Fingering instabilities in Newtonian and non-Newtonian fluids

Kennedy, Kristi E. (2007) Fingering instabilities in Newtonian and non-Newtonian fluids. Doctoral (PhD) thesis, Memorial University of Newfoundland.

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Abstract

Fingering has been studied in different fluid systems. Viscous fingering, which is driven by a difference in viscosity between fluids, has been studied by both experiments and numerical simulations. We used a single fluid with a temperature dependent viscosity and studied the instability for a range of inlet pressures and viscosity ratios. The spreading and fingering of a fluid drop subjected to a centrifugal force, known as spin coating, has also been studied for a range of drop volumes and rotation speeds, both for a Newtonian and a non-Newtonian fluid. -- Experiments on viscous fingering with a single fluid, glycerine, show that an instability occurs at the boundary separating hot and cold fluid. The results indicate that the instability is similar to that which occurs between two miscible fluids. Fingering only occurs for high enough values of the inlet pressure and viscosity ratio. The wavelength of the fingering pattern is found to be proportional to the cell width for the two smallest cell widths used. The fingering patterns seen in the simulations are very similar to the experimental patterns, although there are some quantitative differences. In particular, the wavelength of the instability is seen to depend only weakly on the cell width. -- The spreading of silicone oil, a Newtonian fluid, during spin coating follows the time dependence predicted theoretically, although with a shift in the scaled time variable. Once the radius of the spreading silicone oil drop becomes large enough, fingers form around the perimeter of the drop for all experimental conditions studied. The number of fingers and the growth rate of the fingers are in agreement with theoretical predictions. Fingers are also observed to form for high enough drop volumes and rotation speeds during the spinning of a non-Newtonian fluid drop, Carbopol, which possesses a yield stress. In this case the fingering is a localized effect, occuring once the stress on the drop exceeds the yield stress, rather than the result of an instability as in the Newtonian case.

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