Penetration of impact-induced jets into skin-simulating materials

This study demonstrates that impact-induced liquid jets achieve greater penetration depth in skin-simulating materials than laser-induced jets at similar velocities due to their focused cylindrical structure, and proposes a shear deformation model that successfully explains this penetration mechanism by accounting for liquid viscosity, jet inertia, and material elasticity.

The Gist

The Big Idea: A New Way to Shoot Medicine Without Needles

Imagine you want to give someone a shot of medicine, but you want to avoid the pain and fear of a needle. Scientists have been trying to solve this by shooting a tiny, high-speed stream of liquid at the skin instead. This is called a "needle-free injector."

For a long time, the best way to do this was using lasers. Think of a laser injector like a high-tech water pistol that uses a laser beam to create a super-fast, thin stream of water. It works well, but lasers are expensive, can get hot (which might ruin the medicine), and can be dangerous.

This paper introduces a new, cheaper, and safer method called the "Impact-Induced Jet." Instead of a laser, it uses a simple mechanical "slap." Imagine dropping a syringe onto a hard block. The sudden stop creates a shockwave that squirts a focused stream of liquid out of the nozzle at incredible speeds (over 100 meters per second—faster than a race car!).

The researchers wanted to know: Does this "slap" method work as well as the laser method? And more importantly, how does it actually punch through the skin?

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The Surprise Discovery: It's Not About the Tip, It's About the "Root"

To understand the results, let's use an analogy of a spear thrower.

• The Laser Method (The Spear Tip): When a laser shoots a jet, the very front tip of the liquid is moving super fast, but the part behind it (the "root" or the handle of the spear) is moving much slower. It's like throwing a spear where only the point is moving fast, and the handle is dragging behind.

  • Result: The tip punches a tiny hole, but the slow handle doesn't have enough energy to push it deeper. The hole stays shallow.

• The Impact Method (The Heavy Log): When the "slap" method shoots the liquid, the entire stream is moving fast. The front tip is fast, but the part right behind it (the root) is also moving very fast. It's like pushing a heavy, fast-moving log into soft mud.

  • Result: Because the "handle" (the root) is pushing hard right behind the tip, it drives the liquid much deeper into the material.

The Key Finding: The researchers found that the depth of the hole depends almost entirely on how fast the root of the jet is moving, not just the tip. Since the impact method keeps the root moving fast, it creates much deeper penetration than the laser method, even if the tips are moving at the same speed.

The "Distance Doesn't Matter" Trick

Usually, if you shoot a water jet from a distance, the stream spreads out or slows down, and the hole gets shallower.

• Laser Jets: If you move the laser gun slightly away from the skin, the jet changes shape, and the penetration depth changes. It's finicky.
• Impact Jets: The researchers found that with their "slap" method, it didn't matter how far away the nozzle was from the skin. The jet stayed like a solid, fast-moving cylinder. It was like a bullet train that stays on track regardless of the distance; it hits the target with the same force every time.

The New Physics: Why It Works (The "Shear" Analogy)

Scientists have a standard rule for how things punch through soft stuff (like skin or gelatin). They used to think it was all about friction (viscous shear).

• Old Theory: Imagine dragging a knife through jelly. The friction between the knife and the jelly slows it down. The thicker the jelly (viscosity), the harder it is to push.

The researchers tested this with different thicknesses of liquid (from thin water to thick honey-like oil). The old "friction" theory didn't fit the data.

The New Theory: The "Shear Deformation" Model
Instead of friction, the researchers realized the liquid jet is acting like a crowbar.

• Imagine pushing a stick into a block of soft clay. The clay doesn't just rub against the stick; the clay shears (splits and slides apart) to make room for the stick.
• The energy from the fast-moving liquid isn't lost to friction; it's used to tear and slide the material apart.
• Because the impact jet is a solid, fast cylinder, it acts like a perfect crowbar, efficiently splitting the skin-simulating material open. This explains why it works so well even with thick, sticky liquids.

Why This Matters for You

1. Cheaper Medicine Delivery: You don't need expensive lasers to get deep injections. A simple, low-cost mechanical device can do the job.
2. Better for Thick Meds: Many modern medicines are thick and sticky. Old injectors struggled with these, but this new method handles thick liquids easily.
3. Less Pain: Because the jet is so focused and deep, it can deliver medicine exactly where it needs to go without spreading out and hitting all the pain receptors in the skin.
4. Safety: No lasers means no risk of burning the medicine or damaging the device with heat.

In a Nutshell

This paper shows that by simply "slapping" a syringe to create a jet, we can shoot medicine into the skin deeper and more reliably than using fancy lasers. The secret isn't just how fast the front of the stream is, but how fast the whole "log" of liquid is moving. This discovery gives us a new, simple, and powerful tool for the future of painless, needle-free medicine.

Technical Summary

1. Problem Statement

Needle-free injection (NFI) is a critical technology for avoiding needlestick injuries and pain, yet existing methods face significant trade-offs:

• Conventional NFI (Spring/Gas-driven): Produces diffused jets that cause excessive pain and tissue damage due to large injection volumes and wide dispersion.
• Laser-Induced Jets: Produce highly focused, high-velocity jets suitable for shallow skin delivery but suffer from high costs, potential cavitation damage, and thermal denaturation of drugs.
• The Gap: There is a need for a cost-effective, laser-free method that generates highly focused, high-velocity jets capable of penetrating human skin (requiring velocities >75 m/s) even with high-viscosity liquids. Furthermore, the fundamental penetration mechanisms of these focused jets into soft materials were not fully understood, particularly regarding the role of jet morphology and internal velocity distribution.

2. Methodology

The authors developed and utilized an impact-induced jet generation system and compared it against laser-induced jets using skin-simulating materials (gelatin).

• Experimental Setup:
  • Impact-Induced Jet: A container with liquid is dropped onto a metal block. The abrupt stop creates an impact force that accelerates the liquid through a tapered PVC nozzle, focusing it at a concave gas–liquid interface. This system achieved velocities exceeding 100 m/s.
  • Laser-Induced Jet (Control): A pulsed green laser (532 nm) focused onto a liquid meniscus in a capillary tube to generate a micro-jet.
  • Target Materials: Gelatin solutions (3 wt% and 5 wt%) were used to mimic human subcutis and epidermis stiffness, respectively.
  • Variables: The study systematically varied:
    • Jet tip velocity ($V_{jet\_tip}$) and root velocity ($V_{jet\_root}$).
    • Liquid kinematic viscosity ($\nu$): 1, 10, and 200 mm²/s (covering a wide range).
    • Shear modulus of gelatin ($G$): 978 Pa and 5542 Pa.
    • Offset distance ($D$): Distance from the nozzle meniscus to the target surface.
• Measurement: High-speed cameras (up to 200,000 fps) captured jet ejection and penetration. Velocity distributions were calculated by tracking the centroid displacement of volume elements within the jet.

3. Key Contributions & Findings

A. Penetration Mechanism: Root Velocity vs. Tip Velocity

• Discovery: Contrary to the conventional assumption that penetration is governed by the jet tip velocity, the study found that for impact-induced jets, penetration depth is governed by the velocity of the cylindrical jet root.
• Comparison: Even when impact-induced and laser-induced jets had similar tip velocities (~88 m/s), the impact-induced jet achieved twice the penetration depth (approx. 6 mm vs. 3 mm).
• Reasoning: The impact-induced jet maintains a high, nearly uniform velocity in its root region ($V_{jet\_root} \approx 49.3$ m/s), whereas the laser-induced jet has a much lower root velocity ($V_{jet\_root} \approx 23.8$ m/s). The bulk of the impact-induced jet (the root) continues to drive penetration after the tip enters, whereas the laser jet's bulk is expelled into the air.

B. Independence from Offset Distance ($D$)

• Observation: The penetration depth of impact-induced jets remained constant regardless of the offset distance $D$ between the nozzle and the target.
• Contrast: Laser-induced jets showed variable penetration depths depending on $D$ because their conical tip morphology changes with distance.
• Implication: The cylindrical structure of the impact-induced jet root provides superior controllability and consistency for practical applications.

C. Failure of Conventional Models

• Systematic experiments varying viscosity and stiffness revealed that existing models (based on the Viscous Shear Stress model or elastic Froude number) failed to predict penetration depth across the wide range of parameters. Specifically, the data did not collapse onto a single master curve when plotted against the Reynolds number ($Re$), indicating that viscous shear dissipation along the jet side was not the dominant energy loss mechanism.

D. Proposal of the "Shear Deformation Model"

• New Framework: The authors proposed a Shear Deformation Model based on the observation that voids form between the cylindrical jet and the gelatin, preventing continuous viscous shear contact.
• Mechanism: Penetration is driven by the conversion of the jet's kinetic energy into shear deformation energy of the target material.
• Mathematical Formulation:
  $$\frac{P}{d_{jet}} = 0.91 \cdot \left( \frac{\rho (V_{jet\_root} - U_c)^2}{G} \cdot \frac{l}{d_{jet}} \right)^{1/3}$$
  Where:
  • $P$: Penetration depth
  • $d_{jet}$: Nozzle diameter
  • $V_{jet\_root}$: Root velocity
  • $U_c$: Critical penetration velocity
  • $G$: Shear modulus of the material
  • $l$: Effective jet length
• Validation: The experimental data showed excellent agreement with this model (fitting coefficient 0.60), suggesting that ~66% of the jet's kinetic energy is converted into shear deformation energy.

4. Significance and Impact

• Scientific Advancement: The study fundamentally shifts the understanding of liquid jet penetration in soft materials, identifying the cylindrical root region and shear deformation as the governing factors rather than tip velocity or viscous shear stress.
• Technological Application: The impact-induced jet system offers a low-cost, laser-free alternative for needle-free injection that can handle high-viscosity biofluids (up to 200 mm²/s) with high precision and minimal invasiveness.
• Future Outlook: The proposed shear deformation model provides a unified physical framework for optimizing needle-free drug delivery systems, particularly for targeting specific skin layers (e.g., Langerhans cells) and delivering viscous therapeutics without the thermal risks associated with lasers.

In summary, this paper demonstrates that impact-induced jets outperform laser-induced jets in penetration depth due to their unique high-velocity root structure and proposes a new shear-deformation-based physical model that accurately predicts penetration behavior across a wide range of viscosities and material stiffnesses.