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Mechanical Engineering. UCSB

Monday, August 20, 2007 Can change this on the Master Slide 0


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


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




S. MacKenzie

Schematic of the LIMMPET device.

COMSOL Conference 2019 Boston

5mm




S. MacKenzie

LIMMPET device.


Wimshurst machine.arborsci.com/products/wimshurst-machine

20mm100mm




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




S. MacKenzie

Schematic of the LIMMPET device.


5mm


Operation

S. MacKenzie 7

Charge seeded.


Induced charge

separation.

Charge

separation.

Charge

collection.

4-Step Energy

Harvesting

Process

1

23

4


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


Theory

S. MacKenzie 9

Charge Amplification Factor


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 =


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


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.


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


Integration domains

for 𝑞𝑓 and 𝑞𝑖.

Time dependent charge amplification factor.

Γ = ൗ𝑞𝑓

𝑞𝑖 = 1.43


12


Design Process

1. Channel width ratio

1.43 2.01Γ = ൗ𝑞𝑓

𝑞𝑖



13


Design Process


2. Curvature

1.43 Γ = ൗ𝑞𝑓

𝑞𝑖1.80



14


Design Process


2. Curvature

3. Channel gap distance

1.80 Γ = ൗ𝑞𝑓

𝑞𝑖1.80



15


Design Process


2. Curvature

3. Channel gap distance

1.80

2.32

2.761.43



Results – Charge Amplification Factor



Fabrication and Testing



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


• Match experimental charge accumulation with

predicted charge amplification factor.

• Model the full dynamic process, including droplet

generation and flow dynamics, in COMSOL

Multiphysics®.


S. MacKenzie 19

Thank you!

Questions?


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