Assessing Mechanisms Responsible for

Non-Homogenous Emitter Electrospray from

Large Arrays of FEEP and Colloid Thrusters

capillary feed concept

ionic liquid ion – Colloid Thruster• charged droplets• alternate droplet charge

liquid metal ion – FEEP Thruster• atomic ions• relatively large electric field• high efficiency• liquid metals do not wet Si

Emitter Operation

liqu

id f

eed

Taylor cone

capillary feedand electrode

extractor electrode

ion spray

Taylor cone

extractor electrode

ion spray

needleemitter

liquid pool

• N range for thrust – requires cluster of emitters

• geometry not optimized

single emitter geometry (capillary, slit, ring, needle, …)

array spacing

• unstable emitter operation

• non-homogenous ion emission from arrays of emitters Lozano and Martinez-Sanchez (2005)

Mechanisms investigated:

• internal and external liquid feed structures

• charge depletion with ionic liquids (AC potential)

• wetting characteristics

• extrusion electrode geometry

Mechanisms not yet investigated:

• thin film stability

• surface tension flows (Marangoni)

• body & surface forces via charge

• film rupture (dispersion forces)

• capillary-driven flow (curvature)

Non-Homogenous Emitter Electrospray

single emitter considerations

dependent upon: • single emitter geometry• single emitter operation• array geometry • array operation

Goal is stable liquid feed with homogenous electrospray over emitter array.

Pliq,needle = /R(z)

Pliq,base = /r – 1/Rbase)

Pliq,film = 0

curvature-induced flow

neglecting gas pressure:- liquid pressure decreases towards base of cone- liquid pressure increase at base due to 1/r- liquid pressure lowest in film

Requires external force to stabilize liquid film.

vapor/gas/vacuum

liquid

solid

x

z

h'(x',t')

Ti(x)

J

h0

thin film stability

• surface temperature variations drive Marangoni flow• body forces drive convective flows (gravitational, ion drag, …) • charge accumulation on surface may perturb film • evaporation changes surface temperature • vapor (ion) recoil may perturb film• dispersion forces drive film rupture

Film stabilizing/destabilizing mechanisms not understood.

Technical Approach – Film Stability

One-sided linear stability film evolution:

Surface Tension - Disjoining Pressure Surface Tension - Gravitational

• begin with 1D formulation to determine primary film destabilization mechanisms• conduct simple validation experiments• develop 3D formulation for assessing film stability for specific emitter geometries

Technical Approach – Minimum Energy Film Morphology

Use Surface Evolver to:• determine low energy liquid morphology for emitter array• determine linear stability limits of each morphology• optimize array geometry for stable liquid feed to emitter tips

Minimum energy morphology for fixed liquid volume in a flattened tube for various contact angles. Braun (2008)

Surface Evolver – Energy Minimization Code

Minimum energy and linear stability map for liquid in a cylindrical tube.

Allen, Son & Collicott (2009)

Anticipated Results

Establish stable liquid film:

• define the coupling of mechanisms of which stabilize or destabilize thin liquid films – both metal and ionic liquids

• validate stability model with planar film experiments

• predict film destabilization modes for emitter geometries

• optimize emitter geometry and array pattern for stable film morphology

Establish stable, homogenous elecrospray:

• stable, uniform liquid feed to array of electrodes

• define envelope for operating conditions