Skip to main content
SpringerLink
Log in

Transport Phenomena in Viscoplastic Materials

  • Chapter
  • First Online:
Transport Phenomena in Complex Fluids

Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 598))

  • 891 Accesses

Abstract

This chapter focuses on various transport phenomena in yield stress materials. After a brief introduction, an overview of the phenomenology of the solid–fluid transition is given in Sect. 2. Section 3 introduces a microscopic theory able to describe the solid–fluid transition in both thixotropic and non-thixotropic yield stress materials. A discussion of the hydrodynamic stability of yield stress materials is presented in Sect. 4. Some non-isothermal transport phenomena are discussed in Sect. 5.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    The derivation of Eq. (37) has been related to the shearing force via \(\eta \left( \dot{\gamma }\right) =\frac{f_+}{A \dot{\gamma }}\).

  2. 2.

    This can be easily seen if one retains from the series expansion of the right-hand side of Eq. (37) only the first-order term.

  3. 3.

    This is for now only a plausible assumption and a direct experimental investigation by fluorescent visualisation of the gel network as recently performed by Gutowski et al. (2012) would be highly needed to test it.

References

  • Alain M, Bardet L (1982) Etude energetique de la gelification du carbopol 940. Int J Pharm 12(2):173–183

    Article  Google Scholar 

  • Albaalbaki B, Khayat RE (2011) Pattern selection in the thermal convection of non-newtonian fluids. J Fluid Mech 668:500–550

    Article  MATH  Google Scholar 

  • Arigo MT, McKinley GH (1998) An experimental investigation of negative wakes behind spheres settling in a shear-thinning viscoelastic fluid. Rheol Acta 37(4):307–327

    Article  Google Scholar 

  • Balmforth NJ, Craster RV (1999) A consistent thin-layer theory for bingham plastics. J Non-Newton Fluid Mech 84(1):65–81

    Article  MATH  Google Scholar 

  • Balmforth NJ, Rust AC (2009) Weakly nonlinear viscoplastic convection. J Non-Newton Fluid Mech 158(1–3):36–45

    Article  MATH  Google Scholar 

  • Balmforth NJ, Frigaard IA, Ovarlez G (2014) Yielding to stress: recent developments in viscoplastic fluid mechanics. Ann Rev Fluid Mech 46(1):121–146

    Article  MathSciNet  MATH  Google Scholar 

  • Barnes HA (1999) The yield stress-a review or ‘\(\pi \alpha \nu \tau \alpha \rho \epsilon \iota \)’-everything flows? J Non-Newton Fluid Mech 81(1–2):133–178

    Article  Google Scholar 

  • Barnes HA, Walters K (1985) The yield stress myth? Rheol Acta 24:323–326

    Article  Google Scholar 

  • Barry BW, Meyer MC (1979a) The rheological properties of carbopol gels i. Continuous shear and creep properties of carbopol gels. Int J Pharm 2(1):1–25

    Article  Google Scholar 

  • Barry BW, Meyer MC (1979b) The rheological properties of carbopol gels ii. Oscillatory properties of carbopol gels. Int J Pharm 20(1):27–40

    Article  Google Scholar 

  • Bautista F, Munoz M, Castillo-Tejas J, Pérez-López JH, Puig JE, Manero O (2009) Critical phenomenon analysis of shear-banding flow in polymer-like micellar solutions. 1. Theoretical approach. J Phys Chem B 113(50):16101–16109

    Article  Google Scholar 

  • Bauwens-Crowet C, Bauwens C, Homés G (1972) The temperature dependence of yield of polycarbonate in uniaxial compression and tensile tests. J Mater Sci 7:176–183

    Article  Google Scholar 

  • Beck J, Madsen B, Britt D, Vernon B, Nguyen KT (2007) Islet encapsulation: strategies to enhance islet cell functions. Tissue Eng 13:589–599

    Article  Google Scholar 

  • Beris AN, Tsamopoulos JA, Armstrong RC, Brown RA (1985) Creeping motion of a sphere through a Bingham plastic. J Fluid Mech 158:219–244

    Article  MathSciNet  MATH  Google Scholar 

  • Bird RB, Hassager O, Armstrong RC, Curtiss CF (1977) Dynamics of polymeric liquids, vol 1. Wiley, New York

    Google Scholar 

  • Bird RB, Stewart WE, Lightfoot EN (2002) Transport phenomena. Willey, New York

    Google Scholar 

  • Bodenschatz E, Pesch W, Ahlers G (2000) Recent developments in Rayleigh-Bénard convection. Ann Rev Fluid Mech 32(1):709–778

    Article  MATH  Google Scholar 

  • Bonn D, Denn MM (2009) Yield stress fluids slowly yield to analysis. Science 324(5933):1401–1402

    Article  Google Scholar 

  • Bonn D, Paredes J, Denn MM, Berthier L, Divoux T, Manneville S (2017) Yield stress materials in soft condensed matter. Rev Mod Phys 89:035005

    Article  Google Scholar 

  • Borrega R, Cloitre M, Betremieux I, Ernst B, Leibler L (1999) Concentration dependence of the low-shear viscosity of polyelectrolyte micro-networks: from hard spheres to soft microgels. Europhys Lett 47:729–735

    Article  Google Scholar 

  • Brémaud P (1999) Markov chains: gibbs field, Monte Carlo simulation and queues. Springer, New York

    Book  MATH  Google Scholar 

  • Burghelea T, Wielage-Burchard K, Frigaard I, Martinez DM, Feng JJ (2007) A novel low inertia shear flow instability triggered by a chemical reaction. Phys Fluids 19(8):083102

    Article  MATH  Google Scholar 

  • Burghelea T, Moyers-Gonzalez M, Sainudiin R (2017) A nonlinear dynamical system approach for the yielding behaviour of a viscoplastic material. Soft Matter 13:2024–2039

    Article  Google Scholar 

  • Burghelea TI, Frigaard IA (2011) Unstable parallel flows triggered by a fast chemical reaction. J Non-Newton Fluid Mech 166(9–10):500–514

    Article  Google Scholar 

  • Chandrasekhar S (1961) Hydrodynamic and hydromagnetic stability. Clarendon Press, Oxford

    MATH  Google Scholar 

  • Cloitre M, Borrega R, Monti F, Leibler L (2003) Structure and flow of polyelectrolyte microgels. Comptes Rendus Phys 4:221–230

    Article  Google Scholar 

  • Coussot P (2007) Rheophysics of pastes: a review of microscopic modelling approaches. Soft Matter 3:528–540

    Article  Google Scholar 

  • Coussot P (2014) Yield stress fluid flows: a review of experimental data. J Non-Newton Fluid Mech 211:31–49

    Article  Google Scholar 

  • Coussot P, Nguyen QD, Huynh HT, Bonn D (2002a) Avalanche behavior in yield stress fluids. Phys Rev Lett 88:175501

    Article  Google Scholar 

  • Coussot P, Nguyen QD, Huynh HT, Bonn D (2002b) Viscosity bifurcation in thixotropic, yielding fluids. J Rheol 46(3):573–589

    Article  Google Scholar 

  • Cross MC, Hohenberg PC (1993) Pattern formation outside of equilibrium. Rev Mod Phys 65:851–1112

    Article  MATH  Google Scholar 

  • Curran SJ, Hayes RE, Afacan A, Williams MC, Tanguy PA (2002) Properties of carbopol solutions as models for yield-stress fluids. J Food Sci 67(1):176–180

    Article  Google Scholar 

  • Darbouli M, Metivier C, Piau J-M, Magnin A, Abdelali A (2013) Rayleigh-Bénard convection for viscoplastic fluids. Phys Fluids 25(2):023101

    Article  Google Scholar 

  • Davaille A, Gueslin B, Massmeyer A, Di Giuseppe E (2013) Thermal instabilities in a yield stress fluid: existence and morphology. J Non-Newton Fluid Mechan 193:144–153

    Article  Google Scholar 

  • de Bruyn JR (2013) Modeling the microrheology of inhomogeneous media. J Non-Newton Fluid Mech 193:21–27

    Article  Google Scholar 

  • Denn MM, Bonn D (2011) Issues in the flow of yield-stress liquids. Rheol Acta 50:307–315

    Article  Google Scholar 

  • Dimitriou CJ, McKinley GH (2014) A comprehensive constitutive law for waxy crude oil: a thixotropic yield stress fluid. Soft Matter 10:6619–6644

    Article  Google Scholar 

  • Dinkgreve M, Fazilati M, Denn MM, Bonn D (2018) Carbopol: from a simple to a thixotropic yield stress fluid. J Rheol 62(3):773–780

    Article  Google Scholar 

  • Divoux T, Grenard V, Manneville S (2013) Rheological hysteresis in soft glassy materials. Phys Rev Lett 110:018304

    Article  Google Scholar 

  • Dubois M, Bergé P (1978)Experimental study of the velocity field in Rayleigh-Bénard convection. J Fluid Mech 85(3):641–653

    Article  Google Scholar 

  • Dullaert K, Mewis J (2006) A structural kinetics model for thixotropy. J Non-Newton Fluid Mech 139:21–30

    Article  MATH  Google Scholar 

  • Ern P, Charru F, Luchini P (2003) Stability analysis of a shear flow with strongly stratified viscosity. J Fluid Mech 496:295–312

    Article  MathSciNet  MATH  Google Scholar 

  • Escudier MP, Presti F (1996) Pipe flow of a thixotropic liquid. J Non-Newton Fluid Mech 62(2):291–306

    Article  Google Scholar 

  • Escudier MP, Poole RJ, Presti F, Dales C, Nouar C, Desaubry C, Graham L, Pullum L (2005) Observations of asymmetrical flow behaviour in transitional pipe flow of yield-stress and other shear-thinning liquids. J Non-Newton Fluid Mech 127 (2-3):143–155

    Article  Google Scholar 

  • Eyring H (1936) Viscosity, plasticity, and diffusion as examples of absolute reaction rates. J Chem Phys 4(4):283–291

    Article  Google Scholar 

  • Fraggedakis D, Dimakopoulos Y, Tsamopoulos J (2016) Yielding the yield-stress analysis: a study focused on the effects of elasticity on the settling of a single spherical particle in simple yield-stress fluids. Soft Matter 12:5378–5401

    Article  Google Scholar 

  • Fresno Contreras MJ, Dieguez Ramirez A, Jimenez Soriano MM (2001) Viscosity and temperature relationship in ethanol/water mixtures gellified with carbopol Ultrez 10. Il Farmaco (5–7):443–445

    Article  Google Scholar 

  • Frigaard IA, Nouar C (2005) On the usage of viscosity regularisation methods for visco-plastic fluid flow computation. J Non-Newton Fluid Mech 127(1):1–26

    Article  MATH  Google Scholar 

  • Frigaard IA, Ryan DP (2004) Flow of a visco-plastic fluid in a channel of slowly varying width. J Non-Newton Fluid Mech 123(1):67–83

    Article  MATH  Google Scholar 

  • Frigaard IA, Howison SD, Sobey IJ (1994) On the stability of Poiseuille flow of a Bingham fluid. J Fluid Mech 263:133–150

    Article  MathSciNet  MATH  Google Scholar 

  • Frisch U (1995) Turbulence: the legacy of A.N. Kolmogorov. Cambridge University Press

    Google Scholar 

  • Glasstone S, Keith J, Eyring H (1941) The theory of rate processes. McGraw-Hill Book Co, New York

    Google Scholar 

  • Goveas GL, Olmsted PD (2001) A minimal model for vorticity and gradient banding in complex fluids. Eur Phys J E 6:79–89

    Article  Google Scholar 

  • Griggs DT (1939) A theory of mountain-building. Am J Sci 237:611–650

    Article  Google Scholar 

  • Gutowski I, Lee D, de Bruyn J, Frisken B (2012) Scaling and mesostructure of carbopol dispersions. Rheol Acta 1–10

    Google Scholar 

  • Güzel BT, Burghelea T, Frigaard IA, Martinez DM (2009) Observation of laminar-turbulent transition of a yield stress fluid in Hagen-Poiseuille flow. J Fluid Mech 627:97–128

    Article  MATH  Google Scholar 

  • Herschel WH, Bulkley R (1926a) Konsistenzmessungen von Gummi-Benzollösungen. Kolloid-Zeitschrift 39(4):291–300

    Article  Google Scholar 

  • Herschel WH, Bulkley T (1926b) Measurement of consistency as applied to rubbery benzene solutions. Am Soc Test Proc 26:621–633

    Google Scholar 

  • Heymann L, Aksel N (2007) Transition pathways between solid and liquid state in suspensions. Phys Rev E 75(2):021505–9

    Article  Google Scholar 

  • Hof B, Juel A, Mullin T (2003) Scaling of the turbulence transition threshold in a pipe. Phys Rev Lett 91:244502

    Article  Google Scholar 

  • Hofschuster W, Krämer W (2003) C-XSC 2.0: A C++ library for extended scientific computing. In: Numerical software with result verification, pp 15–35

    Chapter  Google Scholar 

  • Hong W, Zhao X, Zhou J, Suo Z (2008) A theory of coupled diffusion and large deformation in polymeric gels. J Mech Phys Solids 56(5):1779–1793

    Article  MATH  Google Scholar 

  • Hou Q, De Bank PA, Shakesheff KM (2004) Injectable scaffolds for tissue regeneration. J Matter Chem 14:1915

    Article  Google Scholar 

  • Ising E (1925) Beitrag zur theorie des ferromagnetismus. Z Phys 31:253–258

    Article  Google Scholar 

  • Islam MT, Rodríguez-Hornedo N, Ciotti S, Ackermann C (2004) Rheological characterization of topical carbomer gels neutralized to different pH. Pharm Res 21(7):1192–1199

    Article  Google Scholar 

  • Israelachvili JN (2010) Intermolecular and surface forces. Academic Press, 3rd edn, New York

    Google Scholar 

  • Jeong B, Bae YH, Lee DS, Kim SW (1997) Biodegradable block copolymers as injectable drug-delivery systems. Nature 388:860–862

    Article  Google Scholar 

  • Jones R (2009) Compendium of polymer terminology and nomenclature IUPAC recommendations, 2008. Royal Society of Chemistry, Cambridge

    Book  Google Scholar 

  • Joseph DD (1970) Global stability of the conduction-diffusion solution. Arch Ration Mech Anal 36(4):285–292

    Article  MathSciNet  MATH  Google Scholar 

  • Kebiche Z, Castelain C, Burghelea T (2014) Experimental investigation of the Rayleigh-Benard convection in a yield stress fluid. J Non-Newton Fluid Mech 203:9–23

    Article  Google Scholar 

  • Koschmieder EL (1993) Bénard cells and Taylor vortices. Cambridge University Press

    Google Scholar 

  • Lamsaadi M, Naomi M, Hasnaoui M (2005) Natural convection of non-Newtonian power law fluids in a shallow horizontal rectangular cavity uniformly heated from below. Heat Mass Transf 41: 239–249. ISSN 0947-7411

    Google Scholar 

  • Landau LD, Levich B (1972) Dragging of a liquid by a moving plate. Acta Physicochim 388(17):42–54

    Google Scholar 

  • Landau LD, Lifschitz EM (1987) Fluid mechanics. Pergamon Press, Oxford

    Google Scholar 

  • Landau LD, Lisfshits EM (1980) Statistical physics, part 1: volume 5 (Course of theoretical physics, Volume 5), Third edn. Butterworth-Heinemann

    Google Scholar 

  • Landry MP, Frigaard IA, Martinez DM (2006) Stability and instability of Taylor-Couette flows of a bingham fluid. J Fluid Mech 560:321–353

    Article  MathSciNet  MATH  Google Scholar 

  • Larson RG (1999) The structure and rheology of complex fluids. Oxford University Press

    Google Scholar 

  • Le Bars M, Davaille A (2004) Whole layer convection in a heterogeneous planetary mantle. J Geophys Res 109:23

    Google Scholar 

  • Liang SF, Acrivos A (1970) Experiments on buoyancy driven convection in non-Newtonian fluid. Rheol Acta 9(3):447–455

    Article  Google Scholar 

  • Magazu S, Migliardo F, Malomuzh NP, Blazhnov IV (2007) Theoretical and experimental models on viscosity: I. Glycerol. J Phys Chem B 111(32): 9563–9570

    Article  Google Scholar 

  • Martinez-Mardones J, Tiemann R, Walgraef D (2000) Thermal convection thresholds in viscoelastic solutions. J Non-Newton Fluid Mech 93(1):1–15

    Article  MATH  Google Scholar 

  • Meinesz FAV (1947) Major tectonic phenomena and the hypothesis of convection currents in the earth. Q J Geol Soc 103(1–4):191–207

    Article  Google Scholar 

  • Metivier C, Nouar C, Brancher J-P (2005) Linear stability involving the Bingham model when the yield stress approaches zero. Phys Fluids 17(10):104106

    Article  MATH  Google Scholar 

  • Metzner AB, Reed JC (1955) Flow of non-Newtonian fluids: correlation of the laminar, transition, and turbulent-flow regions. AIChE J 1(4):434–440

    Article  Google Scholar 

  • Möller PCF, Mewis J, Bonn D (2006) Yield stress and thixotropy: on the difficulty of measuring yield stress in practice. Soft Matter 2:274–283

    Article  Google Scholar 

  • Moyers-Gonzalez M, Burghelea T, Mak J (2011a) Linear stability analysis for plane-Poiseuille flow of an elastoviscoplastic fluid with internal microstructure for large Reynolds numbers. J Non-Newton Fluid Mechan 166(9–10):515–531

    Article  MATH  Google Scholar 

  • Moyers-Gonzalez M, Burghelea T, Mak J (2011b) Linear stability analysis for plane-Poiseuille flow of an elastoviscoplastic fluid with internal microstructure for large Reynolds numbers. J Non-Newton Fluid Mech 166(9–10):515–531

    Article  MATH  Google Scholar 

  • Newell AC, Whitehead JA (1969) Finite bandwidth, finite amplitude convection. J Fluid Mech 38:279–303

    Article  MathSciNet  MATH  Google Scholar 

  • Nguyen QD, Boger DV (1992) Measuring the flow properties of yield stress fluids. Ann Rev Fluid Mech 24(1):47–88

    Article  MATH  Google Scholar 

  • Nickerson CS, Kornfield JA (2005) A “cleat” geometry for suppressing wall slip. J Rheol 49(4):865–874

    Article  Google Scholar 

  • Oppong FK, de Bruyn JR (2007) Diffusion of microscopic tracer particles in a yield-stress fluid. J Non-Newton Fluid Mech 142:104–111

    Article  MATH  Google Scholar 

  • Oppong FK, Rubatat L, Frisken BJ, Bailey AE, de Bruyn JR (2006) Microrheology and structure of a yield-stress polymer gel. Phys Rev E 73:041405

    Article  Google Scholar 

  • Orowan E (1965) Convection in a non-Newtonian mantle, continental drift, and mountain building. Philos Trans R Soc Lond Ser A Math Phys Sci 258(1088):284–313

    Article  Google 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-Newton Fluid Mech 193:68–79. Viscoplastic fluids: from theory to application

    Article  Google Scholar 

  • Owen DH, Peters JJ, Lavine ML, Katz DF (2003) Effect of temperature and pH on contraceptive gel viscosity. Contraception 67(1):57–64

    Article  Google Scholar 

  • Papanastasiou TC (1987) Flows of materials with yield. J Rheol (1978-present) 31(5):385–404

    Article  MATH  Google Scholar 

  • Park HM, Park KS (2004) Rayleigh-Bénard convection of viscoelastic fluids in arbitrary finite domains. Int J Heat Mass Transf 47(10–11):2251–2259

    Article  MATH  Google Scholar 

  • Park HM, Ryu DH (2001) Rayleigh-Bénard convection of viscoelastic fluids in finite domains. J Non-Newton Fluid Mech 98(2–3):169–184

    Article  MATH  Google Scholar 

  • Park NA, Irvine TF (1997) Liquid density measurements using the falling needle viscometer. Int Commun Heat Mass Transf 24(3):303–312

    Article  Google Scholar 

  • Park NA, Irvine TF Jr (1997) Anomalous viscosity-temperature behaviour of aqueous carbopol solutions. J Rheol 41(1):167–173

    Article  Google Scholar 

  • Peixinho J (2004) Contribution expérimentale a l’étude de la convection thermique en régime laminaire, transitoire et turbulent pour un fluidea seuil en ecoulement dans une conduite. PhD thesis, Université Henri Poincaré, Nancy, France

    Google Scholar 

  • Peixinho J, Nouar C, Desaubry C, Theron B (2005a) Laminar transitional and turbulent flow of yield stress fluid in a pipe. J Non-Newton Fluid Mech 128:172–184

    Article  Google Scholar 

  • Peixinho J, Nouar C, Desaubry C, Theron B (2005b) Laminar transitional and turbulent flow of yield stress fluid in a pipe. J Non-Newton Fluid Mech 128(2–3):172–184

    Article  Google Scholar 

  • Peixinho J, Desaubry C, Lebouche M (2008) Heat transfer of a non-newtonian fluid (Carbopol aqueous solution) in transitional pipe flow. Int J Heat Mass Transf 51(1–2):198–209

    Article  MATH  Google Scholar 

  • Piau JM (2007) Carbopol gels: elastoviscoplastic and slippery glasses made of individual swollen sponges: meso- and macroscopic properties, constitutive equations and scaling laws. J Non-Newton Fluid Mech 144(1):1–29

    Article  Google Scholar 

  • Picard G, Ajdari A, Bocquet L, Lequeux F (2002) Simple model for heterogeneous flows of yield stress fluids. Phys Rev E 66:051501

    Article  Google Scholar 

  • Poumaere A, Moyers-Gonzalez M, Castelain C, Burghelea T (2014) Unsteady laminar flows of a carbopol gel in the presence of wall slip. J Non-Newton Fluid Mech 205:28–40

    Article  Google Scholar 

  • Putz AMV, Burghelea TI (2009) The solid-fluid transition in a yield stress shear thinning physical gel. Rheol Acta 48:673–689

    Article  Google Scholar 

  • Putz AMV, Burghelea TI, Frigaard IA, Martinez DM (2008) Settling of an isolated spherical particle in a yield stress shear thinning fluid. Phys Fluids (20):033102

    Article  MATH  Google Scholar 

  • Qiu Y, Park K (2001) Environment-sensitive hydrogels for drug delivery. Adv Drug Deliv Rev 53(3):321–339

    Article  Google Scholar 

  • Quemada D (1998a) Rheological modeling of complex fluids: I: the concept of effective volume fraction revisited. Eur Phys J AP 1:119–127

    Article  Google Scholar 

  • Quemada D (1998b) Rheological modeling of complex fluids: III: dilatant behaviour of stabilized suspensions. Eur Phys J AP 3:309–320

    Article  Google Scholar 

  • Quemada D (1999) Rheological modeling of complex fluids: IV: thixotropic and “thixoelastic” behaviour. Start-up and stress relaxation, creep tests and hysteresis cycles. Eur Phys J AP (5):191–207

    Article  Google Scholar 

  • Ree T, Eyring H (1955) Theory of non-Newtonian flow. i. Solid plastic system. J Appl Phys 26(7):793–800

    Article  MATH  Google Scholar 

  • Reynolds O (1883) An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels. Philos Trans R Soc Lond 174:935–982

    Article  MATH  Google Scholar 

  • Richeton J, Ahzi S, Daridon L, Rémond Y (2005) A formulation of the cooperative model for the yield stress of amorphous polymers for a wide range of strain rates and temperatures. Polymer 46:6035–6043

    Article  Google Scholar 

  • Roussel N, Le Roy R, Coussot P (2004) Thixotropy modelling at local and macrsocopic scales. J Non-Newton Fluid Mech 117(2–3):85–95

    Article  MATH  Google Scholar 

  • Sainudiin R, Moyers-Gonzalez M, Burghelea T (2014) A microscopic gibbs field model for the macroscopic behavior of a viscoplastic fluid. UCDMS Res Rep 2014(1):1–17

    Google Scholar 

  • Sainudiin R, Moyers-Gonzalez M, Burghelea T (2015a) A microscopic Gibbs field model for the macroscopic yielding behaviour of a viscoplastic fluid. Soft Matter 11:5531–5545

    Article  Google Scholar 

  • Sainudiin R, Moyers-Gonzalez M, Burghelea T (2015b) A microscopic Gibbs field model for the macroscopic yielding behaviour of a viscoplastic fluid. Soft Matter 11:5531–5545

    Article  Google Scholar 

  • Sani R (1964) On the non-existence of subcritical instabilities in fluid layers heated from below. J Fluid Mech 20:315–319, 10

    Article  MathSciNet  MATH  Google Scholar 

  • Segel LA (1969) Distant side-walls cause slow amplitude modulation of cellular convection. J Fluid Mech 38:203–224, 7

    Article  MATH  Google Scholar 

  • Slatter PT (1999) The laminar-turbulent transition in large pipes. In: Problems in fluid mechanics and hydrology, Prague, pp 247–256

    Google Scholar 

  • Slomkowski S, Alemán JV, Gilbert RG, Hess M, Horie K, Jones RG, Kubisa P, Meisel I, Mormann W, Penczek S, Stepto RFT (2011) Terminology of polymers and polymerization processes in dispersed systems (IUPAC recommendations 2011). Pure Appl Chem 83(12):2229–2259

    Article  Google Scholar 

  • Souliès A, Pruvost J, Legrand J, Castelain C, Burghelea TI (2013) Rheological properties of suspensions of the green microalga chlorella vulgaris at various volume fractions. Rheol Acta 52(6):589–605

    Article  Google Scholar 

  • Stanley EH (1987) Phase transitions and critical phenomena. Oxford University Press

    Google Scholar 

  • Taylor GI (1938) The spectrum of turbulence. Proc R Soc Lond Ser A Math Phys Sci 164 (919):476–490

    Article  MATH  Google Scholar 

  • Todica M, Pop CV, Udrescu L, Pop M (2010) Rheological behavior of some aqueous gels of carbopol with pharmaceutical applications. Chin Phys Lett 27(1):018301

    Article  Google Scholar 

  • Turan O, Chakraborty N, Poole RJ (2012) Laminar Rayleigh-Bénard convection of yield stress fluids in a square enclosure. J Non-Newton Fluid Mech 171–172(0):83–96. ISSN 0377-0257

    Article  Google Scholar 

  • Weber E, Moyers-Gonzalez M, Burghelea TI (2012) Thermorheological properties of a carbopol gel under shear. J Non-Newton Fluid Mech 183–184:14–24

    Article  Google Scholar 

  • Zhang J, Vola D, Frigaard IA (2006) Yield stress effects on Rayleigh-Bénard convection. J Fluid Mech 566:389

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire Thermique et Energie, University of Nantes, Nantes, France

    Teodor Burghelea

Authors
  1. Teodor Burghelea
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Teodor Burghelea .

Editor information

Editors and Affiliations

  1. Laboratoire de Thermique et Energie de Nantes, University of Nantes, Nantes, France

    Teodor Burghelea

  2. School of Engineering, University of Liverpool, Liverpool, UK

    Volfango Bertola

Rights and permissions

Reprints and permissions

Copyright information

© 2020 CISM International Centre for Mechanical Sciences, Udine

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Burghelea, T. (2020). Transport Phenomena in Viscoplastic Materials. In: Burghelea, T., Bertola, V. (eds) Transport Phenomena in Complex Fluids. CISM International Centre for Mechanical Sciences, vol 598. Springer, Cham. https://doi.org/10.1007/978-3-030-35558-6_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-35558-6_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-35557-9

  • Online ISBN: 978-3-030-35558-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation