# Governing equations for electro-conjugate fluid flow

K. Hosoda, Kenjiro Takemura, Koji Fukagata, S. Yokota, K. Edamura

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

### Abstract

An electro-conjugation fluid (ECF) is a kind of dielectric liquid, which generates a powerful flow when high DC voltage is applied with tiny electrodes. This study deals with the derivation of the governing equations for electro-conjugate fluid flow based on the Korteweg-Helmholtz (KH) equation which represents the force in dielectric liquid subjected to high DC voltage. The governing equations consist of the Gauss's law, charge conservation with charge recombination, the KH equation, the continuity equation and the incompressible Navier-Stokes equations. The KH equation consists of coulomb force, dielectric constant gradient force and electrostriction force. The governing equation gives the distribution of electric field, charge density and flow velocity. In this study, direct numerical simulation (DNS) is used in order to get these distribution at arbitrary time. Successive over-relaxation (SOR) method is used in analyzing Gauss's law and constrained interpolation pseudo-particle (CIP) method is used in analyzing charge conservation with charge recombination. The third order Runge-Kutta method and conservative second-order-accurate finite difference method is used in analyzing the Navier-Stokes equations with the KH equation. This study also deals with the measurement of ECF ow generated with a symmetrical pole electrodes pair which are made of 0.3 mm diameter piano wire. Working fluid is FF-1EHA2 which is an ECF family. The flow is observed from the both electrodes, i.e., the flow collides in between the electrodes. The governing equation successfully calculates mean flow velocity in between the collector pole electrode and the colliding region by the numerical simulation.

Original language English Proceedings of SPIE - The International Society for Optical Engineering 8923 https://doi.org/10.1117/12.2033791 Published - 2013 Micro/Nano Materials, Devices, and Systems - Melbourne, VIC, AustraliaDuration: 2013 Dec 9 → 2013 Dec 11

### Other

Other Micro/Nano Materials, Devices, and Systems Australia Melbourne, VIC 13/12/9 → 13/12/11

### Fingerprint

Helmholtz equation
Helmholtz equations
fluid flow
Electrode
Fluid Flow
Flow of fluids
Governing equation
Helmholtz Equation
Charge
Conjugation
Electrodes
conjugation
electrodes
Dielectric liquids
Fluid
Fluids
Recombination
Flow velocity
Navier-Stokes equation
Navier Stokes equations

### Keywords

• Electro-conjugate uid
• Functional fluid
• Numerical simulation
• Particle image velocimetry

### ASJC Scopus subject areas

• Applied Mathematics
• Computer Science Applications
• Electrical and Electronic Engineering
• Electronic, Optical and Magnetic Materials
• Condensed Matter Physics

### Cite this

Hosoda, K., Takemura, K., Fukagata, K., Yokota, S., & Edamura, K. (2013). Governing equations for electro-conjugate fluid flow. In Proceedings of SPIE - The International Society for Optical Engineering (Vol. 8923). [89234Z] https://doi.org/10.1117/12.2033791

Governing equations for electro-conjugate fluid flow. / Hosoda, K.; Takemura, Kenjiro; Fukagata, Koji; Yokota, S.; Edamura, K.

Proceedings of SPIE - The International Society for Optical Engineering. Vol. 8923 2013. 89234Z.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Hosoda, K, Takemura, K, Fukagata, K, Yokota, S & Edamura, K 2013, Governing equations for electro-conjugate fluid flow. in Proceedings of SPIE - The International Society for Optical Engineering. vol. 8923, 89234Z, Micro/Nano Materials, Devices, and Systems, Melbourne, VIC, Australia, 13/12/9. https://doi.org/10.1117/12.2033791
Hosoda K, Takemura K, Fukagata K, Yokota S, Edamura K. Governing equations for electro-conjugate fluid flow. In Proceedings of SPIE - The International Society for Optical Engineering. Vol. 8923. 2013. 89234Z https://doi.org/10.1117/12.2033791
Hosoda, K. ; Takemura, Kenjiro ; Fukagata, Koji ; Yokota, S. ; Edamura, K. / Governing equations for electro-conjugate fluid flow. Proceedings of SPIE - The International Society for Optical Engineering. Vol. 8923 2013.
@inproceedings{856232f3fb944034a09024d8a1434978,
title = "Governing equations for electro-conjugate fluid flow",
abstract = "An electro-conjugation fluid (ECF) is a kind of dielectric liquid, which generates a powerful flow when high DC voltage is applied with tiny electrodes. This study deals with the derivation of the governing equations for electro-conjugate fluid flow based on the Korteweg-Helmholtz (KH) equation which represents the force in dielectric liquid subjected to high DC voltage. The governing equations consist of the Gauss's law, charge conservation with charge recombination, the KH equation, the continuity equation and the incompressible Navier-Stokes equations. The KH equation consists of coulomb force, dielectric constant gradient force and electrostriction force. The governing equation gives the distribution of electric field, charge density and flow velocity. In this study, direct numerical simulation (DNS) is used in order to get these distribution at arbitrary time. Successive over-relaxation (SOR) method is used in analyzing Gauss's law and constrained interpolation pseudo-particle (CIP) method is used in analyzing charge conservation with charge recombination. The third order Runge-Kutta method and conservative second-order-accurate finite difference method is used in analyzing the Navier-Stokes equations with the KH equation. This study also deals with the measurement of ECF ow generated with a symmetrical pole electrodes pair which are made of 0.3 mm diameter piano wire. Working fluid is FF-1EHA2 which is an ECF family. The flow is observed from the both electrodes, i.e., the flow collides in between the electrodes. The governing equation successfully calculates mean flow velocity in between the collector pole electrode and the colliding region by the numerical simulation.",
keywords = "Electro-conjugate uid, Functional fluid, Numerical simulation, Particle image velocimetry",
author = "K. Hosoda and Kenjiro Takemura and Koji Fukagata and S. Yokota and K. Edamura",
year = "2013",
doi = "10.1117/12.2033791",
language = "English",
isbn = "9780819498144",
volume = "8923",
booktitle = "Proceedings of SPIE - The International Society for Optical Engineering",

}

TY - GEN

T1 - Governing equations for electro-conjugate fluid flow

AU - Hosoda, K.

AU - Takemura, Kenjiro

AU - Fukagata, Koji

AU - Yokota, S.

AU - Edamura, K.

PY - 2013

Y1 - 2013

N2 - An electro-conjugation fluid (ECF) is a kind of dielectric liquid, which generates a powerful flow when high DC voltage is applied with tiny electrodes. This study deals with the derivation of the governing equations for electro-conjugate fluid flow based on the Korteweg-Helmholtz (KH) equation which represents the force in dielectric liquid subjected to high DC voltage. The governing equations consist of the Gauss's law, charge conservation with charge recombination, the KH equation, the continuity equation and the incompressible Navier-Stokes equations. The KH equation consists of coulomb force, dielectric constant gradient force and electrostriction force. The governing equation gives the distribution of electric field, charge density and flow velocity. In this study, direct numerical simulation (DNS) is used in order to get these distribution at arbitrary time. Successive over-relaxation (SOR) method is used in analyzing Gauss's law and constrained interpolation pseudo-particle (CIP) method is used in analyzing charge conservation with charge recombination. The third order Runge-Kutta method and conservative second-order-accurate finite difference method is used in analyzing the Navier-Stokes equations with the KH equation. This study also deals with the measurement of ECF ow generated with a symmetrical pole electrodes pair which are made of 0.3 mm diameter piano wire. Working fluid is FF-1EHA2 which is an ECF family. The flow is observed from the both electrodes, i.e., the flow collides in between the electrodes. The governing equation successfully calculates mean flow velocity in between the collector pole electrode and the colliding region by the numerical simulation.

AB - An electro-conjugation fluid (ECF) is a kind of dielectric liquid, which generates a powerful flow when high DC voltage is applied with tiny electrodes. This study deals with the derivation of the governing equations for electro-conjugate fluid flow based on the Korteweg-Helmholtz (KH) equation which represents the force in dielectric liquid subjected to high DC voltage. The governing equations consist of the Gauss's law, charge conservation with charge recombination, the KH equation, the continuity equation and the incompressible Navier-Stokes equations. The KH equation consists of coulomb force, dielectric constant gradient force and electrostriction force. The governing equation gives the distribution of electric field, charge density and flow velocity. In this study, direct numerical simulation (DNS) is used in order to get these distribution at arbitrary time. Successive over-relaxation (SOR) method is used in analyzing Gauss's law and constrained interpolation pseudo-particle (CIP) method is used in analyzing charge conservation with charge recombination. The third order Runge-Kutta method and conservative second-order-accurate finite difference method is used in analyzing the Navier-Stokes equations with the KH equation. This study also deals with the measurement of ECF ow generated with a symmetrical pole electrodes pair which are made of 0.3 mm diameter piano wire. Working fluid is FF-1EHA2 which is an ECF family. The flow is observed from the both electrodes, i.e., the flow collides in between the electrodes. The governing equation successfully calculates mean flow velocity in between the collector pole electrode and the colliding region by the numerical simulation.

KW - Electro-conjugate uid

KW - Functional fluid

KW - Numerical simulation

KW - Particle image velocimetry

UR - http://www.scopus.com/inward/record.url?scp=84893920216&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84893920216&partnerID=8YFLogxK

U2 - 10.1117/12.2033791

DO - 10.1117/12.2033791

M3 - Conference contribution

AN - SCOPUS:84893920216

SN - 9780819498144

VL - 8923

BT - Proceedings of SPIE - The International Society for Optical Engineering

ER -