Abstract
A novel design for a microrheometer is simulated and tested using finite element modeling techniques. Non-Newtonian fluid obeying the Carreau viscosity model is driven through a microchannel T-junction using electro-osmosis. A range of shear rates, and hence viscosities, is produced as the fluid is forced to turn the corner of the T-junction. Thus, the design has the potential to enable the constitutive viscous parameters to be determined from a single microfluidic experiment. Three-dimensional simulations are performed for a broad range of Carreau constitutive parameters. The pressure fields on the microchannel walls, floor, and ceiling are shown to be sensitive to the Carreau parameters that determine the fluid’s shear-thinning behavior. The fluid dynamics theory and numerical results described in this article pave the way for a detailed analysis of the corresponding inverse problem, that is, to determine the values of the Carreau constitutive parameters from the pressure field measured by optimal positioning of cheap piezo electric pressure transducers embedded into the inner surface of the microchannel network.
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Notes
SPOOLES is a library for solving sparse real and complex linear systems of equations, written in the C language, and is available from http://www.netlib.org/linalg/spooles/.
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Acknowledgments
WZ acknowledges support from EPSRC Grant Nos. GR/A01435 and GR/S83746. TC would like to thank the University of Sheffield for a doctoral scholarship. We acknowledge support from the EPSRC Grant EP/E01867X/1 (Bridging the Gap between Mathematics, ICT and Engineering Research at Sheffield).
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Craven, T.J., Rees, J.M. & Zimmerman, W.B. Pressure sensor positioning in an electrokinetic microrheometer device: simulations of shear-thinning liquid flows. Microfluid Nanofluid 9, 559–571 (2010). https://doi.org/10.1007/s10404-010-0573-8
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DOI: https://doi.org/10.1007/s10404-010-0573-8