Séminaire

Mardi 5 Février 2019 à 11h00.

Rheological studies of a model viscoplastic material and a natural cave sediment.

''In a first part, I will present the study of the internal dynamics (velocity profiles and shear rate) in the front of free-surface surges made of viscoplastic fluids. These flows are characterized by the presence of solid or quasi-solid zones (plug) that tend to develop close to the free-surface, where the shear stress is low [1]. The coexistence of solid and liquid zones renders the modelling of these free-surface flows particularly difficult. Velocity profile corrections should be taken into account to express the deviation from the steady uniform profile [2]. Our experimental works documents the internal dynamics of free-surface flows made of a model viscoplastic material (Carbopol). Then, these experimental data were compared to our theoretical predictions, based on asymptotic developments of the primitive equations [3]. The zeroth-order approximation, which is equivalent to the lubrication model, appears to satisfactorily capture the dynamics of the flow except in the tip of the surge front [4]. Considering order-1 corrective terms for the velocity profile, the model ensures better predictions for the velocity profiles in the front and remarkably captures the shape of the solid-fluid interface in this strongly non-uniform zone. Correction terms due to the existence of plastic normal stresses, which are specific to viscoplastic rheological behaviour, play an important role [5].
In a second part, I will present a rheological work developed at FAST (UMR 7608, CNRS/ Univ. Paris-Sud), in which I am currently a post-doc. I study there the rheology of a natural material (cave sediment). We showed that the nature of the cations exchanged between clays particles and the bulk plays an important role in the rheological behaviour of the sediment. This problematic becomes an important issue to protect paintings in prehistoric cave, like Lascaux one.

Ref :
1 Balmforth N.J. and Craster R.V. A consistent thin-layer theory for Bingham plastics, J. Non-Newton. Fluid Mech. 84 (1999), 65-81.
2 Ruyer-Quil Ch. and Manneville P. Improved modeling of flows down inclined planes. Eur. Phys. J. B 15 (2000), 357-369.
3 Fernandez-Nieto E. D., Noble P., Vila J.P. Shallow Water equations for Non-Newtonian fluids. J. Non-Newton. Fluid Mech. 165 (2010), 712-732.
4 Freydier P., Chambon G., Naaim M. Experimental characterization of velocity fields within the front of viscoplastic surges down an incline. J. Non-Newton. Fluid Mech. 240 (2017), 56-69.
5 Freydier P, Chambon G., Naaim M., and Vila J.P. Asymptotic expansion of velocity profiles within the front of viscoplastic surges: comparison with experiments, Submitted to J. Fluid Mech. Available on HAL.
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