Analytical-numerical investigation of unequal sized droplets of dilatants' fluid in T-junction with unequal length branches

In this paper we performed an analytical and 3D numerical investigation for breakup of non-Newtonian droplets in a non-Newtonian carrier fluid. The system geometry is T-junction with unequal length branches that can generates unequal sized droplets. Analytical and 3D numerical results of this research have good agreement with each other. We investigated variation of many quantities during the breakup process such as: flow rate ratio of branches, velocity ratio of branches, droplet length in each branch, whole length of droplet, vorticity, pressure and effective viscosity. The analytical results of this paper reveal the variation of flow rate ratio of branches, velocity ratio of branches, droplet length in each branches and whole length of droplet during the breakup process. The results showed the flow rate ratio of branches and the velocity ratio of branches is constant during the breakup process. Also we observed the droplet length in each branches and whole length of droplet increase linearly during the breakup process. The results showed vorticity near the surface of the droplet is 3 to 7 times the vorticity of the inside of the droplet, therefore the mixing of the materials of the droplet inside increases. Also the maximum vorticity is before reaching the droplet to the center of junction.