  Cross-stream migration of a deformable bubble is investigated computationally
in a pressure-driven channel flow of a viscoelastic fluid via
interface-resolved simulations. The flow equations are solved fully coupled
with the Giesekus model equations using the front-tracking method and extensive
simulations are performed for a wide range of flow parameters to reveal the
effects of bubble deformability, fluid elasticity, shear-thinning, and fluid
inertia on the bubble migration dynamics. Migration rate of a bubble is found
to be much higher than that of a solid particle under similar flow conditions
mainly due to free-slip condition on its surface. It is observed that direction
of bubble migration can be altered by varying shear-thinning of the ambient
fluid. With a strong shear-thinning, the bubble migrates towards the wall while
it migrates towards the center of the channel in a purely elastic fluid without
shear-thinning. An onset of elastic flow instability is observed beyond a
critical Weissenberg number, which in turn causes a path instability even for a
nearly spherical bubble. An inertial path instability is also observed once
bubble deformation exceeds a critical value. Shear-thinning is found to be
suppressing the path instability in a viscoelastic fluid with a high polymer
concentration whereas it reverses its role and promotes path instability in a
dilute polymer solution. It is found that bubble migration towards wall induces
a secondary flow with a velocity that is about an order of magnitude higher
than the one induced by a solid particle under similar flow conditions.
