This study is to understand confinement effect on the dynamical behaviour of a droplet immersed in an immiscible liquid subjected to a simple shear flow. The lattice Boltzmann method, which uses a forcing term and a recolouring algorithm to realize the interfacial tension effect and phase separation respectively, is adopted to systematically study droplet deformation and breakup in confined conditions. The effects of capillary number, viscosity ratio of the droplet to the carrier liquid, and confinement ratio are studied. The simulation results are compared against the theoretical predictions, experimental and numerical data available in literature. We find that increasing confinement ratio will enhance deformation, and the maximum deformation occurs at the viscosity ratio of unity. The droplet is found to orient more towards the flow direction with increasing viscosity ratio or confinement ratio. Also, it is noticed that the wall effect becomes more significant for the confinement ratios larger than 0.4. Finally, the critical capillary number, above which the droplet breakup occurs, is found to be mildly affected by the confinement for the viscosity ratio of unity. Upon increasing the confinement ratio, the critical capillary number increases for the viscosity ratios less than unity, but decreases for the viscosity ratios more than unity. 
Droplet dynamics in confinement