Numerical simulation of immiscible liquid-liquid flows in channels

This study investigates interfacial dynamics of two-layer immiscible fluids using direct numerical simulation. A numerical model of two immiscible fluids in a two-dimensional Poiseuille channel flow in an inclined channel is developed. The denser and higher viscosity fluid occupies the lower half of the channel while the lighter one with lower viscosity occupies the upper half. Projection method is applied to solve the set of Navier-stokes equations, and front-tracking technique is used to track the interface between the two fluids. The first aspect of this work examines the capability of the front-tracking technique to handle multi-layer flows. The accuracy of this numerical technique is verified by both experimental and analytical results for certain range of flow parameters such as Reynolds number (Re), Froude number (Fr), Weber number (We), velocity ratio (beta), viscosity ratio (psi) and the inclination angle (theta). The numerical simulation generates both plane and wavy interfacial profile and the results are in good agreement with measured experimental results. The observed instability shows the higher viscosity fluid drawn out as fingers that penetrate into the lower viscosity layer. The predicted interface shape compares well with previously reported experiments.; Finally, interfacial behaviors of multi-layer liquid-liquid flow of non-Newtonian and Newtonian fluids in an inclined channel are investigated. The lighter fluid is replaced by a shear thinning, non-Newtonian fluid. A proper empirical model for viscosity constitutive equation is employed for describing the non-Newtonian behavior of the fluid to allow for numerical computation. A comparative study is conducted with suitable range of flow parameters using non-Newtonian fluid as the lighter fluid occupying the upper layer of channel. The thickness of the PEG layer increases as the degree of shear thinning increases. This effect is observed only with gravity induced wavy interface. Shear induced wavy interface does not manifest any effect of shear thinning of the oil for the range of degree of shear thinning effects considered in this study.