Lattice Boltzmann simulations of drop deformation and breakup in shear flow

The behavior of a single liquid drop suspended in another liquid and subjected to simple shear flow is studied numerically using a diffuse interface free energy lattice Boltzmann method. The system is fully defined by three physical, and two numerical dimensionless numbers: a Reynolds number Re , a capillary number Ca , the viscosity ratio λ , an interface-related Peclet number Pe, and the ratio of interface thickness and drop size (the Cahn number Ch). The influence of Pe , Ch and mesh resolution on accuracy and stability of the simulations is investigated. Drops of moderate resolution (radius less than 30 lattice units) require smaller interface thickness, while a thicker interface should be used for highly resolved drops. The Peclet number is controlled by the mobility coefficient Γ . Based on the results, the simulations are stable when Γ is in the range 1–15. In addition, the numerical tool is verified and validated in a wide range of physical conditions: Re = 0.0625 - 50 , λ = 1 , 2 , 3 and a capillary number range over which drops deform and break. Good agreement with literature data is observed.