Abstract
Combined effects of geometrical confinement and compatibilization on the deformation and orientation of single droplets during steady-state shear flow are investigated in a counter-rotating cell by means of microscopic observations. The model system consists of polydimethylsiloxane droplets of varying sizes and viscosities in a polyisobutylene matrix. To this system, a premade polyisobutylene–polydimethylsiloxane block copolymer is added as compatibilizer in different concentrations. For each droplet, the equilibrium interfacial tension is determined by comparing droplet axes with the predictions of the confined Minale model for uncompatibilized droplets at the appropriate degree of confinement. Although large reductions in interfacial tension are seen for all compatibilized droplets, it is shown that the effect of compatibilization on droplet deformation and orientation can efficiently be taken into account in the equilibrium capillary number. This way, for all viscosity ratios and confinement ratios, steady-state data for compatibilized and uncompatibilized droplets coincide, and agree well with the predictions of the confined Minale model at sub-critical conditions. For near-critical capillary numbers, compatibilization slightly reduces droplet deformation and postpones breakup, irrespective of the degree of confinement.
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References
Abbassi-Sourki F, Huneault MA, Bousmina M (2009) Effect of compatibilization on the deformation and breakup of drops in step-wise increasing shear flow. Polymer 50:645–653
Bazhlekov IB, Anderson PD, Meijer HEH (2006) Numerical investigation of the effect of insoluble surfactants on drop deformation and breakup in simple shear flow. J Colloid Interface Sci 298:369–394
Cardinaels R, Verhulst K, Moldenaers P (2009) Influence of confinement on the steady state behavior of single droplets in shear flow for immiscible blends with one viscoelastic component. J Rheol 53:1403–1424
Cardinaels R, Vananroye A, Van Puyvelde P, Moldenaers P (2011) Breakup criteria for confined droplets: effects of compatibilization and component viscoelasticity. Macromol Mater Eng 296. doi:10.1002/mame.201000305
Christopher GF, Anna SL (2007) Microfluidic methods for generating continuous droplet streams. J Phys, D Appl Phys 40:R319–R336
De Bruijn RA (1993) Tipstreaming of droplets in simple shear flows. Chem Eng Sci 48:277–284
Feigl K, Megias-Alguacil D, Fischer P, Windhab EJ (2007) Simulation and experiments of droplet deformation and orientation in simple shear flow with surfactants. Chem Eng Sci 62:3242–3258
Garstecki P, Fuerstman MJ, Stone HA, Whitesides GM (2006) Formation of droplets and bubbles in a microfluidic T-junction—scaling and mechanism of break-up. Lab Chip 6:437–446
Guido S, Simeone M (1998) Binary collision of drops in simple shear flow by computer-assisted video optical microscopy. J Fluid Mech 357:1–20
Hu YT, Lips A (2003) Estimating surfactant surface coverage and decomposing its effect on drop deformation. Phys Rev Lett 91:044501
Hu YT, Pine DJ, Leal LG (2000) Drop deformation, breakup, and coalescence with compatibilizer. Phys Fluids 12:484–489
Janssen PJA, Anderson PD (2007) Boundary-integral method for drop deformation between parallel plates. Phys Fluids 19:043602
Janssen PJA, Anderson PD (2008) Surfactant-covered drops between parallel plates. Chem Eng Res Des 86:1388–1396
Janssen JJM, Boon A, Agterof WGM (1994) Influence of dynamic interfacial properties on droplet breakup in simple shear flow. AIChE J 40:1929–1939
Janssen JJM, Boon A, Agterof WGM (1997) Influence of dynamic interfacial properties on droplet breakup in plane hyperbolic flow. AIChE J 43:1436–1447
Jeon HK, Macosko CW (2003) Visualization of block copolymer distribution on a sheared drop. Polymer 44:5381–5386
Levitt L, Macosko CW (1999) Shearing of polymer drops with interface modification. Macromolecules 32:6270–6277
Li XF, Pozrikidis C (1997) The effect of surfactants on drop deformation and on the rheology of dilute emulsions in Stokes flow. J Fluid Mech 341:165–194
Maffettone PL, Minale M (1998) Equation of change for ellipsoidal drops in viscous flow. J Non-Newton Fluid Mech 78:227–241
Megias-Alguacil D, Fischer P, Windhab EJ (2006) Determination of the interfacial tension of low density difference liquid–liquid systems containing surfactants by droplet deformation. Chem Eng Sci 61:1386–1394
Migler KB (2001) String formation in sheared polymer blends: coalescence, breakup, and finite size effects. Phys Rev Lett 86:1023–1026
Minale M (2008) A phenomenological model for wall effects on the deformation of an ellipsoidal drop in viscous flow. Rheol Acta 47:667–675
Minale M, Moldenaers P, Mewis J (1997) Effect of shear history on the morphology of immiscible polymer blends. Macromolecules 30:5470–5475
Pathak JA, Davis MC, Hudson SD, Migler KB (2002) Layered droplet microstructures in sheared emulsions: finite-size effects. J Colloid Interface Sci 255:391–402
Pawar Y, Stebe KJ (1996) Marangoni effects on drop deformation in an extensional flow: the role of surfactant physical chemistry. 1. Insoluble surfactants. Phys Fluids 8:1738–1751
Renardy Y (2007) The effects of confinement and inertia on the production of droplets. Rheol Acta 46:521–529
Shapira M, Haber S (1990) Low Reynolds-number motion of a droplet in shear flow including wall effects. Int J Multiph Flow 16:305–321
Sibillo V, Pasquariello G, Simeone M, Cristini V, Guido S (2006) Drop deformation in microconfined shear flow. Phys Rev Lett 97:054502
Stone HA, Leal LG (1990) The effects of surfactants on drop deformation and breakup. J Fluid Mech 220:161–186
Sugiura S, Nakajima M, Iwamoto S, Seki M (2001) Interfacial tension driven monodispersed droplet formation from microfabricated channel array. Langmuir 17:5562–5566
Tufano C, Peters GWM, Meijer HEH (2008) Confined flow of polymer blends. Langmuir 24:4494–4505
Utada AS, Lorenceau E, Link DR, Kaplan PD, Stone HA, Weitz DA (2005) Monodisperse double emulsions generated from a microcapillary device. Science 308:537–541
Van Puyvelde P, Velankar S, Mewis J, Moldenaers P (2002) Effect of Marangoni stresses on the deformation and coalescence in compatibilized immiscible polymer blends. Polym Eng Sci 42:1956–1964
Van Puyvelde P, Vananroye A, Cardinaels R, Moldenaers P (2008) Review on morphology development of immiscible blends in confined shear flow. Polymer 49:5363–5372
Vananroye A, Van Puyvelde P, Moldenaers P (2006a) Effect of confinement on droplet breakup in sheared emulsions. Langmuir 22:3972–3974
Vananroye A, Van Puyvelde P, Moldenaers P (2006b) Structure development in confined polymer blends: steady-state shear flow and relaxation. Langmuir 22:2273–2280
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
Vananroye A, Cardinaels R, Van Puyvelde P, Moldenaers P (2008) Effect of confinement and viscosity ratio on the dynamics of single droplets during transient shear flow. J Rheol 52:1459–1475
Velankar S, Van Puyvelde P, Mewis J, Moldenaers P (2001) Effect of compatibilization on the breakup of polymeric drops in shear flow. J Rheol 45:1007–1019
Verhulst K, Moldenaers P, Minale M (2007) Drop shape dynamics of a Newtonian drop in a non-Newtonian matrix during transient and steady shear flow. J Rheol 51:261–273
Vlahovska PM, Blawzdziewicz J, Loewenberg M (2009) Small-deformation theory for a surfactant-covered drop in linear flows. J Fluid Mech 624:293–337
Yon S, Pozrikidis C (1998) A finite-volume/boundary-element method for flow past interfaces in the presence of surfactants, with application to shear flow past a viscous drop. Comput Fluids 27:879–902
Acknowledgements
The authors acknowledge the Research Foundation—Flanders (FWO Vlaanderen—post doctoral fellowship of A. Vananroye) and Onderzoeksfonds K.U.Leuven (GOA09/002) for financial support.
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Vananroye, A., Van Puyvelde, P. & Moldenaers, P. Deformation and orientation of single droplets during shear flow: combined effects of confinement and compatibilization. Rheol Acta 50, 231–242 (2011). https://doi.org/10.1007/s00397-011-0535-4
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DOI: https://doi.org/10.1007/s00397-011-0535-4