Surfactant-laden droplet behavior on wetting solid wall with non-Newtonian fluid rheology

We develop a coupled lattice-Boltzmann with finite-difference (LB-FD) method to simulate surfactant-laden droplet behaviors on wetting solid wall with non-Newtonian fluid rheology. The effects of the power-law exponent, wettability, force direction, and viscosity ratio on the droplet movement under the shear flow or body force are investigated. It is found that the surfactant-laden droplet moves faster and breaks up more easily than the clean droplet owing to the decreased local interfacial tension. During the initial period of the droplet movement, with the decrease of the power-law exponent of the matrix fluid, the unbalanced Young's force plays a significant role in prompting droplet spreading along the hydrophilic wall whereas making the droplet recoil along the hydrophobic wall. Under the influence of the shear force, the droplet deformation is strengthened in the shear thickening matrix fluid due to high viscous stress from the external flow. However, under the influence of the body force, droplet deformation is strengthened in the shear thinning matrix fluid because the reduction of the matrix fluid apparent viscosity generates less viscous drag force. Furthermore, the shear thickening pendent droplet is more elongated and shows more flexible behavior than the shear thinning droplet during its falling in the Newtonian matrix fluid. The decrease of the viscosity ratio causes the shear thickening droplet to form the shape of a spherical cap, compared with the shear thinning droplet behaving like a rigid object. The present work not only demonstrates the capacity of the coupled LB-FD method but also sheds light on the mechanism of surfactant-laden droplet dynamics on wetting solid wall where non-Newtonian rheology is considered.