Inertio-capillary cross-streamline drift of droplets in Poiseuille flow using dissipative particle dynamics simulations

We find using dissipative particle dynamics (DPD) simulations that a deformable droplet sheared in a narrow microchannel migrates to steady-state position that depends upon the dimensionless particle capillary number Ca-p = V-max mu(f)/Gamma (2R/H), which controls the droplet deformability (with V-max the centerline velocity, mu(f) the fluid viscosity, Gamma the surface tension, R the droplet radius, and H the gap), the droplet (particle) Reynolds number Re-p = rho VmaxH/mu(f) (4R(2)/H-2), which controls inertia, where rho is the fluid density, as well as on the viscosity ratio of the droplet to the suspending fluid kappa = mu(d)/mu(f). We find that when the Ohnesorge number Oh = root Ca-p/Re-p is around 0.06, so that inertia is stronger than capillarity, at small capillary number Ca-p < 0.1, the droplet migrates to a position close to that observed for hard spheres by Segre and Silberberg, around 60% of the distance from the centerline to the wall, while for increasing Ca-p the droplet steady-state position moves smoothly towards the centerline, reaching around 20% of the distance from centerline to the wall when Ca-p reaches 0.5 or so. For higher Oh, the droplet position is much less sensitive to Ca-p, and remains at around 30% of the distance from centerline to the wall over the whole accessible range of Ca-p. The results are insensitive to viscosity ratios from unity to the highest value studied here, around 13, and the drift towards the centerline for increasing Ca-p is observed for ratios of droplet diameter to gap size ranging from 0.1 to 0.3. We also find consistency between our predictions and existing perturbation theory for small droplet or particle size, as well as with experimental data. Additionally, we assess the accuracy of the DPD method and conclude that with current computer resources and methods DPD is not readily able to predict cross-stream-line drift for small particle Reynolds number (much less than unity), or for droplets that are less than one tenth the gap size, owing to excessive noise and inadequate numbers of DPD particles per droplet.