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Accueil du site > Évènements > Séminaires > Séminaires IUSTI > Archives IUSTI > 2016

Vendredi 29 Janvier 2016 / IUSTI

publié le

Séminaire régulier IUSTI

Some issues regarding the momentum and the heat transfer in yield stress fluids - about things should never happen (but actually do happen !)

Orateur : Téodor Burghelea
UMR 6607, Laboratoire de Thermocinétique de Nantes

Résumé : A straightforward way of testing our current understanding of the coupling between the flow and the rheological properties and microstructure of a non Newtonian fluid relates to describing “simple” hydrodynamic problems involving such fluids. One such problem is the slow (low Reynolds number) sedimentation of a spherical object. In the case of a yield stress fluid modelled by either the Bingham and Herschel-Bulkley model the numerical simulations reveal a fore-aft symmetric flow pattern as well as two symmetric rigid plugs located at the poles of the spherical object [1, 2]. Experiments performed with a Carpool gel reveal a strikingly different flow picture, however [3]. No fore-aft symmetry of the flow pattern is observed and, even more intriguing, a negative wake similar to that observed during experiments with a viscoelastic fluid is observed. Through the first part of the talk I will present in detail these experimental findings that “ring” a first bell that our understanding of the momentum transfer in a real viscoelastic fluid is far from being complete. A second basic fluid dynamics experiment universally recognised as a paradigm of pattern forming systems and bifurcation phenomena is the Rayligh-Bénard experiment. In the case of a viscoelastic fluid modelled by either the Bingham or the Herschel-Buckley model the hydrodynamic system is found to be linearly stable [4] and nonlinearly unstable, i.e. the convective states may be triggered if perturbation with a finite amplitude is applied [5]. The recent experimental results I will describe in the second part of my talk are at odds with both theoretical predictions, [6]. Thus, for the case of Carbopol gels with yield stresses spanning an extended range I will show that a transition to convective states is observed in the very absence of a finite perturbation via an imperfect bifurcation described by the Landau theory. The scope of the third part of my talk would be to theoretically “rationalise” the rather unexpected experimental findings presented in the first two parts. For this purpose I will present a “Poor Man Model” for the yielding of a Carbopol gel and test it against both shear and oscillatory rheological measurements, [7]. In spite of its simplicity (that fully justifies its name), the model is able to predict both irreversibility of the deformation states (rheological hysteresis) and elastic effects near the onset of the solid-fluid transition. Last and if the time permits, I will present a microscopic model of yielding derived from first principles by constructing a microscopic viscoplastic Hamiltonian and a partition function. It will be shown that this model is able to recover the main features of the solid-fluid transition observed in experiments and first captured by the “Poor Man Model”, [8].

  1. A. N. Beris, J. A. Tsamopoulos, R. C. Armstrong, and R. A. Brown, “Creeping motion of a sphere through a Bingham plastic,” J. Fluid Mech. 158, 219 1985.
  2. A. Putz, PhD thesis, University of British Columbia, Vancouver Canada.
  3. A. M. V. Putz, T. I. Burghelea, I. A. Frigaard and D. M. Martinez, “Settling of an isolated spherical particle in a yield stress shear thinning fluid ” Phys. Fluids 20, 033102 2008.
  4. J. Zhang, D. Vola, I.A. Frigaard, “Yield stress effects on Rayleigh–Bénard convection”, Journal of Fluid Mechanics 566 (2006) 389.
  5. N.J. Balmforth, A.C. Rust, “Weakly nonlinear viscoplastic convection”, Journal of Non-Newtonian Fluid Mechanics 158 (1–3) (2009) 36–45.
  6. Zineddine Kebiche, Cathy Castelain, Teodor Burghelea, “Experimental investigation of the Rayleigh– Bénard convection in a yield stress fluid” Journal of Non-Newtonian Fluid Mechanics 203 (2014) 9–23.
  7. A.M.V. Putz, T.I. Burghelea, “The solid–fluid transition in a yield stress shear thinning physical gel”, Rheologica Acta 48 (2009) 673–689.
  8. Raazesh Sainudiin, Miguel Moyers-Gonzalez and Teodor Burghelea, “A microscopic Gibbs field model for the macroscopic yielding behaviour of a viscoplastic fluid”, Soft Matter, 2015,11, 5531

    Date et lieu : le Vendredi 29 Janvier à 11h, salle 250, IUSTI