1. Andrew S. Ylitalo
Laboratory of Interfacial & Small Scale Transport {LIS2T}
Applied Physics
California Institute of Technology
Pasadena, CA 91125
Acknowledgments
Prof. Sandra M. Troian, Mentor and SURF Sponsor
Theodore G. Albertson, Co-mentor
Chengzhe Zhou, helpful discussions
Numerical Simulations of Taylor Cone Formation in
Microfluidic Electrospray Propulsion Systems
August 18, 2016 – Jorgensen 133
1

2. {LIS2T} Research Group 2
Micropropulsion  Micronewton
qz.com
Motivation - Micropropulsion
Hubble Telescope
Network of CubeSat Satellites
 Improved micropropulsion has
two key future space applications
amsat-uk.org
lisa.nasa.gov
LISA G-wave Detector

3. 3
SEM Image of Microemitter tips
(300 µm height)
Microfluidic Electrospray Propulsion (MEP)
MEP Device
{LIS2T} Research Group
3 MEP device operation – currently facing setbacks
microdevices.jpl.nasa.gov
microdevices.jpl.nasa.gov

4. 0.5 µm
4
Taylor Cone Dynamics
t = 0 – 106.164 nsec
Made by: T G Albertson
{LIS2T} Research Group
4
 The Taylor cone dynamics inform MEP
since Taylor cones are MEP ion sources
 Taylor cones are formed under strong
electric fields
 Taylor cones were studied in a parallel-
plate electrode geometry

5. Geometry and Domains
{LIS2T} Research Group
5
Vacuum
Liquid Metal
Liquid Surface
No-slip surfaces
Electrode Plate
r (nondimensional)
z(nondimensional) Dynamic variables
Φ Electric
potential
E Electric field
u(r,z,t) Velocity field
pLiq Pressure in
liquid
τ Rate-of-
strain tensor
=μ(∇u+(∇u)T)
Physical constants
r Liquid density
m Dynamic
viscosity
g Surface tension
e0 Vacuum
permittivity
2) Normal Stress Balance at surface
  2
Liq
u
u u p u
t
r m
 
      
 
Navier-Stokes equations
  20
ˆ ˆ ˆ
2
Liq Liqp n E n n
e
g      %
0u 
Incompressibility
2
0   E 
Boundary conditions:
0
0 (Top electrode)
(Liquid interface)V
 
 
Vacuum
Liquid Metal
Laplace’s equation
Boundary conditions:
1) No slip/impenetrability
0 (at solid boundary)u 
Numerical Model – System Definition

6. 6
Mesh
Zdnet.com
Increasing pixels = Increasing mesh density
Moving mesh (ALE)
Numerical Model – Meshing

7. 7
Model Improvements – Discarding Non-physical Results
{LIS2T} Research Group
7
 “Tip-streaming”: thin streams of liquid
extending vertically from Taylor cone tip
 Onset delayed by increasing mesh
density  non-physical
 Mesh can always be made dense
enough that field evaporation threshold
reached before tip-streaming
Mesh Elt. Length = L Mesh Elt. Length = L/4
Tip-streaming
Mesh
refinement

8. Model Improvements – Increasing Mesh Order
{LIS2T} Research Group
8
1st Order 2nd Order
Normal Stress Balance
along Liquid Surface
 
e
g  e      %20
ˆ ˆ ˆ
2
Liq Liqp n E n n
Capillary
Stress
Electric
Stress
Liquid
Metal
Vacuum
Capillary
Stress
Electric
Stress
 Normal stress balance errors were
reduced by increasing mesh order
Dynamic variables
E Electric field
pLiq Pressure in liquid
τ Rate-of-strain tensor
=μ(∇u+(∇u)T)
Physical constants
g Surface tension
e0 Vacuum permittivity

9. {LIS2T} Research Grou 9
Preliminary Results with
Improved Model

10. Preliminary Results – Comparison with Theory
(Zubarev 2001)
{LIS2T} Research Group
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

  /
2( ) ,
3elec cap cp t t
Critical "blow up" time
("coniccusping singularity")
ct 
*Assumes no vorticity in fluid
Predicted Behavior*
    /log logelec cap cp t t const
  Y X const
    /X log , logc elec capt t Y p
 Zubarev was the first to identify power
law behavior for cone formation dynamics
Comparison with theory for MEP conditions
 Disagreement in exponent β, but
preliminary results show power law
behavior persists
Log-log plot – slope gives exponent β
Slope-intercept form

11. Summary
{LIS2T} Research Group
11
 Importance of understanding Taylor
cone dynamics for micropropulsion
development
 Improvement of numerical model
 Comparison with mathematical theory
amsat-uk.org

12. {LIS2T} Research Grou 12
Thank you for your attention –
Questions?