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A fractional differential equation for a MEMS viscometer used in the oil industry. [In special issue: Analysis and Numerical Approximation of Singular Problems]

A fractional differential equation for a MEMS viscometer used in the oil industry. [In special issue: Analysis and Numerical Approximation of Singular Problems]
A fractional differential equation for a MEMS viscometer used in the oil industry. [In special issue: Analysis and Numerical Approximation of Singular Problems]
A mathematical model is developed for a micro-electro-mechanical system (MEMS) instrument that has been designed primarily to measure the viscosity of fluids that are encountered during oil well exploration. It is shown that, in one mode of operation, the displacement of the device satisfies a fractional differential equation (FDE). The theory of FDEs is used to solve the governing equation in closed form and numerical solutions are also determined using a simple but efficient central difference scheme. It is shown how knowledge of the exact and numerical solutions enables the design of the device to be optimised. It is also shown that the numerical scheme may be extended to encompass the case of a nonlinear spring, where the resulting FDE is nonlinear.
fractional differential equation, viscometer, densimeter, mems device
0377-0427
373-381
Fitt, A.D.
51b348d7-b553-43ac-83f2-3adbea3d69ab
Goodwin, A.R.H.
73088122-b05f-4a88-bc9b-eb4f5127489e
Ronaldson, K.A.
974f8386-7c90-4b24-819d-4f057e0d069d
Wakeham, W.A.
88549729-a39a-497f-b112-feaa6be2c449
Fitt, A.D.
51b348d7-b553-43ac-83f2-3adbea3d69ab
Goodwin, A.R.H.
73088122-b05f-4a88-bc9b-eb4f5127489e
Ronaldson, K.A.
974f8386-7c90-4b24-819d-4f057e0d069d
Wakeham, W.A.
88549729-a39a-497f-b112-feaa6be2c449

Fitt, A.D., Goodwin, A.R.H., Ronaldson, K.A. and Wakeham, W.A. (2009) A fractional differential equation for a MEMS viscometer used in the oil industry. [In special issue: Analysis and Numerical Approximation of Singular Problems]. Journal of Computational and Applied Mathematics, 229 (2), 373-381. (doi:10.1016/j.cam.2008.04.018).

Record type: Article

Abstract

A mathematical model is developed for a micro-electro-mechanical system (MEMS) instrument that has been designed primarily to measure the viscosity of fluids that are encountered during oil well exploration. It is shown that, in one mode of operation, the displacement of the device satisfies a fractional differential equation (FDE). The theory of FDEs is used to solve the governing equation in closed form and numerical solutions are also determined using a simple but efficient central difference scheme. It is shown how knowledge of the exact and numerical solutions enables the design of the device to be optimised. It is also shown that the numerical scheme may be extended to encompass the case of a nonlinear spring, where the resulting FDE is nonlinear.

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More information

Submitted date: 19 May 2007
Published date: 15 July 2009
Keywords: fractional differential equation, viscometer, densimeter, mems device

Identifiers

Local EPrints ID: 66696
URI: http://eprints.soton.ac.uk/id/eprint/66696
ISSN: 0377-0427
PURE UUID: 56e8aa14-d1d0-4a41-9c03-a896d5db531b

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Date deposited: 10 Jul 2009
Last modified: 26 Apr 2022 17:19

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Contributors

Author: A.D. Fitt
Author: A.R.H. Goodwin
Author: K.A. Ronaldson
Author: W.A. Wakeham

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