Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-12-01T00:48:51.126Z Has data issue: false hasContentIssue false
  • English
  • Français

Pinch-off of a viscous suspension thread

Published online by Cambridge University Press:  03 August 2018

Joris Château ,
Élisabeth Guazzelli Open the ORCID record for Élisabeth Guazzelli [Opens in a new window]  and
Henri Lhuissier Open the ORCID record for Henri Lhuissier [Opens in a new window]
Joris Château
Affiliation:
Aix Marseille Univ, CNRS, IUSTI, 13453 Marseille, France
Élisabeth Guazzelli
Affiliation:
Aix Marseille Univ, CNRS, IUSTI, 13453 Marseille, France
Henri Lhuissier*
Affiliation:
Aix Marseille Univ, CNRS, IUSTI, 13453 Marseille, France
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

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 $t^{\ast }\sim \unicode[STIX]{x1D702}_{e}h^{\ast }/\unicode[STIX]{x1D70E}$.

JFM classification

Drops and Bubbles: Breakup/coalescence Interfacial Flows (free surface): Capillary flows Complex Fluids: Suspensions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 852 , 10 October 2018 , pp. 178 - 198
Copyright
© 2018 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Blanc, F., Peters, F. & Lemaire, E. 2011 Local transient rheological behavior of concentrated suspensions. J. Rheol. 55, 835–854.Google Scholar
Bonnoit, C., Bertrand, T., Clément, E. & Lindner, A. 2012 Accelerated drop detachment in granular suspensions. Phys. Fluids 24, 043304.Google Scholar
Boyer, F., Guazzelli, É. & Pouliquen, O. 2011a Unifying suspension and granular rheology. Phys. Rev. Lett. 107, 188301.Google Scholar
Boyer, F., Pouliquen, O. & Guazzelli, É. 2011b Dense suspensions in rotating-rod flows: normal stresses and particle migration. J. Fluid Mech. 686, 5–25.Google Scholar
Cheal, O. & Ness, C. 2018 Rheology of dense granular suspensions under extensional flow. J. Rheol. 62, 501–512.Google Scholar
Coussot, P. & Gaulard, F. 2005 Gravity flow instability of viscoplastic materials: the ketchup drip. Phys. Rev. E 72, 031409.Google Scholar
Day, R. F., Hinch, E. J. & Lister, J. R. 1998 Self-similar capillary pinchoff of an inviscid fluid. Phys. Rev. Lett. 80 (4), 704–707.Google Scholar
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, 403–412.Google Scholar
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, 1–27.Google Scholar
Eggers, J. 1993 Universal pinching of 3D axisymmetric free surface flow. Phys. Rev. Lett. 71 (21), 3458–3460.Google Scholar
Eggers, J. & Villermaux, E. 2008 Physics of liquid jets. Rep. Prog. Phys. 71, 036601.Google Scholar
Furbank, R. & Morris, J. 2004 An experimental study of particle effects on drop formation. Phys. Fluids 16, 1777–1790.Google Scholar
Furbank, R. J. & Morris, J. 2007 Pendant drop thread dynamics of particle-laden liquids. Intl J. Multiphase Flow 33, 448–468.Google Scholar
Gallier, S., Lemaire, E., Peters, F. & Lobry, L. 2014 Rheology of sheared suspensions of rough frictional particles.. J. Fluid Mech. 757, 514–549.Google Scholar
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, 2500–2507.Google Scholar
Hoath, S. D., Hsiao, W. K., Hutchings, I. M. & Tuladhar, T. R. 2014 Jetted mixtures of particle suspensions and resins. Phys. Fluids 26, 101701.Google Scholar
Huisman, F. M., Friedman, S. R. & Taborek, P. 2012 Pinch-off dynamics in foams, emulsions and suspensions. Soft Matt. 8, 6767–6774.Google Scholar
Ingold, C. T. & Hadland, S. A. 1959 The ballistics of Sordaria. New Phytol. 58, 44–57.Google Scholar
Korkut, S., Saville, D. A. & Aksay, I. A. 2008 Collodial cluster arrays by electrohydrodynamic printing. Langmuir 24, 12196–12201.Google Scholar
Mathues, W., McIlroy, C., Harlen, O. G. & Clasen, C. 2015 Capillary breakup of suspensions near pinch-off. Phys. Fluids 27, 093301.Google Scholar
McIlroy, C. & Harlen, O. G. 2014 Modelling capillary break-up of particulate suspensions. Phys. Fluids 26, 033101.Google Scholar
McKinley, G. H. & Sridhar, T. 2002 Filament-stretching rheometry of complex fluids. Annu. Rev. Fluid Mech. 34, 375–415.Google Scholar
Miskin, M. & Jaeger, H. 2012 Droplet formation and scaling in dense suspensions. Proc. Natl Acad. Sci. 109, 4389–4394.Google Scholar
Morris, J. 2009 A review of microstructure in concentrated suspensions and its implications for rheology and bulk flow. Rheol. Acta 48, 909–923.Google Scholar
Morris, J. F. & Boulay, F. 1999 Curvilinear flows of noncolloidal suspensions: the role of normal stresses. J. Rheol. 43, 1213–1237.Google Scholar
Olsson, P. & Teitel, S. 2007 Critical scaling of shear viscosity at the jamming transition. Phys. Rev. Lett. 99 (17), 178001.Google Scholar
Papageorgiou, D. T. 1995 On the breakup of viscous liquid threads. Phys. Fluids 7, 1529.Google Scholar
Sami, S.1996 Stockesian dynamics simulation of Brownian suspensions in extensional flow. PhD thesis, California Institute of Technology.Google Scholar
Seto, R., Giusteri, G. G. & Martiniello, A. 2017 Microstructure and thickening of dense suspensions under extensional and shear flows. J. Fluid Mech. 825, R3.Google Scholar
Souzy, M., Lhuissier, H., Villermaux, E. & Metzger, B. 2017 Stretching and mixing in sheared particulate suspensions. J. Fluid Mech. 812, 611–635.Google Scholar
Stickel, J. & Powell, R. 2005 Fluid mechanics and rheology of dense suspsensions. Annu. Rev. Fluid Mech. 37, 129–149.Google Scholar
Trulsson, M., Degiuli, E. & Wyart, M. 2017 Effect of friction on dense suspension flows of hard particles. Phys. Rev. E 95, 012605.Google Scholar
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, 185–220.Google Scholar

Château et al. supplementary movie 1

Pinch-off of a capillary bridge of a suspension of particles with a diameter d = 10 micrometers and a particle volume fraction phi = 48%, suspended in pure PEG (close to 2500 times as viscous as water). In order to compensate for the continuously increasing rates of deformation at the bridge neck, the time in the movies is increasingly slowed down as pinching proceeds. The duration, t_0 - t, remaining before the pinch-off is indicated at the top. The width of the image is 4.45 mm.

Download Château et al. supplementary movie 1(Video)
Video 1.4 MB

Château et al. supplementary movie 2

Pinch-off of a capillary bridge of a suspension of particles with a diameter d = 135 micrometers and a particle volume fraction phi = 50%, suspended in pure PEG (close to 2500 times as viscous as water). In order to compensate for the continuously increasing rates of deformation at the bridge neck, the time in the movies is increasingly slowed down as pinching proceeds. The duration, t_0 - t, remaining before the pinch-off is indicated at the top. The width of the image is 4.45 mm.

Download Château et al. supplementary movie 2(Video)
Video 1.6 MB