Bed of polydisperse viscous spherical drops under thermocapillary effects

Article

Abstract

Viscous flow past an ensemble of polydisperse spherical drops is investigated under thermocapillary effects. We assume that the collection of spherical drops behaves as a porous media and estimates the hydrodynamic interactions analytically via the so- called cell model that is defined around a specific representative particle. In this method, the hydrodynamic interactions are assumed to be accounted by suitable boundary conditions on a fictitious fluid envelope surrounding the representative particle. The force calculated on this representative particle will then be extended to a bed of spherical drops visualized as a Darcy porous bed. Thus, the “effective bed permeability” of such a porous bed will be computed as a function of various parameters and then will be compared with Carman–Kozeny relation. We use cell model approach to a packed bed of spherical drops of uniform size (monodisperse spherical drops) and then extend the work for a packed bed of polydisperse spherical drops, for a specific parameters. Our results show a good agreement with the Carman–Kozeny relation for the case of monodisperse spherical drops. The prediction of overall bed permeability using our present model agrees well with the Carman–Kozeny relation when the packing size distribution is narrow, whereas a small deviation can be noted when the size distribution becomes broader.

Keywords

Cell model Thermocapillary Polydisperse spherical drops Overall bed permeability 

Mathematics Subject Classification

76D07 76S05 60E05 76A15 82D15 82D30 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  • V. Sharanya
    • 1
  • G. P. Raja Sekhar
    • 1
  • Christian Rohde
    • 2
  1. 1.Department of MathematicsIndian Institute of TechnologyKharagpurIndia
  2. 2.Institute of Applied Analysis and Numerical SimulationUniversity of StuttgartStuttgartGermany

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