Numerical Study Of Droplet Deformation In Shear Flow Using The DUGKS Approach

A droplet suspended in another immiscible fluid can deform when subjected to a ambient flow shear.When the shear rate is large enough,the droplet will have large deformation and even break up into several satellite droplets.Droplet deformation and breakup subjected to a uniform shear in immiscible two-phase fluids are widely encountered in many engineering and biomedical applications such as microfluidic technology and emulsion processing.The deformation of an isolated droplet in shear flow can be governed by the ratio of shear and interfacial stresses(),the viscosity ratio of droplet and surrounding fluid,and the ratio of inertia force and viscous force(i.e.,Reynolds number).In practice,such as in a microfluidic chip,the flow and droplet deformation in the tube are affected by the wall confinement,thus the wall confinement effect must be considered.In this study,the deformation behavior of an initially circular droplet in 2D moving wall driven shear flow is studied by using the discrete uniform gas kinetic scheme(DUGKS)combined with the phase field model.Besides the above physical parameters,two numerical parameters affecting the droplet deformation are also considered.They are the Peclet number(the ratio of advective transport to the phase-field inherent diffusive transport)and the Cahn number(,the ratio of the numerical interfacial thickness,W,and initial radius of droplet,R)which can affect the numerical accuracy and numerical stability.The main part of the research is to analyze the effects of capillary number,viscosity ratio,wall confinement and Reynolds number on droplet deformation.By conducting a series of numerical experiments,it is found that for low shear rate cases the numerical dissipation becomes too large to simulate correctly the deformation when the Peclet number is smaller than one and the initial droplet radius is fixed at 10 W.For a given W,the numerical dissipation increases with increasing Ch.Numerical results show that,if R is less than 10 W or Ch is larger than 0.1,the deformation parameter cannot be accurately simulated.An initially circular droplet deforms to an approximate ellipse when the capillary number is sufficiently small.The larger the capillary number,the larger the deformation parameter is and the smaller the inclination angle is.Considering the wall effect,the deformation parameters of two-dimensional droplets in shear flow under different viscosity ratios depend roughly linearly on the capillary number.The scaling factor is related to the wall constraint and the viscosity ratio.When the wall confinement parameter is larger than 0.4,the Taylor model is no longer applicable even if the droplet deforms into an ellipse,indicating that the wall effect cannot be neglected.The DUGKS results at large capillary number and viscosity ratio deviate from 3D numerical results in the literature.But our 2D DUGKS results are in good agreement with the prediction for 2D droplet deformation in the existing literature,meaning that the 2D droplet deformation problem is quantitatively different from the 3D problem and our phase-field DUGKS simulations provide additional data for this difference.We also find that,when the fluid inertia is considered as reflected by a finite Re and a finite Ca,the steady-state droplet shape deviates from ellipse,and this deviation is further enhanced by wall confinement.This study proves that the two-phase DUGKS model combined with the phase field can be successfully applied to liquid-liquid two-phase flow research.