Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-28T17:09:11.808Z Has data issue: false hasContentIssue false
  • English
  • Français

Chaos in a melting pot

Published online by Cambridge University Press:  19 May 2021

Rawad Himo Open the ORCID record for Rawad Himo [Opens in a new window] ,
Cathy Castelain Open the ORCID record for Cathy Castelain [Opens in a new window]  and
Teodor Burghelea Open the ORCID record for Teodor Burghelea [Opens in a new window]
Rawad Himo
Affiliation:
Université de Nantes, CNRS, Laboratoire de Thermique et Énergie de Nantes, LTeN, UMR 6607, F-44000Nantes, France
Cathy Castelain
Affiliation:
Université de Nantes, CNRS, Laboratoire de Thermique et Énergie de Nantes, LTeN, UMR 6607, F-44000Nantes, France
Teodor Burghelea*
Affiliation:
Université de Nantes, CNRS, Laboratoire de Thermique et Énergie de Nantes, LTeN, UMR 6607, F-44000Nantes, France
*
†Email address for correspondence: teodor.burghelea@univ-nantes.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

A novel flow instability emerging during a rheometric flow of a phase change material sheared in the vicinity of the melting point is reported. Right above the onset of the flow-induced crystallisation, the presence of the crystals in the flow leads to a primary bifurcation towards an oscillatory flow state. A further decrease of the temperature beyond this point leads to an increase of both the volume fraction and the size of the crystals, which ultimately triggers a fully developed chaotic flow. A full stability diagram as a function of the imposed deformation rate and the temperature is obtained experimentally. The systematic experimental observations reported herein could trigger further studies of the hydrodynamics of phase change materials and may find a number of interesting applications in polymer processing and thermal storage. The experimental findings are complemented by the analysis of a simple numerical model which provides further insights into the physical origins and mechanism of the instability.

JFM classification

Instability: Instability Non-Newtonian Flows: Rheology Phase change: Phase change
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 918 , 10 July 2021 , A47
Check for updates
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Andrade, D.E.V. & Coussot, P. 2019 Brittle solid collapse to simple liquid for a waxy suspension. Soft Matt. 15, 8766–8777.CrossRefGoogle ScholarPubMed
Barthelet, P., Charru, F. & Fabre, J. 1995 Experimental study of interfacial long waves in a two-layer shear flow. J. Fluid Mech. 303, 23–53.CrossRefGoogle Scholar
Bénard, H. 1900 Les tourbillons cellulaires dans une nappe liquide. Rev. Gen. Sci. Pures Appl. 11, 1261.Google Scholar
Boomkamp, P.A.M. & Miesen, R.H.M. 1996 Classification of instabilities in parallel two-phase flow. Intl J. Multiphase Flow 22, 67–88.CrossRefGoogle Scholar
Brooks, A.N. & Hughes, T.J.R. 1982 Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier–Stokes equations. Comput. Meth. Appl. Mech. Engng 32 (1), 199–259.CrossRefGoogle Scholar
Burghelea, T., Wielage-Burchard, K., Frigaard, I., Martinez, D.M. & Feng, J.J. 2007 A novel low inertia shear flow instability triggered by a chemical reaction. Phys. Fluids 19 (8), 083102.CrossRefGoogle Scholar
Burghelea, T.I. & Frigaard, I.A. 2011 Unstable parallel flows triggered by a fast chemical reaction. J. Non-Newtonian Fluid Mech. 166 (9–10), 500–514.CrossRefGoogle Scholar
Chang, C., Boger, D.V. & Nguyen, Q.D. 1998 The yielding of waxy crude oils. Ind. Engng Chem. Res. 37 (4), 1551–1559.CrossRefGoogle Scholar
Charles, M.E., Govier, G.W. & Hodgson, G.W. 1961 The horizontal pipeline flow of equal density oil-water mixtures. Can. J. Chem. Engng 39 (1), 27–36.CrossRefGoogle Scholar
Charles, M.E. & Lilleleht, L.U. 1965 An experimental investigation of stability and interfacial waves in co-current flow of two liquids. J. Fluid Mech. 22 (2), 217–224.CrossRefGoogle Scholar
Charru, F. & Hinch, E.J. 2000 ‘Phase diagram’ of interfacial instabilities in a two-layer Couette flow and mechanism of the long-wave instability. J. Fluid Mech. 414, 195–223.CrossRefGoogle Scholar
Dimitriou, C.J. & McKinley, G.H. 2014 A comprehensive constitutive law for waxy crude oil: a thixotropic yield stress fluid. Soft Matt. 10, 6619–6644.CrossRefGoogle ScholarPubMed
Divoux, T., Fardin, M.A., Manneville, S. & Lerouge, S. 2016 Shear banding of complex fluids. Annu. Rev. Fluid Mech. 48 (1), 81–103.CrossRefGoogle Scholar
Falconer, I., Gottwald, G.A., Melbourne, I. & Wormnes, K. 2007 Application of the 0–1 test for chaos to experimental data. SIAM J. Appl. Dyn. Syst. 6 (2), 395–402.CrossRefGoogle Scholar
Gentile, L., Silva, B.F.B., Lages, S., Mortensen, K., Kohlbrecher, J. & Olsson, U. 2013 Rheochaos and flow instability phenomena in a nonionic lamellar phase. Soft Matt. 9, 1133–1140.CrossRefGoogle Scholar
Geri, M., Venkatesan, R., Sambath, K. & McKinley, G.H. 2017 Thermokinematic memory and the thixotropic elasto-viscoplasticity of waxy crude oils. J. Rheol. 61 (3), 427–454.CrossRefGoogle Scholar
Gottwald, G.A. & Melbourne, I. 2004 A new test for chaos in deterministic systems. Proc. R. Soc. Lond. A 460 (2042), 603–611.CrossRefGoogle Scholar
Gottwald, G.A. & Melbourne, I. 2005 Testing for chaos in deterministic systems with noise. Physica D 212 (1), 100–110.CrossRefGoogle Scholar
Govindarajan, R. & Sahu, K.C. 2014 Instabilities in viscosity-stratified flow. Annu. Rev. Fluid Mech. 46 (1), 331–353.CrossRefGoogle Scholar
Hecht, F. 2006 Bamg: bidimensional anisotropic mesh generator. https://www.ljll.math.upmc.fr/hecht/ftp/bamg/bamg.pdf.Google Scholar
Hecht, F. 2012 New development in Freefem$++$. J. Numer. Maths 20 (3–4), 251–265.Google Scholar
Herle, V., Fischer, P. & Windhab, E.J. 2005 Stress driven shear bands and the effect of confinement on their structures–rheological, flow visualization, and rheo-SALS study. Langmuir 21 (20), 9051–9057, pMID: 16171332.CrossRefGoogle ScholarPubMed
Hickox, C.E. 1971 Instability due to viscosity and density stratification in axisymmetric pipe flow. Phys. Fluids 14 (2), 251–262.CrossRefGoogle Scholar
Hooper, A.P. 1985 Long-wave instability at the interface between two viscous fluids: thin layer effects. Phys. Fluids 28 (6), 1613–1618.CrossRefGoogle Scholar
Hooper, A.P. & Boyd, W.G.C. 1983 Shear-flow instability at the interface between two viscous fluids. J. Fluid Mech. 128, 507–528.CrossRefGoogle Scholar
Kantz, H. & Schreiber, T. 2003 Nonlinear Time Series Analysis, 2nd edn. Cambridge University Press.CrossRefGoogle Scholar
van Keken, P.E., King, S.D., Schmeling, H., Christensen, U.R., Neumeister, D. & Doin, M.-P. 1997 A comparison of methods for the modeling of thermochemical convection. J. Geophys. Res.: Solid Earth 102 (B10), 22477–22495.CrossRefGoogle Scholar
Landau, L.D. & Lifschitz, E.M. 1987 Fluid Mechanics. Pergamon Press.Google Scholar
Li, Q., Fu, Z. & Yuan, N. 2015 Beyond Benford's law: distinguishing noise from chaos. PLoS ONE 10 (6), 1–11.Google ScholarPubMed
Marshall, A.G. & Lawton, R.O. 2007 Asphaltenes, Heavy Oils, and Petroleomics, 2nd edn. Springer.Google Scholar
Matthews, P. 2009 0–1 test for chaos. https://www.mathworks.com/matlabcentral/fileexchange/25050-0-1-test-for-chaos.Google Scholar
Rossetti, F., Ranalli, G. & Faccenna, C. 1999 Rheological properties of paraffin as an analogue material for viscous crustal deformation. J. Struct. Geol. 21 (4), 413–417.CrossRefGoogle Scholar
Roux, D., Nallet, F. & Diat, O. 1993 Rheology of lyotropic lamellar phases. Europhys. Lett. 24 (1), 53–58.CrossRefGoogle Scholar
Sangalli, M., Gallagher, C.T., Leighton, D.T., Chang, H.-C. & McCready, M.J. 1995 Finite-amplitude waves at the interface between fluids with different viscosity: theory and experiments. Phys. Rev. Lett. 75, 77–80.CrossRefGoogle ScholarPubMed
Sprakel, J., Spruijt, E., Cohen Stuart, M.A., Besseling, N.A.M., Lettinga, M.P. & van der Gucht, J. 2008 Shear banding and rheochaos in associative polymer networks. Soft Matt. 4, 1696–1705.CrossRefGoogle ScholarPubMed
Takens, F. 1981 Detecting strange attractors in turbulence. In Dynamical Systems and Turbulence, Warwick 1980 (ed. D. Rand & L.-S. Young), pp. 366–381. Springer.CrossRefGoogle Scholar
Taylor, C. & Hood, P. 1973 A numerical solution of the Navier-Stokes equations using the finite element technique. Comput. Fluids 1 (1), 73–100.CrossRefGoogle Scholar
Valluri, P., Naraigh, L.O, Ding, H. & Spelt, P.D.M. 2010 Linear and nonlinear spatio-temporal instability in laminar two-layer flows. J. Fluid Mech. 656, 458–480.CrossRefGoogle Scholar
Valsakumar, M.C., Satyanarayana, S.V.M. & Sridhar, V. 1997 Signature of chaos in power spectrum. Pramana 10 (48), 69.CrossRefGoogle Scholar
Visintin, R.F.G., Lapasin, R., Vignati, E., D'Antona, P. & Lockhart, T.P. 2005 Rheological behavior and structural interpretation of waxy crude oil gels. Langmuir 21 (14), 6240–6249, pMID: 15982026.CrossRefGoogle ScholarPubMed
Yiantsios, S.G. & Higgins, B.G. 1988 Linear stability of plane Poiseuille flow of two superposed fluids. Phys. Fluids 31 (11), 3225–3238.CrossRefGoogle Scholar
Yih, C.-S. 1967 Instability due to viscosity stratification. J. Fluid Mech. 27 (2), 337–352.CrossRefGoogle Scholar