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Hybrid LBM for Surfactant-Covered Droplets

  • Hassan Farhat
  • Joon Sang Lee
  • Sasidhar Kondaraju
Chapter

Abstract

This chapter describes a novel hybrid lattice Boltzmann model for the study of the droplet flow behavior in an immiscible medium with insoluble nonionic surfactant adhering to its interface. The evolution of the surfactant concentration on the interface is modeled by the time-dependent surfactant convection-diffusion equation and solved by a finite difference scheme. The fluid velocity field, the pressure, and the interface curvature are calculated using the lattice Boltzmann method (LBM) for binary fluid mixtures. The coupling between the LBM and the finite difference scheme is achieved through the LBM macroscopic variables and the surfactant equation of state. The Gunstensen LBM is used here because it provides local and independent application of a distinct interfacial tension on the individual nodes of the droplet interface. The hybrid model is developed and successfully applied to droplets deformations and surfactant distribution under simple shear flow, uniaxial flow, and buoyancy.

Keywords

Interfacial Tension Surfactant Concentration Capillary Number Lattice Boltzmann Method Terminal Velocity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Supplementary material

C4.3.2.1

3Dshear. 3D view of phase field density contours of droplet under the influence of shear and the corresponding change in the surfactant concentration along the interface is shown here. (see Fig. 4.9) (WMV 126 kb)

C4.3.2.1

Surfshear. 3D view of phase field density contours of droplet under the influence of shear and the corresponding change in the surfactant concentration along the interface is shown here (see Fig. 4.9) (WMV 142 kb)

C4.3.3.1

3Dextensional. 3D view of phase field density contours of droplet under the influence of extensional flow and the corresponding change in the surfactant concentration along the interface is shown here. (see Fig. 4.15) (WMV 134 kb)

C4.3.3.1

Surf_ext. 3D view of phase field density contours of droplet under the influence of extensional flow and the corresponding change in the surfactant concentration along the interface is shown here (see Fig. 4.15) (WMV 150 kb)

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Hassan Farhat
    • 1
  • Joon Sang Lee
    • 2
  • Sasidhar Kondaraju
    • 3
  1. 1.Department of Mechanical EngineeringWayne State UniversityDetroitUSA
  2. 2.Yonsei UniversitySeoulRepublic of (South Korea)
  3. 3.Department of Mechanical EngineeringIndian Institute of TechnologyDelhiIndia

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