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Drop deformation under small-amplitude oscillatory shear flow

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Abstract.

The deformation of an isolated drop in an immiscible liquid undergoing oscillatory shear flow is experimentally investigated as a function of frequency and up to moderate amplitudes. Oscillatory shear flow is generated by using a parallel plate apparatus. Drop shape is observed by video light microscopy along the vorticity direction of the shear flow. The two principal axes and the orientation of the drop in the plane of shear are measured by image analysis. In the small amplitude range, the time dependence of the axes is also harmonic, but not in phase with the applied strain, the phase difference being a decreasing function of the imposed frequency. The linear range (where the major axis is proportional to the amplitude) extends up to strains of 0.5. Good quantitative agreement was found with the Palierne linear viscoelastic model (Palierne, J. F., Linear rheology of viscoelastic emulsions with interfacial tension, Rheol. Acta, 29, 204–214, 1990), thus providing a further example of the good agreement between experiments and small deformation theory.

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References

  • Barthés-Biesel D, Acrivos A (1973) Deformation and burst of a liquid droplet freely suspended in a linear shear field. J Fluid Mech 61:1–21

    Google Scholar 

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

    Google Scholar 

  • Bousmina M (1999) Rheology of polymer blends: linear model for viscoelastic emulsions. Rheol Acta 38:73–83

    Google Scholar 

  • Chaffey CE, Brenner H (1967) A second-order theory for shear deformation of drops. J Coll Interface Sci 24:258–269

    Google Scholar 

  • Choi SJ, Schowalter WR (1975) Rheological properties of nondilute suspensions of deformable particles. Phys Fluids 18:420–427

    Google Scholar 

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

    Google Scholar 

  • de Bruijn RA (1989) Deformation and breakup of drops in simple shear flows. PhD thesis, Technische Universiteit Eindhoven

  • Doi M, Otha T (1991) Dynamics and rheology of complex interfaces. Int J Chem Phys 95:1242–1248

    Google Scholar 

  • Frankel NA, Acrivos A (1970) The constitutive equation for a dilute emulsion. J Fluid Mech 44:65–78

    Google Scholar 

  • Graebling D, Froelich D, Muller R (1989) Viscoelastic properties of polydimethylsiloxane-polyoxyethylene blends in the melt. Emulsion model. J Rheol 33:1283–1291

    Google Scholar 

  • Graebling D, Muller R, Palierne JF (1993) Linear viscoelastic behavior of some incompatible polymer blends in the melt. Interpretation of data with a model of emulsion of viscoelastic liquids. Macromolecules, 26:320–329

  • Gramespacher H, Meissner J (1992) Interfacial tension between polymer melts measured by shear oscillations of their blends. J Rheol 36:1127–1141

    Google Scholar 

  • Guido S, Greco F (2001) Drop shape under slow steady shear flow and during relaxation. Experimental results and comparison with theory. Rheol Acta 40:176–184

    Google Scholar 

  • Guido S, Simeone M (1998) Binary collisions of drops in simple shear flow by computer assisted video optical microscopy. J Fluid Mech 357:1–20

    Google Scholar 

  • Guido S, Villone M (1998) Three-dimensional shape of a drop under simple shear flow. J Rheol 42:395–415

    Google Scholar 

  • Guido S, Villone M (1999) Measurement of interfacial tension by drop retraction analysis. J Colloid Interface Sci 209:247–250

    Google Scholar 

  • Guido S, Simeone M, Villone M (1999) Diffusion effects on the interfacial tension of immiscible polymer blends. Rheol Acta 38:287–296

    Google Scholar 

  • Jacobs U, Fahrländer M, Winterhalter J, Friederich C (1999) Analysis of Palierne's emulsion model in the case of viscoelastic interfacial properties. J Rheol 43:1495–1509

    Google Scholar 

  • Janssen J (1993) Dynamics of liquid-liquid mixing. Ph.D. thesis, Eindhoven University

  • Jansseune T, Mewis J, Moldenaers P, Minale M, Maffettone PL (2000) Rheology and rheological morphology determination in immiscible two-phase polymer model blends. J Non-Newtonian Fluid Mech 93:153–165

    Google Scholar 

  • Kennedy MR, Pozrikidis C, Skalak R (1994) Motion and deformation of liquid drops, and the rheology of dilute emulsions in simple shear flow. Comput Fluids 23:251–278

    Google Scholar 

  • Kerner EH (1956) Elastic and thermoelastic properties of composite media. Proc Phys Soc B69:808–813

    Google Scholar 

  • Lee HM, Park OO (1994) Rheology and dynamics of immiscible polymer blends. J Rheol 38:1405–1425

    Google Scholar 

  • Oldroyd JG (1953) The elastic and viscous properties of emulsions and suspensions. Proc Roy Soc A218:122–132

    Google Scholar 

  • Oldroyd JG (1955) The effect of interfacial stabilizing films on the elastic and viscous properties of emulsions. Proc R Soc A232:567–577

    Google Scholar 

  • Palierne JF (1990) Linear rheology of viscoelastic emulsions with interfacial tension. Rheol Acta 29:204–214

    Google Scholar 

  • Rallison JM (1984) The deformation of small viscous drops and bubbles in shear flows. Ann Rev Fluid Mech 16:45–66

    Google Scholar 

  • Rumscheidt FD, Mason SG (1961) Particle motions in sheared suspensions. XII. Deformation and burst of fluid drops in shear and hyperbolic flow. J Colloid Interface Sci 16:238–261

    Google Scholar 

  • Stone HA (1994) Dynamics of drop deformation and breakup in viscous fluids. Ann Rev Fluid Mech 26:65–102

    Google Scholar 

  • Taylor GI (1932) The viscosity of a fluid containing small drops of another fluid. Proc R Soc A138:41–48

    Google Scholar 

  • Taylor GI (1934) The formation of emulsions in definable fields of flow. Proc R Soc A146:501–523

    Google Scholar 

  • Torza S, Cox RG, Mason SG (1972) Particle motion in sheared suspensions. XXVII. Transient and steady deformation and burst of liquid drops. J Colloid Interface Sci 38:395–411

    Google Scholar 

  • Uijttewaal WSJ, Nijhof EJ (1995) The motion of a droplet subjected to linear shear flow including the presence of a plane wall. J Fluid Mech 302:45–63

    Google Scholar 

  • Vinckier I, Moldenaers P, Mewis J (1996) Relationship between rheology and morphology of model blends in steady shear flow. J Rheol 40:613–631

    Google Scholar 

  • Wannaborworn S, Mackley MR (2000) Deformation and breakup of viscous drops in oscillatory shear. Proceedings of the 13th International Congress on Rheology, vol 2, pp 250–252

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Acknowledgements.

The authors wish to thank J.F. Palierne for helpful explanations on his model at the early stage of this work, and F. Greco for critical reading of the manuscript.

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Correspondence to Stefano Guido.

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Cavallo, R., Guido, S. & Simeone, M. Drop deformation under small-amplitude oscillatory shear flow. Rheol Acta 42, 1–9 (2003). https://doi.org/10.1007/s00397-002-0245-z

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