Journal
MEASUREMENT SCIENCE AND TECHNOLOGY
Volume 22, Issue 12, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0957-0233/22/12/125402
Keywords
inverse problems; non-Newtonian flows; rheology; xanthan gum; fluid dynamics
Funding
- University of Sheffield
- EPSRC [EP/D004748, GR/S83746, EP/E01867X/1]
- Royal Academy of Engineering
- EPSRC [EP/E01867X/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/D004748/1, EP/E01867X/1] Funding Source: researchfish
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This paper is concerned with the determination of the constitutive viscous parameters of dilute solutions of xanthan gum by means of an inverse method used in conjunction with finite element modeling of the governing system of partial differential equations. At low concentrations xanthan gum behaves as a shear-thinning, power-law non-Newtonian fluid. Finite element modeling is used to simulate the pressure-driven flow of xanthan gum solutions in a microchannel T-junction. As the flow is forced to turn the corner of the T-junction a range of shear rates, and hence viscosities, is produced. It is shown that the statistical properties of the velocity field are sensitive to the constitutive parameters of the power-law model. The inverse method is shown to be stable and accurate, with measurement error in the velocity field translating to small errors in the rheological parameter estimation. Due to the particular structure of the inverse map, the error propagation is substantially less than the estimate from the Hadamard criterion.
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