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Droplet dynamics in sub-critical complex flows

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Abstract

A newly designed eccentric cylinder device has been used to study the deformation and orientation of single Newtonian droplets immersed in an immiscible Newtonian liquid in a controlled complex flow field. Optical microscopy coupled with image acquisition analysis allows monitoring the dynamics of droplets flowing in the gap between the eccentric cylinders. Throughout the experiments, the flow intensity was kept below the critical conditions for droplet break-up. The experimental results are compared with predictions which are obtained using the transient form of the phenomenological model of Maffettone and Minale (J Non-Newtonian Fluid Mech 78:227–241, 1998; J Non-Newtonian Fluid Mech 84:105–106, 1999), incorporating a flow type parameter that accounts for the relative amount of elongational effects in the flow field and adapting the capillary number to mixed flows. For all the sub-critical flows studied here, good agreement was found between model predictions and experimental data, providing, for the first time, a quantitative assessment of drop shape predictions in complex flows.

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References

  • Almusallam AS, Larson RG, Solomon MJ (2000) A constrained volume model for the prediction of droplet shapes and stresses in immiscible blends. J Rheol 44:1055–1083

    Article  ADS  CAS  Google Scholar 

  • Ballal BY, Rivlin RS (1976) Flow of a Newtonian fluid between eccentric rotating cylinders—inertial effects. Arch Rat Mech Anal 62:237–294

    Article  MATH  MathSciNet  Google Scholar 

  • Bentley BL, Leal LG (1986) An experimental investigation of drop deformation and break-up in steady two-dimensional linear flows. J Fluid Mech 167:241–283

    Article  MATH  ADS  CAS  Google Scholar 

  • Chin HB, Han CD (1980) Studies on droplet deformation and break-up. 2. Break-up of a droplet in a nonuniform shear flow. J Rheol 24:1–37

    Article  MATH  ADS  CAS  Google Scholar 

  • Cox RG (1969) The deformation of a drop in a general time-dependent fluid flow. J Fluid Mech 37:601–623

    Article  MATH  ADS  Google Scholar 

  • Cristini V, Hooper RW, Macosko CW, Simeone M, Guido S (2002) A numerical and experimental investigation of lamellar blends morphologies. Ind Eng Chem Res 41:6305–6311

    Article  CAS  Google Scholar 

  • de Bruijn RA (1989) Deformation and break-up of drops in simple shear flows. Ph.D. thesis, Eindhoven University of Technology, The Netherlands

  • Diprima RC, Stuart JT (1972) Flow between eccentric rotating cylinders. ASME J Lubr Tech 94:266–274

    Google Scholar 

  • Feigl K, Kaufmann SFM, Fischer P, Windhab EJ (2003) A numerical procedure for calculating droplet deformation in dispersing flows and experimental verification. Chem Eng Sci 58:2351–2363

    Article  CAS  Google Scholar 

  • Godbille FD, Picot JJC (2000) Drop break-up in combined shear and elongational flow conditions. Adv Polym Tech 19:14–21

    Article  CAS  Google Scholar 

  • Grace HP (1982) Dispersion phenomena in high-viscosity immiscible fluid systems and application of static mixers as dispersion devices in such systems. Chem Eng Commun 14:225–277

    Article  CAS  Google Scholar 

  • Guido S, Greco F (2004) Dynamics of a liquid drop in a flowing immiscible liquid. Rheology Reviews 2004, The British Society of Rheology: 99–142

  • Guido S, Minale M, Maffettone PL (2000) Drop shape dynamics under shear-flow reversal. J Rheol 44:1385–1399

    Article  ADS  CAS  Google Scholar 

  • Han CD, Funatsu K (1978) Experimental study of droplet deformation and break-up in pressure driven flows through converging and uniform channels. J Rheol 22:113–133

    Article  ADS  CAS  Google Scholar 

  • Janssen JMH, Meijer HEH (1993) Droplet breakup mechanisms: stepwise equilibrium versus transient dispersion. J Rheol 37:597–608

    Article  ADS  CAS  Google Scholar 

  • Kamal MM (1966) Separation in the flow between eccentric rotating cylinders. ASME J Basic Eng 88:717–724

    Google Scholar 

  • Kaufmann SFM, Fischer P, Windhab EJ (2000) Investigation of droplet dispersing processes in shear and elongational flow. In: Fischer P, Marti I, Windhab EJ (eds) Second international symposium on food rheology and structure. Laboratory of Food Process Engineering, Zurich, Switzerland, pp 404–405

    Google Scholar 

  • Khayat RE, Luciani A, Utracki LA, Godbille FD, Picot JJC (2000) Influence of shear and elongation on drop deformation in convergent–divergent flows. Int J Multiphase Flow 26:17–44

    Article  MATH  CAS  Google Scholar 

  • Kusch HA, Ottino JM (1992) Experiments on mixing in continuous chaotic flows. J Fluid Mech 236:319–348

    Article  ADS  CAS  MathSciNet  Google Scholar 

  • Maffettone PL, Minale M (1998) Equation of change for ellipsoidal drops in viscous flow. J Non-Newtonian Fluid Mech 78:227–241

    Article  MATH  CAS  Google Scholar 

  • Maffettone PL, Minale M (1999) Equation of change for ellipsoidal drops in viscous flows (vol 78, p 227, 1998). J Non-Newtonian Fluid Mech 84:105–106

    Article  CAS  Google Scholar 

  • Mietus WGP, Matar OK, Lawrence CJ, Briscoe BJ (2002) Droplet deformation in confined shear and extensional. Chem Eng Sci 57:1217–1230

    Article  CAS  Google Scholar 

  • Minale M (2004) Deformation of a non-Newtonian ellipsoidal drop in a non-Newtonian matrix: extension of the Maffettone–Minale model. J Non-Newtonian Fluid Mech 123:151–160

    Article  MATH  CAS  Google Scholar 

  • Okamoto K, Takahashi M, Yamane H, Kashihara H, Watanabe H, Masuda T (1999) Shape recovery of dispersed droplet phase and stress relaxation after application of step shear strains in a polystyrene/polycarbonate blend melt. J Rheol 43:951–965

    Article  ADS  CAS  Google Scholar 

  • Ottino JM, Leong CW, Rising H, Swanson PD (1988) Morphological structures produced by mixing in chaotic flows. Nature 333:419–425

    Article  ADS  CAS  Google Scholar 

  • Ottino JM, De Roussel P, Hansen S, Khakhar DV (1999) Mixing and dispersion of viscous liquids and powdered solids. Adv Chem Eng 25:105–204

    Article  Google Scholar 

  • Priore BE, Walker LM (2001) Small angle light scattering analysis of morphology development of a model immiscible polymer blend in transient slit-contraction flows. J Rheol 45:383–402

    Article  ADS  CAS  Google Scholar 

  • Rasband WS (1997–2007) Image J. U. S. National Institutes of Health, Bethesda, Maryland, USA

  • Stone HA (1994) Dynamics of drop deformation in viscous liquids. Annu Rev Fluid Mech 26:65–102

    Article  ADS  Google Scholar 

  • Stone HA, Leal LG (1989) The influence of initial deformation on drop break-up in sub-critical time-dependent flows at low Reynolds numbers. J Fluid Mech 206:223–263

    Article  ADS  CAS  Google Scholar 

  • Stone HA, Bentley BL, Leal LG (1986) An experimental study of transient effects in the break-up of viscous drops. J Fluid Mech 173:131–158

    Article  ADS  CAS  Google Scholar 

  • Taylor GI (1932) The viscosity of a fluid containing small drops of another fluid. Proc Roy Soc Lond Math Phys Sci 138:41–48

    Article  MATH  ADS  CAS  Google Scholar 

  • Taylor GI (1934) The formation of emulsions in definable fields of flow. Proc Roy Soc Lond Math Phys Sci 146:501–523

    Article  ADS  CAS  Google Scholar 

  • Testa C, Sigillo I, Grizzuti N (2001) Morphology evolution of immiscible polymer blends in complex flow fields. Polymer 42:5651–5659

    Article  CAS  Google Scholar 

  • Tjahjadi M, Ottino JM (1991) Stretching and breakup of droplets in chaotic flows. J Fluid Mech 232:191–219

    Article  ADS  CAS  MathSciNet  Google Scholar 

  • Tucker CL, Moldenaers P (2002) Microstructural evolution in polymer blends. Annu Rev Fluid Mech 34:177–210

    Article  ADS  MathSciNet  Google Scholar 

  • Utracki LA (1989) Polymer alloys and blends. Hanser, Munich

    Google Scholar 

  • Van der Reijden-Stolk C, Sara A (1986) A study on polymer blending microrheology. 3. Deformation of Newtonian drops submerged in another Newtonian fluid flowing through a converging cone. Polym Eng Sci 26:1229–1239

    Article  Google Scholar 

  • Van Puyvelde P, Yang H, Mewis J, Moldenaers P (2000) Break-up of filaments in blends during simple shear flow. J Rheol 44:1401–1415

    Article  ADS  Google Scholar 

  • Vananroye A, Van Puyvelde P, Moldenaers P (2006) Structure development in confined polymer blends: Steady-state shear flow and relaxation. Langmuir 22:2273–2280

    Article  PubMed  CAS  Google Scholar 

  • Vananroye A, Van Puyvelde P, Moldenaers P (2007) Effect of confinement on the steady-state behavior of single droplets during shear flow. J Rheol 51:139–153

    Article  ADS  CAS  Google Scholar 

  • Wannier GH (1950) A contribution to the hydrodynamics of lubrication. Quart Appl Math 8:1–32

    MATH  MathSciNet  Google Scholar 

  • Windhab EJ, Dressler M, Feigl K, Fischer P, Megias-Alguacil D (2005) Emulsion processing—from single-drop deformation to design of complex processes and products. Chem Eng Sci 60:2101–2113

    Article  CAS  Google Scholar 

  • Yamane H, Takahashi M, Hayashi R, Okamoto K, Kashihara H, Masuda T (1998) Observation of deformation and recovery of poly(isobutylene) droplet in a poly(isobutylene)/ poly(dimethyl siloxane) blend after application of step shear strain. J Rheol 42:567–579

    Article  ADS  CAS  Google Scholar 

  • Yu W, Bousmina M (2003) Ellipsoidal model for droplet deformation in emulsions. J Rheol 47:1001–1039

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank Ing. Bart Caerts for his valuable input during the design of the new ECD as well as Dr. Maarten Vanierschot and Dr. Tim Persoons of the Mechanical Engineering Department of the KULeuven for their help with the PIV measurements. This work has been financially supported by Onderzoeksfonds K.U.Leuven (GOA 03/06 and GOA 09/002).

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Authors and Affiliations

  1. Department of Chemical Engineering and Leuven MRC, Katholieke Universiteit Leuven, Willem de Croylaan 46, 3001, Leuven, Belgium

    Elia Boonen, Peter Van Puyvelde & Paula Moldenaers

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  1. Elia Boonen
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  2. Peter Van Puyvelde
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  3. Paula Moldenaers
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Correspondence to Paula Moldenaers.

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Boonen, E., Van Puyvelde, P. & Moldenaers, P. Droplet dynamics in sub-critical complex flows. Rheol Acta 48, 359–371 (2009). https://doi.org/10.1007/s00397-008-0322-z

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  • DOI: https://doi.org/10.1007/s00397-008-0322-z

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