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Open mathematical problems regarding non-Newtonian fluids

Wilson, HJ; (2012) Open mathematical problems regarding non-Newtonian fluids. NONLINEARITY , 25 (3) R45 - R51. 10.1088/0951-7715/25/3/R45. Green open access

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We present three open problems in the mathematical modelling of the ow of non-Newtonian fluids. The first problem is rather long standing: a discontinuity in the dependence of the rise velocity of a gas bubble on its volume. This is very well characterised experimentally but not, so far, reproduced either numerically or analytically. The other two are both instabilities. The first is observed experimentally but never fully predicted analytically or numerically. In the second instability, numerical studies reproduce the experimental observations but there is as yet no analytical or semi-analytical prediction of the linear instability which must be present.

Title:Open mathematical problems regarding non-Newtonian fluids
Open access status:An open access version is available from UCL Discovery
Publisher version:http://dx.doi.org/10.1088/0951-7715/25/3/R45
Additional information:© 2012 IOP Publishing Ltd & London Mathematical Society
UCL classification:UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Mathematics

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