High specific impulse electrospray propulsion with small capillary emitters

This study demonstrates that using smaller capillary emitters (15–50 μm) with ionic liquids enables stable cone-jet operation at lower flow rates, effectively doubling specific impulse to 3000 s while revealing that propellant losses at low flow rates can compromise time-of-flight measurements.

The Gist

Imagine you are trying to push a heavy shopping cart up a hill. The "fuel" you use is a special liquid, and the "push" comes from a powerful electric field. This is the basic idea behind electrospray propulsion, a technology used to steer tiny satellites in space.

For a long time, scientists thought that to get the best performance (called "specific impulse," or how far you can go on a drop of fuel), you needed a specific size of nozzle. But this new study from the University of California, Irvine, discovered a surprising secret: smaller nozzles actually work much better.

Here is the breakdown of their discovery using some everyday analogies:

1. The Problem: The "Big Hose" vs. The "Fine Mist"

Think of the propellant (the fuel) as water.

• Old Method (Large Emitters): Imagine trying to spray water using a garden hose with a wide opening. To get a steady stream, you need a lot of water pressure and a high flow rate. The water comes out in big, heavy droplets. In space terms, these heavy droplets don't travel very fast, so the satellite doesn't get a very efficient "kick."
• New Method (Small Emitters): Now, imagine using a very fine misting nozzle, like the kind on a perfume bottle. You can get a steady, ultra-fine mist with very little water. The droplets are tiny and light.

The researchers tested this by making "nozzles" (called capillary emitters) out of tiny glass tubes. They made them in different sizes, ranging from a thick straw (50 micrometers) down to a very fine needle (15 micrometers).

2. The Surprise: Smaller is More Stable

The big surprise was that the smallest nozzles were actually more stable than the big ones.

• The Analogy: Think of a Taylor cone (the shape the liquid makes before it sprays) like a spinning top. With a wide nozzle, the top wobbles if you try to spin it too slowly. But with the tiny needle, the top spins perfectly steady even at very low speeds.
• The Result: Because the tiny nozzles could handle much lower flow rates without breaking apart, the researchers could spray the fuel much more slowly. Slower flow meant the electric field could accelerate the particles to much higher speeds.

3. The Payoff: Double the Efficiency

Because they could spray the fuel so slowly and steadily with the tiny nozzles, they achieved twice the specific impulse compared to the larger nozzles.

• What this means: If a satellite usually needs 100 units of fuel to change its orbit, with these new tiny nozzles, it might only need 50 units to do the same job. This is a massive deal for satellites, which are often limited by how much fuel they can carry.
• The Numbers: They reached speeds equivalent to an efficiency of 3,000 seconds (a standard way to measure rocket efficiency), which is incredibly high for this type of engine.

4. The "Ghost" Problem: When Fuel Disappears

There was a catch, though. When they turned the flow down to the absolute minimum (the "pure ion" mode), they noticed something weird.

• The Analogy: Imagine you are paying for a taxi ride. You pay the driver (the electric field) to take you somewhere. But at very low speeds, some of the passengers (the fuel) decided to jump out of the car and walk away before the driver could pick them up.
• The Science: At these extremely low flow rates, the liquid gets so hot from the electricity (like friction) that some of it evaporates into invisible gas before it gets pushed. This gas doesn't get accelerated, so it's wasted fuel.
• The Lesson: This made their measurement tools (which calculate speed based on how long it takes particles to fly) unreliable at the very lowest settings because they were counting "ghost" fuel that wasn't actually contributing to the push.

5. Why This Matters

This study proves that by shrinking the size of the spray nozzle, we can make satellite thrusters much more efficient.

• Before: You needed a "garden hose" approach, which was okay but not great.
• Now: We know that a "perfume mist" approach works better, allowing satellites to stay in space longer, maneuver more precisely, and carry less fuel.

In a nutshell: By making the spray nozzle smaller, the researchers found a way to turn a heavy, slow spray into a lightning-fast, efficient mist, doubling the performance of these tiny space engines.

Technical Summary

1. Problem Statement

Electrospray propulsion (ESP) is a promising micropropulsion technology for satellites, offering high specific impulse ($I_{sp}$) and efficiency. However, traditional ESP systems using capillary emitters (internally fed) typically operate in a droplet-dominated regime, limiting their maximum $I_{sp}$ compared to externally wetted or porous emitters, which can achieve ion-dominated regimes.

A prevailing theory in electrospray physics suggests that the minimum stable flow rate ($\dot{m}_{min}$) of a cone-jet is determined solely by the propellant's physical properties (viscosity, conductivity, surface tension) and is independent of the emitter's geometric dimensions, provided the emitter diameter is significantly larger than the jet diameter. This study challenges that assumption, hypothesizing that reducing the capillary emitter tip diameter could stabilize smaller Taylor cones, lower the minimum flow rate, and thereby significantly increase the achievable specific impulse while retaining the operational robustness of capillary emitters.

2. Methodology

The researchers conducted an experimental investigation using four different ionic liquids as propellants:

• EMI-Im (1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide)
• EMI-TFA (1-ethyl-3-methylimidazolium trifluoroacetate)
• EAN (Ethylammonium nitrate)
• BMI-TCM (1-butyl-3-methylimidazolium tricyanomethanide)

Experimental Setup:

• Emitters: Fused silica capillaries with tip diameters ranging from 15 µm to 50 µm. The tips were coated with iridium for electrical conductivity.
• Environment: Experiments were performed in a vacuum chamber ($10^{-3}$ Pa).
• Operation: A high voltage (up to ~1.5 kV) was applied between the emitter and a grounded extractor to form a stable Taylor cone-jet.
• Measurements:
  • Mass Flow Rate: Measured directly via a flow meter capillary (hydraulic resistance method) and indirectly via Time-of-Flight (TOF) integration.
  • Performance: Thrust, $I_{sp}$, and efficiency were derived from TOF signals and current measurements at an acceleration voltage of 10 kV.
  • Stability: The minimum flow rate was defined as the lowest flow rate where emission remained stable for >90% of the test duration.

3. Key Contributions

1. Geometric Dependence of Minimum Flow Rate: The study provides experimental evidence that the minimum stable flow rate is not solely a function of propellant properties but is significantly influenced by the emitter tip diameter. Smaller emitters allow for stable operation at much lower flow rates.
2. High $I_{sp}$ with Capillary Emitters: By utilizing 15 µm emitters, the authors achieved specific impulses up to 3000 s (for EAN), effectively doubling the performance previously observed with larger (50 µm) capillary emitters.
3. Regime Transitions: The research maps the continuous transition from droplet-dominated to mixed ion-droplet, and finally to pure ion-dominated regimes as flow rates decrease. Notably, the pure ion regime (previously associated only with porous/externally wetted emitters) was achieved with capillary emitters using BMI-TCM.
4. Limitations of TOF at Low Flow Rates: The study identifies a critical discrepancy between direct mass flow measurements and TOF-derived estimates at low flow rates, revealing that a significant fraction of propellant is lost as uncharged neutrals due to self-heating, rendering TOF unreliable for calculating $I_{sp}$ in ion-dominated regimes.

4. Key Results

• Emitter Size vs. Minimum Flow Rate: Reducing the emitter diameter from 50 µm to 15 µm reduced the minimum stable flow rate by more than an order of magnitude for all tested liquids. For example, EAN's minimum flow rate dropped from $5.0 \times 10^{-11}$ kg/s to $2.8 \times 10^{-12}$ kg/s.
• Specific Impulse ($I_{sp}$):
  • $I_{sp}$ scales inversely with the mass flow rate ($I_{sp} \propto \dot{m}^{-1/4}$).
  • With 15 µm emitters, $I_{sp}$ values reached ~3000 s (EAN) and ~1300 s (EMI-Im) at 10 kV, compared to ~600 s for 50 µm emitters.
  • Efficiencies remained above 50%, with some liquids reaching ~80% at higher flow rates.
• Beam Composition:
  • High Flow Rates: Droplet-dominated regime.
  • Intermediate Flow Rates: Mixed regime (ions and droplets).
  • Low Flow Rates: Pure ion regime (observed for BMI-TCM), where the beam consists almost entirely of ions, similar to porous emitters.
• Self-Heating Effects: Significant ohmic and viscous dissipation caused temperature rises of up to 700°C in the jet. This drastically altered propellant properties (conductivity, viscosity) and led to the evaporation of neutral species at low flow rates.
• TOF Bias: At low flow rates, the ratio of TOF-derived mass flow to actual mass flow ($\dot{m}'/\dot{m}$) dropped significantly (e.g., below 0.5), indicating that TOF underestimates mass loss due to neutral evaporation. Consequently, TOF-based $I_{sp}$ calculations become unreliable in the ion-dominated regime.

5. Significance

This study fundamentally alters the design paradigm for electrospray thrusters:

• Performance Optimization: It demonstrates that miniaturizing capillary emitters is a viable strategy to achieve the high specific impulse of porous emitters without sacrificing the stability and direct flow control of capillary systems.
• Mission Flexibility: The ability to operate in pure ion regimes with capillary emitters allows for higher thrust-to-power ratios and more efficient orbit raising maneuvers compared to traditional liquid metal FEEP thrusters.
• Theoretical Insight: The findings challenge the assumption that far-field geometry is irrelevant to cone-jet stability, suggesting that emitter diameter plays a crucial role in stabilizing the transition region at low flow rates.
• Diagnostic Warning: The paper highlights a critical limitation in current diagnostic techniques (TOF), showing that they may overestimate performance in ion-dominated regimes due to unmeasured neutral propellant losses caused by self-heating.

In conclusion, the authors successfully demonstrated that using sub-20 µm capillary emitters can double the specific impulse of ionic liquid electrospray thrusters, bridging the performance gap between capillary and porous emitter technologies.