Abstract
During detachment of a viscous fluid extruded from a nozzle, a filament linking the droplet to the latter is formed. Under the effect of surface tension, the filament thins until pinch-off and final detachment of the droplet. In this paper, we study the effect of the presence of individual particles trapped in the filament on the detachment dynamics using granular suspensions of small volume fractions (ϕ < 6 %). We show that even a single particle strongly modifies the detachment dynamics. The particle perturbs the thinning of the thread, and a large droplet of fluid around the particle is formed. This perturbation leads to an acceleration of the detachment of the droplet compared to the detachment observed for a pure fluid. We quantify this acceleration for single particles of different sizes and link it to similar observations for suspensions of small volume fractions. Our study also gives more insight into particulate effects on detachment of denser suspensions and allows to explain the accelerated detachment close to final pinch-off observed previously (Bonnoit et al. Phys Fluids 24(4):043304, 2012).
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References
Amarouchene Y, Bonn D, Meunier J, Kellay H (2001) Inhibition of the finite-time singularity during droplet fission of a polymeric fluid. Phys Rev Lett 86(16):3558–3561. doi:10.1103/PhysRevLett.86.3558
Anna SL, McKinley GH (2001) Elasto-capillary thinning and breakup of model elastic liquids. J Rheol 45(1):115. doi:10.1122/1.1332389
Basaran OA (2002) Small-scale free surface flows with breakup: drop formation and emerging applications. AIChE J 48(9):1842–1848. doi:10.1002/aic.690480902
Bertrand T, Bonnoit C, Clément E, Lindner A (2012) Dynamics of drop formation in granular suspensions: the role of volume fraction. Granul Matter 1–6:169–174. doi:10.1007/s10035-012-0318-3
Bonnoit C, Darnige T, Clement E, Lindner A (2010) Inclined plane rheometry of a dense granular suspension. J Rheol 54(1):65–79, doi:10.1122/1.3258076
Bonnoit C, Bertrand T, Clement E, Lindner A (2012) Accelerated drop detachment in granular suspensions. Phys Fluids 24(4):043304. doi:10.1063/1.4704801
Carroll BJ (1984) The equilibrium of liquid drops on smooth and rough circular cylinders. J Colloid Interface Sci 97(1):195–200. doi:10.1016/0021-9797(84)90286-8
Christanti Y, Walker LM (2001) Surface tension driven jet break up of strain-hardening polymer solutions. J Non-Newtonian Fluid Mech 100(1–3):9–26. doi:10.1016/S0377-0257(01)00135-5
Christanti Y, Walker LM (2002) Effect of fluid relaxation time of dilute polymer solutions on jet breakup due to a forced disturbance. J Rheol 46(3):733. doi:10.1122/1.1463418
Clasen C, Phillips PM, Palangetic L, Vermant, Jan (2012) Dispensing of rheologically complex fluids: the map of misery. AIChE J 58(10):3242–3255. doi:10.1002/aic.13704
Coussot P, Gaulard F (2005) Gravity flow instability of viscoplastic materials: the ketchup drip. Phys Rev E 72(3):031, 409. doi:10.1103/PhysRevE.72.031409, part 1
Eggers J (1993) Universal pinching of 3d axisymmetric free-surface flow. Phys Rev Lett 71(21):3458–3460. doi:10.1103/PhysRevLett.71.3458
Eggers J (1997) Nonlinear dynamics and breakup of free-surface flows. Rev Mod Phys 69(3):865. doi:10.1103/RevModPhys.69.865
Fall A, Denn M, Bonn D (2013) Why is (wet) granular rheology so complicated? Soft Matter (in press)
Furbank R, Morris J (2004) An experimental study of particle effects on drop formation. Phys Fluids 16(5):1777–1790. doi:10.1063/1.1691034
Furbank R, Morris J (2007) Pendant drop thread dynamics of particle-laden liquids. Int J Multiph Flow 33(4):448–468. doi:10.1016/j.ijmultiphaseflow.2006.02.021
Gier S, Wagner C (2012) Visualization of the flow profile inside a thinning filament during capillary breakup of a polymer solution via particle image velocimetry and particle tracking velocimetry. Phys Fluids 24(5):053, 102. doi:10.1063/1.4718675
Hameed M, Morris J (2009) Breakup of a liquid jet containing solid particles: a singularity approach. SIAM J Appl Math 70:885. doi:10.1137/080715986
Lespiat R, Hohler R, Biance AL, Cohen-Addad S (2010) Experimental study of foam jets. Phys Fluids 22(3):033, 302. doi:10.1063/1.3335816
Lohse D, Bergmann R, Mikkelsen R, Zeilstra C, van der Meer D, Versluis M, van der Weele K, van der Hoef M, Kuipers H (2004) Impact on soft sand: void collapse and jet formation. Phys Rev Lett 93(19):198, 003. doi:10.1103/PhysRevLett.93.198003
McKinley GH, Tripathi A (2000) How to extract the newtonian viscosity from capillary breakup measurements in a filament rheometer. J Rheol 44(3):653–670. doi:10.1122/1.551105
Miskin MZ, Jaeger HM (2012) Droplet formation and scaling in dense suspensions. Proc Natl Acad Sci 109(12):4389–4394. doi:10.1073/pnas.1111060109
Morrison NF, Harlen OG (2010) Viscoelasticity in inkjet printing. Rheol Acta 49:619. doi:10.1007/s00397-009-0419-z
Papageorgiou D (1995) On the breakup of viscous liquid threads. Phys Fluids 7:1529. doi:10.1063/1.868540
Pignatel F, Nicolas M, Guazzelli E, Saintillan D (2009) Falling jets of particles in viscous fluids. Phys Fluids 21(12):123, 303. doi:10.1063/1.3276235
Roché M, Kellay H, Stone HA (2011) Heterogeneity and the role of normal stresses during the extensional thinning of non-brownian shear-thickening fluids. Phys Rev Lett 107:134, 503. doi:10.1103/PhysRevLett.107.134503
Rothert A, Richter R, Rehberg I (2003) Formation of a drop: viscosity dependence of three flow regimes. New J Phys 5:59. doi:10.1088/1367-2630/5/1/359
Royer JR, Evans DJ, Oyarte L, Guo Q, Kapit E, Mobius ME, Waitukaitis SR, Jaeger HM (2009) High-speed tracking of rupture and clustering in freely falling granular streams. Nature 459(7250):1110–1113. doi:10.1038/nature08115
Sattler R, Wagner C, Eggers J (2008) Blistering pattern and formation of nanofibers in capillary thinning of polymer solutions. Phys Rev Lett 100(16):164, 502, doi:10.1103/PhysRevLett.100.164502
Tirtaatmadja V, McKinley GH, Cooper-White JJ (2006) Drop formation and breakup of low viscosity elastic fluids: effects of molecular weight and concentration. Phys Fluids 18(4):043, 101. doi:10.1063/1.2190469
Zarraga I, Hill D, Leighton Jr D (2000) The characterization of the total stress of concentrated suspensions of noncolloidal spheres in Newtonian fluids. J Rheology 44:185. doi:10.1122/1.551083
Acknowledgements
MvD would like to thank the French embassy in The Netherlands for their funding under the Bourses d’excellence “Descartes” program. We thank Martin van Hecke and Marc Miskin for interesting discussions and P.-B. Bintein for help with the experimental setup.
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Special issue devoted to novel trends in rheology.
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van Deen, M.S., Bertrand, T., Vu, N. et al. Particles accelerate the detachment of viscous liquids. Rheol Acta 52, 403–412 (2013). https://doi.org/10.1007/s00397-013-0691-9
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DOI: https://doi.org/10.1007/s00397-013-0691-9