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Motion onset in simple yield stress fluids

Published online by Cambridge University Press:  05 February 2021

K.D. Jadhav
Affiliation:
Department of Mechanical, Industrial and Aerospace Engineering, Concordia University, Montreal, QCH3G1M8, Canada
P. Rossi
Affiliation:
Department of Mechanical, Industrial and Aerospace Engineering, Concordia University, Montreal, QCH3G1M8, Canada
I. Karimfazli*
Affiliation:
Department of Mechanical, Industrial and Aerospace Engineering, Concordia University, Montreal, QCH3G1M8, Canada
*
Email address for correspondence: [email protected]

Abstract

We present an experimental investigation of motion onset in simple yield stress fluids. In this context, motion onset refers to the transition from the motionless steady state to a steady flow, as well as the development of motion in a fluid initially at rest. We consider the natural convection of carbopol microgels in a square cavity with differentially heated sidewalls. We use particle image velocimetry and thermometry to reveal the evolution of both temperature and velocity fields. It is a hallmark of yield stress fluids that a critical ratio of the yield stress and buoyancy stresses exists above which the steady state is motionless. We observe this critical behaviour in our experiments. Contrary to the theoretical predictions, however, systematic motion is evident at the onset of all experiments, even when the steady state is motionless. Above the critical limit, extremely slow motion is observed immediately after the onset of the experiment. This is followed by very slow decay to rest, reminiscent of creep behaviour. Below the critical limit, the initial slow dynamics is followed by flow development patterns similar to theoretical predictions based on the Bingham model. We show that motion onset in carbopol microgels is dominated by subyield motion and fluidization, key processes that are not captured by viscoplastic models.

Type
JFM Papers
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Balmforth, N.J., Frigaard, I.A. & Ovarlez, G. 2014 Yielding to stress: recent developments in viscoplastic fluid mechanics. Annu. Rev. Fluid Mech. 46, 121146.CrossRefGoogle Scholar
Barnes, H.A. & Walters, K. 1985 The yield stress myth? Rheol. Acta 24 (4), 323326.CrossRefGoogle Scholar
Bonn, D., Denn, M.M., Berthier, L., Divoux, T. & Manneville, S. 2017 Yield stress materials in soft condensed matter. Rev. Mod. Phys. 89 (3), 035005.CrossRefGoogle Scholar
Bristeau, M.O. 1975 Application de lamthode des lments finis la rsolution numrique d'inquations variationnelles de type bingham. PhD thesis, These de 3me cycle, University of Paris VI, Juin.Google Scholar
Chevalier, T., Chevalier, C., Clain, X., Dupla, J.C., Canou, J., Rodts, S. & Coussot, P. 2013 Darcy's law for yield stress fluid flowing through a porous medium. J. Non-Newtonian Fluid Mech. 195, 5766.CrossRefGoogle Scholar
Coussot, P. 2014 Yield stress fluid flows: a review of experimental data. J. Non-Newtonian Fluid Mech. 211, 3149.CrossRefGoogle Scholar
Coussot, P., Nguyen, Q.D., Huynh, H.T. & Bonn, D. 2002 a Avalanche behavior in yield stress fluids. Phys. Rev. Lett. 88 (17), 175501.CrossRefGoogle ScholarPubMed
Coussot, P., Raynaud, J.S., Bertrand, F., Moucheront, P., Guilbaud, J.P., Huynh, H.T., Jarny, S. & Lesueur, D. 2002 b Coexistence of liquid and solid phases in flowing soft-glassy materials. Phys. Rev. Lett. 88 (21), 218301.CrossRefGoogle ScholarPubMed
Coussot, P., Tabuteau, H., Chateau, X., Tocquer, L. & Ovarlez, G. 2006 Aging and solid or liquid behavior in pastes. J. Rheol. 50 (6), 975994.CrossRefGoogle Scholar
Coussot, P., Tocquer, L., Lanos, C. & Ovarlez, G. 2009 Macroscopic vs. local rheology of yield stress fluids. J. Non-Newtonian Fluid Mech. 158 (1–3), 8590.CrossRefGoogle Scholar
Darbouli, M., Métivier, C., Piau, J.-M., Magnin, A. & Abdelali, A. 2013 Rayleigh–Bénard convection for viscoplastic fluids. Phys. Fluids 25 (2), 023101.CrossRefGoogle Scholar
Davaille, A., Gueslin, B., Massmeyer, A. & Di Giuseppe, E. 2013 Thermal instabilities in a yield stress fluid: existence and morphology. J. Non-Newtonian Fluid Mech. 193, 144153.CrossRefGoogle Scholar
Dinkgreve, M., Paredes, J., Denn, M.M. & Bonn, D. 2016 On different ways of measuring “the” yield stress. J. Non-Newtonian Fluid Mech. 238, 233241.CrossRefGoogle Scholar
Divoux, T., Barentin, C. & Manneville, S. 2011 From stress-induced fluidization processes to Herschel–Bulkley behaviour in simple yield stress fluids. Soft Matt. 7, 84098418.CrossRefGoogle Scholar
Divoux, T., Grenard, V. & Manneville, S. 2013 Rheological hysteresis in soft glassy materials. Phys. Rev. Lett. 110 (1), 018304.CrossRefGoogle ScholarPubMed
Divoux, T., Tamarii, D., Barentin, C. & Manneville, S. 2010 Transient shear banding in a simple yield stress fluid. Phys. Rev. Lett. 104 (20), 208301.CrossRefGoogle Scholar
Divoux, T., Tamarii, D., Barentin, C., Teitel, S. & Manneville, S. 2012 Yielding dynamics of a Herschel–Bulkley fluid: a critical-like fluidization behaviour. Soft Matt. 8 (15), 41514164.CrossRefGoogle Scholar
Glowinski, R., Lions, J.L. & Trémolières, R. 1981 Numerical Analysis of Variational Inequalities. North-Holland. (Translated from French).Google Scholar
Hormozi, S., Martinez, D.M. & Frigaard, I.A. 2011 Stable core-annular flows of viscoelastic fluids using the visco-plastic lubrication technique. J. Non-Newtonian Fluid Mech. 166 (23-24), 13561368.CrossRefGoogle Scholar
Karimfazli, I. & Frigaard, I.A. 2016 Flow, onset and stability: qualitative analysis of yield stress fluid flow in enclosures. J. Non-Newtonian Fluid Mech. 238, 224232.CrossRefGoogle Scholar
Karimfazli, I., Frigaard, I.A. & Wachs, A. 2016 Thermal plumes in viscoplastic fluids: flow onset and development. J. Fluid Mech. 787, 474507.CrossRefGoogle Scholar
Karimfazli, I., Frigaard, I.A. & Wachs, A. 2015 A novel heat transfer switch using the yield stress. J. Fluid Mech. 783, 526566.CrossRefGoogle Scholar
Kebiche, Z., Castelain, C. & Burghelea, T. 2014 Experimental investigation of the Rayleigh–Bénard convection in a yield stress fluid. J. Non-Newtonian Fluid Mech. 203, 923.CrossRefGoogle Scholar
Lidon, P., Villa, L. & Manneville, S. 2017 Power-law creep and residual stresses in a carbopol gel. Rheol. Acta 56 (3), 307323.CrossRefGoogle Scholar
Lyubimova, T.P. 1977 Numerical investigation of convection in a viscoplastic liquid in a closed region. Fluid Dyn. 12 (1), 15.CrossRefGoogle Scholar
Moller, P., Fall, A., Chikkadi, V., Derks, D. & Bonn, D. 2009 An attempt to categorize yield stress fluid behaviour. Phil. Trans. R. Soc. A 367 (1909), 51395155.CrossRefGoogle ScholarPubMed
Mosolov, P.P. & Miasnikov, V.P. 1966 On stagnant flow regions of a viscous-plastic medium in pipes. Z. Angew. Math. Mech. 30 (4), 841854.CrossRefGoogle Scholar
Nguyen, Q.D. & Boger, D.V. 1992 Measuring the flow properties of yield stress fluids. Annu. Rev. Fluid Mech. 24 (1), 4788.CrossRefGoogle Scholar
Ovarlez, G., Cohen-Addad, S., Krishan, K., Goyon, J. & Coussot, P. 2013 On the existence of a simple yield stress fluid behavior. J. Non-Newtonian Fluid Mech. 193, 6879.CrossRefGoogle Scholar
Putz, A.M.V. & Burghelea, T.I. 2009 The solid–fluid transition in a yield stress shear thinning physical gel. Rheol. Acta 48 (6), 673689.CrossRefGoogle Scholar
Schmidt, R.J. & Milverton, S.W. 1935 On the instability of a fluid when heated from below. Proc. R. Soc. Lond. A 152 (877), 586594.Google Scholar
Thielicke, W. & Stamhuis, E.J. 2014 PIVlab – Towards user-friendly, affordable and accurate digital particle image velocimetry in MATLAB. J. Open Res. Soft. 2 (1), e30.Google Scholar
Turan, O., Chakraborty, N. & Poole, R.J. 2010 Laminar natural convection of Bingham fluids in a square enclosure with differentially heated side walls. J. Non-Newtonian Fluid Mech. 165 (15–16), 901913.CrossRefGoogle Scholar
Vikhansky, A. 2009 Thermal convection of a viscoplastic liquid with high Rayleigh and Bingham numbers. Phys. Fluids 21 (10), 103103.CrossRefGoogle Scholar
Vikhansky, A. 2010 On the onset of natural convection of Bingham liquid in rectangular enclosures. J. Non-Newtonian Fluid Mech. 165 (23–24), 17131716.CrossRefGoogle Scholar
Weber, E., Moyers-González, M. & Burghelea, T.I. 2012 Thermorheological properties of a carbopol gel under shear. J. Non-Newtonian Fluid Mech. 183, 1424.CrossRefGoogle Scholar
Yang, W.J. & Yeh, H.C. 1965 Free convective flow of Bingham plastic between two vertical plates. J. Heat Transfer 87 (2), 319320.CrossRefGoogle Scholar
Zhang, J., Vola, D. & Frigaard, I.A. 2006 Yield stress effects on Rayleigh–Bénard convection. J. Fluid Mech. 566, 389419.CrossRefGoogle Scholar