators, which are prone to satellite droplets (due to Rayleigh-Plateau instability) and nozzle clogging (from solvent evaporation and particle agglomeration). Prior techniques include inkjet (with advanced waveform control), electrohydrodynamic, acoustophoretic, laser-induced, and microfluidic methods, which expand capabilities but increase cost and complexity. Previous studies described drop impact on hydrophobic/superhydrophobic meshes, penetration dynamics, and cavity formation/jetting on flat hydrophobic surfaces, but did not identify the physical cause of recoil ejection beyond elevated local pressures. This work builds on those insights, leveraging cavity-collapse singularity constrained by sieve pores to achieve controlled, satellite-free ejection, and expands printable ink palettes beyond typical Z-number ranges reported for standard drop-on-demand systems.

• Superhydrophobic sieve preparation: Copper meshes (pore openings 76.2–533.4 µm; wire diameters specified per mesh type) were nanostructured by immersion in aqueous 2.5 M NaOH and 0.1 M ammonium persulfate for 15 min at room temperature to grow nanowires, then functionalized in 1H,1H,2H,2H-perfluorooctyltriethoxysilane overnight to achieve superhydrophobicity (water contact angle ~159°, CAH <5°). Mesh types included #0.012 (L=533.4 µm, W=304.8 µm), #0.009, #0.0075, #0.0055, #0.0045, #0.0020 (L=76.2 µm, W=50.8 µm). To access smaller pore openings, #0.0020 was copper-electroplated to reduce L to ~32 µm; the electroplated mesh was etched to restore superhydrophobicity.
• Printing setup: A 6 cm² superhydrophobic mesh was clamped; a syringe pump dispensed droplets (D0 ~2.55–2.56 mm) from heights 2–5 cm onto the mesh. High-speed imaging (Photron FastCam, up to 75,000 fps) recorded impact dynamics. Substrates (Teflon- or APTES-coated glass) were placed ~1 mm below the mesh to collect ejected droplets. For high mass loading tests, the mesh was slightly tilted to recycle droplets to a sealed reservoir.
• Impact experiments and regimes: The balance between impinging droplet dynamic pressure (~ρU²) and sieve breakthrough pressure (~4γ/L) determined outcomes. At low U (e.g., U=69 cm/s, We=17), penetration failed. With increased U, single-droplet ejection occurred not during impact but during recoil (recoil ejection). Two cavity modes were identified: (i) impact cavity (IC), formed by capillary waves at impact, and (ii) recoil cavity (RC), formed when initially penetrated liquid recoils upward, overfills the initial cavity, and generates a new cavity during upward motion. Collapse of either cavity, laterally constrained by the pore, focuses kinetic energy and ejects a single droplet.
• Ejection modes and scaling: Two ejection-volume modes were observed: collapse-penetration mode (CPM), where initial penetration retracts and the ejected volume originates from collapse-driven penetration; and impact-penetration mode (IPM), where non-retracting initial penetration combines with collapse-driven inflow to yield larger ejected volume (notably for #0.012). Ejected droplet diameters were measured (ImageJ) and related to pore opening; electroplating enabled minimum droplet diameter ~42 µm.
• Parametric studies: Liquids included water, glycerol-water (viscosity up to 33 mPa·s), PEG-water and ethanol-water (surface tension down to 32 mN/m), and viscoelastic xanthan gum solutions (printing up to 20 mPa·s). Printable regime mapped in Ohnesorge (Oh) vs Reynolds (Re) space; Z=Oh⁻¹ compared with other techniques. A timescale factor (TSF) analysis compared droplet impact timescale τa∝ρD³/γ with penetration/retraction timescales: inertial τp∝L³/γ and viscous τημW/γ, with a crossover Ohcr~0.03; TSF threshold ~0.04 delineated CPM vs IPM.
• Particle and mass-loading tests: Suspensions of polystyrene beads up to 20 µm were printed using meshes down to L=76.2 µm; ZrO2 nanoparticle suspensions in 10 vol% PEG were formulated over a range of mass loadings up to 71%. Droplet size consistency (arrays of 50) and exit angle/positioning accuracy were assessed. Residue removal protocol: mild DI water jet followed by N2 purging.
• Application demonstrations: Biological printing with RBC suspensions, single-cell printing (MDA-MB-231) in 0.268 nL drops, wettability gradient patterning via DMEM droplets on Teflon; electronic printing of silver ink (4% v/v) and PEDOT:PSS lines, characterization (SEM, IV), diode fabrication (silver/PEDOT:PSS junction); flexible and large-area patterning; 3D ZrO2 pillars; polymeric microposts (polyacrylic acid 1.25% w/w) on APTES-coated glass.

• Mechanism: Single, satellite-free microdroplet ejection is driven by hydrodynamic cavity-collapse during droplet recoil on a superhydrophobic sieve. Two cavity formation modes (IC and RC) produce ejection constrained laterally by pore size L.
• Satellite-free ejection: Recoil ejection inherently focuses energy over the pore length scale, aiding short-neck separation without satellite droplets. Hydrophobic (non-superhydrophobic) meshes in impact-ejection mode produced satellites, underscoring the role of recoil ejection.
• Scaling with pore size: Ejected droplet diameter scales approximately with pore opening L. Using various meshes, single droplets from ~94 µm to 926 µm diameter were produced; with electroplated mesh (L32 µm), droplets as small as ~42 µm were printed.
• Ejection modes: For most meshes, CPM dominated; #0.012 exhibited IPM, yielding larger droplet volumes due to non-retracting initial penetration combining with collapse-driven inflow.
• Broad ink palette: Single-droplet printing achieved for viscosities up to 33 mPa·s and surface tensions as low as 32 mN/m; droplet diameter was largely independent of viscosity and surface tension, with slight increases upon CPM→IPM transitions.
• Printable regime: In Oh–Re space, the technique covers a broad region. Z-number (Oh⁻¹) range was ~3–200, exceeding typical 1–14 ranges of common drop-on-demand methods; below Z<3, penetration fails due to viscous dominance.
• Timescale analysis: Critical Ohcr≈0.03 marks inertial–viscous crossover. A critical timescale factor TSF≈0.04 separates CPM from IPM; #0.012 tends to IPM even in inertial regime due to large mesh size.
• Large particle printing: Successfully dispensed 20 µm polystyrene beads using mesh with L=76.2 µm in ~80 µm droplets; effective L/Dp ratio down to ~4 (vs conventional guidance ~100 for inkjets). Probability of capturing a single 20 µm bead in a 0.268 nL drop was 32%.
• High mass loading: Repeatable ejection achieved up to 71% mass loading (ZrO2 in 10 vol% PEG). Single-print deposition thickness reached 16.9 µm (base diameter 990 µm with #0.009). Printed droplet diameter remained approximately constant with mass loading. Post-drying average solid mass loading for 50 drops was 66% ± 1.5% (vs 71% nominal), attributed to settling during printing.
• Accuracy and consistency: Monodisperse deposited droplet sizes: 559 ± 11 µm (#0.009) and 83 ± 2 µm (#0.0020). Positioning accuracy (substrate 1.5 mm below mesh): worst-case deviations ~30 µm lateral, ~10 µm longitudinal.
• Electronics demonstrations: Silver line (4% v/v): width ~450 µm, length 2.5 mm, height ~0.655 µm, resistance ~31 Ω. PEDOT:PSS line: same footprint, height ~2.1 µm, resistance ~2.7 kΩ. Silver–PEDOT:PSS diode exhibited knee voltage ~0.75 V and on-resistance ~1.1 kΩ; LED connection demonstrated.
• Biological and polymer printing: RBC droplet arrays with controllable cell counts per droplet; single MDA-MB-231 cell trapping in 0.268 nL drops; wettability gradient patterning with DMEM; polyacrylic acid microposts (875 µm diameter, 2 µm height) printed; 3D ZrO2 pillars and parallelized multi-impact printing demonstrated.

The findings demonstrate that replacing a nozzle with a superhydrophobic sieve and exploiting cavity-collapse during droplet recoil achieves robust, satellite-free single-droplet ejection. This directly addresses key limitations of conventional inkjet systems—satellite formation and nozzle clogging—especially for high mass-loading inks and large particles. The lateral constraint imposed by the pore localizes the recoil-driven inertial focusing, enabling clean separation and droplet sizes that scale with pore opening. The technique exhibits broad compatibility with liquid properties (Z≈3–200), allowing viscosities up to 33 mPa·s and low surface tensions down to 32 mN/m, and uniquely handles large particles (L/Dp≈4) and very high mass loadings (up to 71%) without clogging due to the transient (~10 ms) liquid–pore contact and open-sieve geometry. Accuracy metrics (monodispersity and positional deviations) are competitive relative to droplet sizes, while the simple setup and ability to tailor droplet size via pore selection provide flexibility. The demonstrations across biological, electronic, and materials applications validate the method’s relevance and scalability (including multi-impact parallelization).

This work introduces a simple, cost-effective drop-on-demand printing technique based on droplet impact on a superhydrophobic sieve, where recoil-phase cavity collapse yields satellite-free single droplet ejection. The approach enables tunable droplet sizes (≈42–926 µm), broad ink compatibility (Z≈3–200; viscosities up to 33 mPa·s; surface tension down to 32 mN/m), and uniquely supports high mass loading (up to 71%) and large particle printing (to 20 µm) without clogging. The method produces monodisperse droplets with adequate placement accuracy and is demonstrated for biological patterning, single-cell printing, wettability gradients, conductive polymer/metal lines, diode devices, and 3D structures. Potential future directions include: improving alignment and control of droplet exit angle via integrated imaging and motorized stages; enhancing handling of higher-viscosity viscoelastic inks through setup augmentation; implementing sealed or controlled environments for volatile/expensive inks; and further scaling via parallel multi-impact arrays and refined pore engineering (e.g., microfabricated meshes).

• Printing resolution and positional accuracy are lower than some advanced techniques (e.g., EHD printing), though adequate for the demonstrated conditions.
• Extremely viscous or strongly viscoelastic inks beyond ~20–33 mPa·s require setup augmentation; below Z<3 penetration fails.
• At highest mass loading, impacting droplets can leave residues on the sieve, limiting the lifetime of a given impact site; however, residues are removable via DI water wash and N2 purging.
• Droplet exit angle can vary with mesh–syringe alignment; maintaining fixed alignment is necessary for consistent placement.
• Hydrophobic (not superhydrophobic) meshes in impact-ejection mode generate satellites, emphasizing the need for proper surface treatment.
• Some ink loss due to evaporation can occur without a fully sealed system (though minimal over short timescales).