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Mechanical Engineering. UCSB
Monday, August 20, 2007 Can change this on the Master Slide 0
Mechanical Engineering. UCSB
Improved Charge Amplification in the
Liquid-Metal Microfluidic Portable
Energy Transducer (LiMMPET)
10/3/2019
S. MacKenzie, A. Eden, M. Prichard, B. Dutcher, C. Meinhart, D. Huber, M.T. Napoli, D. Weld, S. Pennathur
Department of Mechanical Engineering, University of California, Santa Barbara
Department of Physics, University of California, Santa Barbara
Mechanical Engineering. UCSB
Background: Energy Harvesters
COMSOL Conference 2019 Boston S. MacKenzie 2
F.-R. Fan, et al., Flexible triboelectric generator,
Nano Energy (2012)
Dagdeviren et al., Conformal piezoelectric
energy harvesting, PNAS (2014)
Gupta et al., Broadband Energy Harvester,
Scientific Reports (2017)
Source: R. Niewiroski, Wikipedia Source: AF.mil
Wang et al., Microsyst Technol
(2009) 15:941–951
Electromagnetic
Reverse Electrowetting
Piezoelectric
Triboelectric
Hybrid
Yang et al., Nano Energy (2016)
31:450-455
Mechanical Engineering. UCSB
Liquid-Metal Microfluidic Portable
Energy Transducer (LiMMPET)
S. MacKenzie
Schematic of the LIMMPET device.
COMSOL Conference 2019 Boston
5mm
Mechanical Engineering. UCSB
Liquid-Metal Microfluidic Portable
Energy Transducer (LiMMPET)
S. MacKenzie
LIMMPET device.
COMSOL Conference 2019 Boston
Wimshurst machine.arborsci.com/products/wimshurst-machine
20mm100mm
Mechanical Engineering. UCSB
Liquid-Metal Microfluidic Portable
Energy Transducer (LiMMPET)
S. MacKenzieCOMSOL Conference 2019 Boston
Electrostatic
induction causes
net charge
imbalance
Neutral droplet 𝑞𝑓 experiences induced
charge separation due to charged
droplets 𝑞𝑖 in lower channel.
Charge is transported out of 𝑞𝑓 if
connected to a conductor
Droplet 𝑞𝑓 maintains net charge
imbalance after pulling away
from conductor
Mechanical Engineering. UCSB
Liquid-Metal Microfluidic Portable
Energy Transducer (LiMMPET)
S. MacKenzie
Schematic of the LIMMPET device.
COMSOL Conference 2019 Boston
5mm
Mechanical Engineering. UCSB
Operation
S. MacKenzie 7
Charge seeded.
COMSOL Conference 2019 Boston
Induced charge
separation.
Charge
separation.
Charge
collection.
4-Step Energy
Harvesting
Process
1
23
4
Mechanical Engineering. UCSB
Theory
S. MacKenzie 8COMSOL Conference 2019 Boston
Breakdown-limited
max power output
Power dissipated
due to viscous drag
Efficiency
𝑃𝑚𝑎𝑥 =𝑞𝑚𝑎𝑥
𝐶𝑑𝑟𝑜𝑝𝑙𝑒𝑡2𝜋𝜎𝑚𝑎𝑥𝑣𝑤 = 𝜀0𝜀𝑟𝐸𝑚𝑎𝑥
2 𝜋𝑤2𝑣
𝑃𝑑𝑖𝑠𝑠𝑖𝑝𝑎𝑡𝑒𝑑 = Δ𝑃 = 32𝜂𝐿𝑣2
𝛼 =𝑃𝑚𝑎𝑥
𝑃𝑚𝑎𝑥 + 𝑃𝑑𝑖𝑠𝑠𝑖𝑝𝑎𝑡𝑒𝑑=
𝜀0𝜀𝑟𝐸𝑚𝑎𝑥2 𝜋𝑤2𝑣
𝜀0𝜀𝑟𝐸𝑚𝑎𝑥2 𝜋𝑤2𝑣 + 32𝜂𝐿𝑣2
𝜶 > 𝟗𝟓%Efficiency
Device Performance
Mechanical Engineering. UCSB
Theory
S. MacKenzie 9
Charge Amplification Factor
COMSOL Conference 2019 Boston
Effect of Γ on Power Generation
𝑄 = 𝐶 ∙ 𝑉
Analytical Calculation
Maxwell
Capacitance
Matrix
Charge
Accumulation
Rate
Γ = ൗ𝑞𝑓
𝑞𝑖Where 𝑞𝑓 is the induced charge on a droplet
and 𝑞𝑖 is the charge on an inducing droplet.
𝐶 =
Mechanical Engineering. UCSB
2D COMSOL Multiphysics ® Model: Overview
S. MacKenzie 10
Laminar Two-Phase Flow Equations
Electric Currents Equations
𝜕𝜙
𝜕𝑡+ 𝒖 ∙ ∇𝜙 = ∇ ∙
𝛾𝜆
𝜀2∇𝜓
𝜓 = −∇ ∙ 𝜀∇𝜙 + 𝜙2 − 1 +𝜀2
𝜆Τ𝜕f 𝜕𝜙
𝛾 = 𝜒𝜀2
∇ ∙ 𝑱 = 𝑄𝑗,𝑣
𝑱 = 𝜎𝑬 +𝜕𝐷
𝜕𝑡
𝑬 = −∇𝑉
Boundary Conditions
Electric Currents: 𝑉 = 0
Phase Field: Outlet
Initial Conditions
Electric Currents: 𝑉 = 0
Phase Field (droplets): 𝜙 = −1
Phase Field (else): 𝜙 = 1
1 11 2
2
2 2
Current Sources
𝑄𝑗,𝑣 = −𝑄0 ∗ 𝑓 𝑡
𝑄𝑗,𝑣 = 𝑄0 ∗ 𝑓 𝑡
1
2
Navier-Stokes
decomposed
Cahn-Hilliard
Equation
Charge Conservation
Ohm’s Law
Electric Potential
𝜌𝜕𝒖
𝜕𝑡+ 𝜌 𝒖 ∙ 𝛻 𝒖 = −𝑝𝑰 + 𝜇 𝛻𝒖 + 𝛻𝒖𝑇 + 𝑭𝑠𝑡
Mobility parameter
COMSOL Conference 2019 Boston
Material Oil Mercury
Density 1.766 g/cm3 13.55 g/cm3
Relative Permittivity 2.09 1
Conductivity 10-11 S/m 104384 S/m
Approximately 181,000 mesh elements in model.
Mechanical Engineering. UCSB
2D COMSOL Multiphysics ® Model: Results
S. MacKenzie 11
Field lines and space charge density for positively (red) and negatively (blue) charged droplets.
Time-Dependent Charge Redistribution Charge Amplification Factor
COMSOL Conference 2019 Boston
Integration domains
for 𝑞𝑓 and 𝑞𝑖.
Time dependent charge amplification factor.
Γ = ൗ𝑞𝑓
𝑞𝑖 = 1.43
Mechanical Engineering. UCSB
12
2D COMSOL Multiphysics ® Model: Results
Design Process
1. Channel width ratio
1.43 2.01Γ = ൗ𝑞𝑓
𝑞𝑖
S. MacKenzieCOMSOL Conference 2019 Boston
Mechanical Engineering. UCSB
13
2D COMSOL Multiphysics ® Model: Results
Design Process
1. Channel width ratio
2. Curvature
1.43 Γ = ൗ𝑞𝑓
𝑞𝑖1.80
S. MacKenzieCOMSOL Conference 2019 Boston
Mechanical Engineering. UCSB
14
2D COMSOL Multiphysics ® Model: Results
Design Process
1. Channel width ratio
2. Curvature
3. Channel gap distance
1.80 Γ = ൗ𝑞𝑓
𝑞𝑖1.80
S. MacKenzieCOMSOL Conference 2019 Boston
Mechanical Engineering. UCSB
15
2D COMSOL Multiphysics ® Model: Results
Design Process
1. Channel width ratio
2. Curvature
3. Channel gap distance
1.80
2.32
2.761.43
S. MacKenzieCOMSOL Conference 2019 Boston
Mechanical Engineering. UCSB
Results – Charge Amplification Factor
S. MacKenzie 16COMSOL Conference 2019 Boston
Mechanical Engineering. UCSB
Fabrication and Testing
S. MacKenzie 17COMSOL Conference 2019 Boston
Mechanical Engineering. UCSB
Summary
• COMSOL Multiphysics® was used to improve
charge amplification factor in the LIMMPET.
• Numerical analysis demonstrated the importance
of key geometric parameters such as channel
width ratio and curvature.
S. MacKenzie 18
Future Directions
COMSOL Conference 2019 Boston
• Match experimental charge accumulation with
predicted charge amplification factor.
• Model the full dynamic process, including droplet
generation and flow dynamics, in COMSOL
Multiphysics®.
Mechanical Engineering. UCSB
S. MacKenzie 19
Thank you!
Questions?
COMSOL Conference 2019 Boston
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