A novel way to measure the rheology of liquids
Thesis DisciplineMechanical Engineering
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
Many liquid samples do not easily lend themselves to standard rheometry techniques. Consequently, it is important to find a novel way of measuring the rheology of liquids without using a rheometer.
This thesis explores the rheology measurement of Newtonian and non-Newtonian fluids by monitoring the effect of flow perturbation on the free surface velocity. A dam-break problem was considered, in which the release of a gate initially separating two fluid pools of different depths was performed. Three different liquids were used to implement the experiment, namely silicone oil, aqueous glycerol, and molasses. By seeding the free surface with buoyant particles, the flow velocity was measured using particle tracking velocimetry. A mathematical model based on the lubrication approximation for fluids with a power-law rheology was developed. This model was validated against a similarity solution, which could be obtained for the spreading of a gravity current under its own weight, and by neglecting surface tension.
The parametric identification of the rheological parameters was validated with synthetic data. Subsequently, the identification procedure was tested with noisy synthetic dataset and was found to be valid even when up to 40% noise was added to the ideal dataset. Minimizing the difference between the free surface velocity fields obtained numerically and those measured experimentally enabled the identification of rheological parameters. The methodology was tested on silicone oil, aqueous glycerol, and molasses, and the results were compared with the rheometer measurements. We found that the silicone oil and the aqueous glycerol were Newtonian, whereas the molasses were non-Newtonian. Moreover, the power-law model worked precisely with Newtonian fluids. Consequently, the Ellis rheological model was suggested. The model was validated against a Navier–Stokes solver. The identification process of the rheological parameters mentioned above was repeated with the same validation and testing procedures in terms of the Ellis model. The parametric identification results in terms of the Ellis model matched closer with the rheometer data compared to the power law model for the molasses.
Finally, the parametric identification of the rheological parameters of both the power-law and Ellis models were based on the lubrication approximation. The lubrication approximation is an approximation form of the Navier–Stokes equations. The difference between the two models was calculated using the reconstructed rheological parameters of the fluids used. We found that the difference between the lubrication approximation and the Navier–Stokes equations was influenced by the inertia effects and the aspect ratio. This implies the lubrication approximation cannot accurately predict the dynamics of the flow when the inertia effects are high. When the aspect ratio is significant, the lubrication approximation cannot accurately capture the behaviour of the dam-break flow configuration. An extension of this part is the non-dimensionalisation of the lubrication approximation and the Navier–Stokes equations based on the power law initially, followed by the Ellis model. The non-dimensionalisation process was implemented by substituting scale variables into the lubrication approximation and the Navier–Stokes equations, where dimensionless expressions for both models including the Reynolds, Froude, and Bond numbers were obtained. Here, an important aspect is the effect of using the range of dimensionless numbers that agree between the two models. The results show that the compatibility is better with the Reynolds number of approximately 1 and an aspect ratio of up to 0.02.
The following papers and conference, based on sections of this thesis, have appeared or published under review.
-Morris, S., Sellier, M. and AL-Behadili, A.J.M. (2017). Comparison of lubrication approximation and Navier–Stokes solutions for dam-break flows in thin films. - AL-Behadili, A.J.M., Sellier, M., Nokes, R., Moyers, M. and Geoghegan, P.H. (2017). Rheology Based On Free Surface Velocity. Submitted under review in Inverse Problem in Science and Engineering. - Sellier, M., AL-Behadili, A.J.M. and Morris, S. (2017). Rheometry based of free surface velocity for the dam-break problem. In: The 8th Biennial Australian Colloid & Interface Symposium (ACIS), Sydney, Australia. Pages 1-22. - Sellier, M., AL-Behadili, A.J.M. Hewett, J. and Devaud, L. (2017). Spreading laws of gravity current and their application to lava viscometry. In: Viscoplastic Fluids Workshop: From Theory to Applications, Rotorua, New Zealand.