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Thixotropic gravity currents

  • Duncan R. Hewitt (a1) and Neil J. Balmforth (a2)

We present a model for thixotropic gravity currents flowing down an inclined plane that combines lubrication theory for shallow flow with a rheological constitutive law describing the degree of microscopic structure. The model is solved numerically for a finite volume of fluid in both two and three dimensions. The results illustrate the importance of the degree of initial ageing and the spatio-temporal variations of the microstructure during flow. The fluid does not flow unless the plane is inclined beyond a critical angle that depends on the ageing time. Above that critical angle and for relatively long ageing times, the fluid dramatically avalanches downslope, with the current becoming characterized by a structured horseshoe-shaped remnant of fluid at the back and a raised nose at the advancing front. The flow is prone to a weak interfacial instability that occurs along the border between structured and de-structured fluid. Experiments with bentonite clay show broadly similar phenomenological behaviour to that predicted by the model. Differences between the experiments and the model are discussed.

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Alexandrou A. N., Constantinou N. & Georgiou G. 2009 Shear rejuvenation, aging and shear banding in yield stress fluids. J. Non-Newtonian Fluid Mech. 158, 617.
Balmforth N. J. & Craster R. V. 1999 A consistent thin-layer theory for Bingham plastics. J. Non-Newtonian Fluid Mech. 84, 6581.
Balmforth N. J., Craster R. V., Perona P., Rust A. C. & Sassi R. 2006a Viscoplastic dam breaks and the Bostwick consistometer. J. Non-Newtonian Fluid Mech. 142, 6378.
Balmforth N. J., Craster R. V., Rust A. C. & Sassi R. 2006b Viscoplastic flow over an inclined surface. J. Non-Newtonian Fluid Mech. 139, 103127.
Balmforth N. J., Craster R. V. & Sassi R. 2002 Shallow viscoplastic flow on an inclined plane. J. Fluid Mech. 470, 129.
Balmforth N. J., Craster R. V. & Toniolo C. 2003 Interfacial instability in non-Newtonian fluid layers. Phys. Fluids 15, 33703384.
Barnes H. A. 1997 Thixotropy – a review. J. Non-Newtonian Fluid Mech. 70, 133.
Bonn D., Tanaka H., Coussot P. & Meunier J. 2004 Ageing, shear rejuvenation and avalanches in soft glassy materials. J. Phys.: Condens. Matt. 16, S4987S4992.
Chen K. P. 1993 Wave formation in the gravity-driven low Reynolds number flow of two liquid films down an inclined plane. Phys. Fluids A 5, 3038.
Coussot P., Nguyen Q. D., Huynh H. T. & Bonn D. 2002a Avalanche behaviour in yield stress fluids. Phys. Rev. Lett. 88, 175501.
Coussot P., Nguyen Q. D., Huynh H. T. & Bonn D. 2002b Viscosity bifurcation in thixotropic, yielding fluids. J. Rheol. 46, 573589.
Coussot P., Roussel N., Jarny S. & Chanson H. 2005 Continuous or catastrophic solid–liquid transition in jammed systems. Phys. Fluids 17, 011704.
Dullaert K. & Mewis J. 2006 A structural kinetics model for thixotropy. J. Non-Newtonian Fluid Mech. 139, 2130.
Henriquez J. & Simms P. 2009 Dynamics imaging and modelling of multilayer deposition of gold paste tailings. Minerals Engng 22, 128139.
Huppert H. E. 1982 The propagation of two-dimensional and axisymmetric viscous gravity currents over a rigid horizontal surface. J. Fluid Mech. 121, 4358.
Huynh H. T., Roussel N. & Coussot P. 2005 Ageing and free surface flow of a thixotropic fluid. Phys. Fluids 17, 033101.
Khaldoun A., Moller P., Fall A., Wegdam G., De Leeuw B., Méheust Y., Fossum J. O. & Bonn D. 2009 Quick clay and landslides of clayey soils. Phys. Rev. Lett. 103, 188301.
Lister J. R. 1992 Viscous flows down an inclined plane from point and line sources. J. Fluid Mech. 242, 631653.
Liu K. F. & Mei C. C. 1989 Slow spreading of a sheet of Bingham fluid on an inclined plane. J. Fluid Mech. 207, 505529.
Mewis J. & Wagner N. J. 2009 Thixotropy. Adv. Colloid Interface Sci. 147–148, 214227.
Moller P., Fall A., Chikkadi V., Derks D. & Bonn D. 2009 An attempt to categorize yield stress fluid behaviour. Phil. Trans. R. Soc. Lond. A 367, 51395155.
Moller P., Mewis J. & Bonn D. 2006 Yield stress and thixotropy: on the difficulty of measuring yield stress in practice. Soft Matt. 2, 274283.
Putz A. M. V. & Burghelea T. I. 2009 The solid–fluid transition in a yield stress shear thinning physical gel. Rheol. Acta 48, 673689.
Simms P., Williams M. P. A., Fitton T. G. & McPhail G. 2011 Beaching angles and evolution of stack geometry for thickened tailings – a review. In Paste 2011 Proceedings of the 14th International Seminar on Paste and Thickened Tailings, Perth, Australia (ed. Jewell R.J. & Fourie A.B.), pp. 323338.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
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