Numerical
Simulation of Deformation of Newtonian and Viscoelastic Droplets in Shear Flows
Department of Mechanical Engineering,
Graduate
2-1, Yamadaoka,
The deformation of Newtonian and viscoelastic droplets in shear flows was numerically simulated. The droplet deformation deeply relates the flow of emulsions. Emulsions are dispersions of immiscible liquids and are found in foodstuffs, pharmaceutical products, cosmetics, and coating materials. It is important to investigate the droplet deformation in lows because it relates both the function and properties of emulsion products. In addition, it is also interesting to analyze the relation between rheology of emulsions and the deformation behavior of droplets in flows. In the present simulation, the interface between two liquids is implicitly expressed using a color function F, which takes a value of 1 in one liquid and 0 in the other liquid. The interface is expressed by a contour of F = 0.5. The movement of the interface is described by an advection equation of F. The advection equation was solved with the CIP (Cubic-Interpolated Propagation) method. The flow of surrounding liquid was computed with the MAC method. The Phan Thien Tanner model was employed as a constitutive equation for viscoelastic liquids. The effect of interfacial tension was introduced with the CSF model. The deformation of droplets under shear flows between parallel plates was numerically simulated. Both the upper and the lower plates move in the counter direction to each other. Periodic boundary conditions were applied to the boundaries except for the upper and lower plates. Moreover, the droplet deformation after the cessation of shear was also simulated. The numerical simulation predicted that viscoelastic droplets deform more easily than Newtonian droplets because the viscoelastic fluid has shear-thinning viscosity. The stress in a viscoelastic droplet rapidly increased at an early stage of deformation and relaxed with time. This phenomenon is typical for viscoelastic droplets and appeared more remarkably for a fluid with stronger stretch-thickening property in elongation viscosity. Furthermore, the present computation can simulate the emergence of satellite droplets at the breakup of droplet, which has been experimentally observed. The predictions of the present numerical simulation qualitatively agree with experimental results and hence the present approach will be applicable for the simulation of flows of emulsion.