Ternary phase-field simplified multiphase lattice Boltzmann method and its application to compound droplet dynamics on solid surface in shear flow

A ternary phase-field simplified multiphase lattice Boltzmann method (TPF-SMLBM) is developed in a numerical investigation of a compound droplet placed on solid substrate in shear flow at moderate Reynolds numbers. Three major kinematic modes are recovered: quasi-steady sliding (QSS), tumbling-sliding, and tumbling-detachment. Analysis of QSS dynamics explains the wetting length exponential shrinking rate in the early evolution stage. A new dimensionless parameter, the Tumbling number (Tu), is proposed to identify the mode transition towards tumbling. The dynamics of detachment is also investigated, showing that the critical Capillary number of detachments can be described by a scaling law.