Skip to main content Accessibility help

Pinch-off of a viscous suspension thread

  • Joris Château (a1), Élisabeth Guazzelli (a1) and Henri Lhuissier (a1)


The pinch-off of a capillary thread is studied at large Ohnesorge number for non-Brownian, neutrally buoyant, mono-disperse, rigid, spherical particles suspended in a Newtonian liquid with viscosity $\unicode[STIX]{x1D702}_{0}$ and surface tension $\unicode[STIX]{x1D70E}$ . Reproducible pinch-off dynamics is obtained by letting a drop coalesce with a bath. The bridge shape and time evolution of the neck diameter, $h_{\mathit{min}}$ , are studied for varied particle size $d$ , volume fraction $\unicode[STIX]{x1D719}$ and liquid contact angle $\unicode[STIX]{x1D703}$ . Two successive regimes are identified: (i) a first effective-viscous-fluid regime which only depends upon $\unicode[STIX]{x1D719}$ and (ii) a subsequent discrete regime, depending both on $d$ and $\unicode[STIX]{x1D719}$ , in which the thinning localises at the neck and accelerates continuously. In the first regime, the suspension behaves as an effective viscous fluid and the dynamics is solely characterised by the effective viscosity of the suspension, $\unicode[STIX]{x1D702}_{e}\sim -\unicode[STIX]{x1D70E}/{\dot{h}}_{\mathit{min}}$ , which agrees closely with the steady shear viscosity measured in a conventional rheometer and diverges as $(\unicode[STIX]{x1D719}_{c}-\unicode[STIX]{x1D719})^{-2}$ at the same critical particle volume fraction, $\unicode[STIX]{x1D719}_{c}$ . For $\unicode[STIX]{x1D719}\gtrsim 35\,\%$ , the thinning rate is found to increase by a factor of order one when the flow becomes purely extensional, suggesting non-Newtonian effects. The discrete regime is observed from a transition neck diameter, $h_{\mathit{min}}\equiv h^{\ast }\sim d\,(\unicode[STIX]{x1D719}_{c}-\unicode[STIX]{x1D719})^{-1/3}$ , down to $h_{\mathit{min}}\approx d$ , where the thinning rate recovers the value obtained for the pure interstitial fluid, $\unicode[STIX]{x1D70E}/\unicode[STIX]{x1D702}_{0}$ , and lasts $t^{\ast }\sim \unicode[STIX]{x1D702}_{e}h^{\ast }/\unicode[STIX]{x1D70E}$ .


Corresponding author

Email address for correspondence:


Hide All
Blanc, F., Peters, F. & Lemaire, E. 2011 Local transient rheological behavior of concentrated suspensions. J. Rheol. 55, 835854.
Bonnoit, C., Bertrand, T., Clément, E. & Lindner, A. 2012 Accelerated drop detachment in granular suspensions. Phys. Fluids 24, 043304.
Boyer, F., Guazzelli, É. & Pouliquen, O. 2011a Unifying suspension and granular rheology. Phys. Rev. Lett. 107, 188301.
Boyer, F., Pouliquen, O. & Guazzelli, É. 2011b Dense suspensions in rotating-rod flows: normal stresses and particle migration. J. Fluid Mech. 686, 525.
Cheal, O. & Ness, C. 2018 Rheology of dense granular suspensions under extensional flow. J. Rheol. 62, 501512.
Coussot, P. & Gaulard, F. 2005 Gravity flow instability of viscoplastic materials: the ketchup drip. Phys. Rev. E 72, 031409.
Day, R. F., Hinch, E. J. & Lister, J. R. 1998 Self-similar capillary pinchoff of an inviscid fluid. Phys. Rev. Lett. 80 (4), 704707.
van Deen, M. S., Bertrand, T., Vu, N., Quéré, D., Clément, E. & Lindner, A. 2013 Particles accelerate the detachment of viscous liquids. Rheol. Acta 52, 403412.
Doshi, P., Suryo, R., Yildirim, O. E., McKinley, G. H. & Basaran, O. A. 2003 Scaling in pinch-off of generalized Newtonian fluids. J. Non-Newton. Fluid Mech. 113, 127.
Eggers, J. 1993 Universal pinching of 3D axisymmetric free surface flow. Phys. Rev. Lett. 71 (21), 34583460.
Eggers, J. & Villermaux, E. 2008 Physics of liquid jets. Rep. Prog. Phys. 71, 036601.
Furbank, R. & Morris, J. 2004 An experimental study of particle effects on drop formation. Phys. Fluids 16, 17771790.
Furbank, R. J. & Morris, J. 2007 Pendant drop thread dynamics of particle-laden liquids. Intl J. Multiphase Flow 33, 448468.
Gallier, S., Lemaire, E., Peters, F. & Lobry, L. 2014 Rheology of sheared suspensions of rough frictional particles.. J. Fluid Mech. 757, 514549.
He, Y. 2008 Application of flow-focusing to the break-up of an emulsion jet for the production of matrix-structured microparticles. Chem. Engng Sci. 63, 25002507.
Hoath, S. D., Hsiao, W. K., Hutchings, I. M. & Tuladhar, T. R. 2014 Jetted mixtures of particle suspensions and resins. Phys. Fluids 26, 101701.
Huisman, F. M., Friedman, S. R. & Taborek, P. 2012 Pinch-off dynamics in foams, emulsions and suspensions. Soft Matt. 8, 67676774.
Ingold, C. T. & Hadland, S. A. 1959 The ballistics of Sordaria. New Phytol. 58, 4457.
Korkut, S., Saville, D. A. & Aksay, I. A. 2008 Collodial cluster arrays by electrohydrodynamic printing. Langmuir 24, 1219612201.
Mathues, W., McIlroy, C., Harlen, O. G. & Clasen, C. 2015 Capillary breakup of suspensions near pinch-off. Phys. Fluids 27, 093301.
McIlroy, C. & Harlen, O. G. 2014 Modelling capillary break-up of particulate suspensions. Phys. Fluids 26, 033101.
McKinley, G. H. & Sridhar, T. 2002 Filament-stretching rheometry of complex fluids. Annu. Rev. Fluid Mech. 34, 375415.
Miskin, M. & Jaeger, H. 2012 Droplet formation and scaling in dense suspensions. Proc. Natl Acad. Sci. 109, 43894394.
Morris, J. 2009 A review of microstructure in concentrated suspensions and its implications for rheology and bulk flow. Rheol. Acta 48, 909923.
Morris, J. F. & Boulay, F. 1999 Curvilinear flows of noncolloidal suspensions: the role of normal stresses. J. Rheol. 43, 12131237.
Olsson, P. & Teitel, S. 2007 Critical scaling of shear viscosity at the jamming transition. Phys. Rev. Lett. 99 (17), 178001.
Papageorgiou, D. T. 1995 On the breakup of viscous liquid threads. Phys. Fluids 7, 1529.
Sami, S.1996 Stockesian dynamics simulation of Brownian suspensions in extensional flow. PhD thesis, California Institute of Technology.
Seto, R., Giusteri, G. G. & Martiniello, A. 2017 Microstructure and thickening of dense suspensions under extensional and shear flows. J. Fluid Mech. 825, R3.
Souzy, M., Lhuissier, H., Villermaux, E. & Metzger, B. 2017 Stretching and mixing in sheared particulate suspensions. J. Fluid Mech. 812, 611635.
Stickel, J. & Powell, R. 2005 Fluid mechanics and rheology of dense suspsensions. Annu. Rev. Fluid Mech. 37, 129149.
Trulsson, M., Degiuli, E. & Wyart, M. 2017 Effect of friction on dense suspension flows of hard particles. Phys. Rev. E 95, 012605.
Zarraga, I. E., Hill, D. A. & Leighton, D. T. Jr 2000 The characterization of the total stress of concentrated suspensions of noncolloidal spheres in Newtonian fluids. J. Rheol. 44, 185220.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed