A capsule motion inside a microfluidic channel has attracted a lot

of attention in recent decades owing to its important applications in

industrial, pharmaceutical and physiological systems such as in cell

sorting, targeted drug delivery and blood flow. In this dissertation, we

computationally investigate an elastic capsule's lateral migration inside

a constricted microfluidic device under Stokes flow conditions. We use

the Membrane Spectral Boundary Element (MSBE) method to determine the

capsule dynamics due to its high computational accuracy and versatility

in dealing with complex solid geometries.

In the bounded Poiseuille flow of the microfluidic constriction, a capsule,

placed initially off-centered will migrate away from the wall

and move toward the channel centerline. The capsule's lateral migration

behavior is caused by the combination of the wall effects due to the

existence of the channel boundary, the shear gradient generated by the

non-linear velocity distribution of the flow, and the lift force created

by the capsule deformation. We use a constricted device instead of

a straight channel to do the simulations, because the capsule's lateral

migration in a straight channel is too slow to be observed easily, while

the existence of the converging connection of the constricted device

increases the capsule's lateral velocity and thus facilitates its migration.

The main goal of our research is to investigate the effects of the capsule's

physical properties on its lateral migration behavior. We released various

deformable capsules at different initial positions, membrane hardness,

viscosity ratios, and capsule volumes inside the constricted channel

and computed their deformation behavior and migration trajectories. Our

results show that changing a capsule's viscosity ratio or the membrane

hardness does not strongly affect the capsule's lateral migration due

to the capsule's weak inner circulation. On the other hand, changing

the capsule's initial position and capsule volume strongly affect its

migration trajectories. Thus soft particles with different sizes can

be separated and identified.