Mathematical modelling of MEMS viscometers and densitometers
Mathematical modelling of MEMS viscometers and densitometers
Measurements of the density and viscosity of fluids are required to determine optimal production strategies in the exploitation of fossil fuel reservoirs and the monetary value of the fluid produced. In this work, we consider the analysis of two different designs of Micro Electrical Mechanical Systems (MEMS) that have been developed to determine both density and viscosity of fluids in situ.
The first device is a transversely oscillating plate, known as the spider. It is about 1.6 mm wide, 2.4 mm long and 200 μm thick. It is suspended from a 0.4 mm thick support by 24 square cross-section legs each of length 0.5 mm. Mathematical models have been produced for the plate operating in either forced or transient mode, intended for use in both Newtonian and non-Newtonian fluids. We only consider the general case of incompressible fluids, using the one dimensional diffusion equation to model Newtonian fluid motion and a reduced form of Maxwell’s equations for viscoelastic fluid motion.
The second MEMS device is based on a vibrating plate clamped along one edge, with dimensions of the order of 1 mm and a mass of ≈ 0.1 mg. The plate is set in motion when an alternating current is passed through the coil mounted on the plate in the presence of a magnetic field. At resonance, the plate motion is observed using a strain gauge. Mathematical models have been used in different limiting cases to analyse the behaviour of the device. Densities in the range (1 to 1800) kg m-3 and viscosities in the range (10 – 300000) Pa.s were determined experimentally with the vibrating plate in argon, methane, nitrogen, n-octane, methylbenzene and heptane.
University of Southampton
Ronaldson, Kelly Anne
da7c196f-7f45-4372-99d4-bf1cd9f6ea0e
2007
Ronaldson, Kelly Anne
da7c196f-7f45-4372-99d4-bf1cd9f6ea0e
Ronaldson, Kelly Anne
(2007)
Mathematical modelling of MEMS viscometers and densitometers.
University of Southampton, Doctoral Thesis.
Record type:
Thesis
(Doctoral)
Abstract
Measurements of the density and viscosity of fluids are required to determine optimal production strategies in the exploitation of fossil fuel reservoirs and the monetary value of the fluid produced. In this work, we consider the analysis of two different designs of Micro Electrical Mechanical Systems (MEMS) that have been developed to determine both density and viscosity of fluids in situ.
The first device is a transversely oscillating plate, known as the spider. It is about 1.6 mm wide, 2.4 mm long and 200 μm thick. It is suspended from a 0.4 mm thick support by 24 square cross-section legs each of length 0.5 mm. Mathematical models have been produced for the plate operating in either forced or transient mode, intended for use in both Newtonian and non-Newtonian fluids. We only consider the general case of incompressible fluids, using the one dimensional diffusion equation to model Newtonian fluid motion and a reduced form of Maxwell’s equations for viscoelastic fluid motion.
The second MEMS device is based on a vibrating plate clamped along one edge, with dimensions of the order of 1 mm and a mass of ≈ 0.1 mg. The plate is set in motion when an alternating current is passed through the coil mounted on the plate in the presence of a magnetic field. At resonance, the plate motion is observed using a strain gauge. Mathematical models have been used in different limiting cases to analyse the behaviour of the device. Densities in the range (1 to 1800) kg m-3 and viscosities in the range (10 – 300000) Pa.s were determined experimentally with the vibrating plate in argon, methane, nitrogen, n-octane, methylbenzene and heptane.
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Published date: 2007
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Local EPrints ID: 466109
URI: http://eprints.soton.ac.uk/id/eprint/466109
PURE UUID: 634e8b62-9f3f-487c-b5aa-e14bc9ef6efd
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Date deposited: 05 Jul 2022 04:22
Last modified: 16 Mar 2024 20:31
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Author:
Kelly Anne Ronaldson
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