  Recent experimental studies have shown that particle transfer across
streamlines can be controlled passively using stratified flows of co-flowing
streams at a finite Reynolds number. The stratification modifies the forces
acting on particles through the curvature of the undisturbed velocity profile.
In this study, we numerically analyze the particle migration in stratified flow
of two liquids of different viscosities flowing parallel to each other between
two infinite parallel plates. Particle migration in two different flow fields
is considered: (i) Couette flow and (ii) Poiseuille flow. A numerical approach
using an immersed boundary method is employed to perform two dimensional
simulations and determine conditions when particle migration from one fluid to
the other can occur. This has implications in separating particles from a fluid
without a membrane. The effect of the viscosity ratio, flowrate ratio, Reynolds
number and particle size on focusing position are analyzed to identify
conditions under which the particle migrates from one fluid to the other. It is
shown that the particle migrates to the fluid with a lower viscosity in case of
stratified Couette flow when the holdup of the low viscous fluid is
sufficiently high. In Poiseuille flow, particle migrates to the less viscous
fluid beyond a critical flowrate ratio for a fixed viscosity ratio. This
critical flowrate ratio increases with particle size.
