  This work focuses on the dynamics of a train of unconfined bubbles flowing in
microchan- nels. We investigate the transverse position of a train of bubbles,
its velocity and the associated pressure drop when flowing in a microchannel
depending on the internal forces due to viscosity, inertia and capillarity.
Despite the small scales of the system, inertia, referred to as inertial
migration force, play a crucial role in determining the transverse equilibrium
position of the bubbles. Beside inertia and viscosity, other effects may also
affect the transverse migration of bubbles such as the Marangoni surface
stresses and the surface deformability. We look at the influence of surfactants
in the limit of infinite Marangoni effect which yields rigid bubble interface.
The resulting migration force may balance external body forces if present such
as buoyancy, Dean or magnetic ones. This balance not only determines the
transverse position of the bubbles but, consequently, the surrounding flow
structure, which can be determinant for any mass/heat transfer process
involved. Finally, we look at the influence of the bubble deformation on the
equilibrium position and compare it to the inertial migration force at the
centred position, explaining the stable or unstable character of this position
accordingly. A systematic study of the influence of the parameters - such as
the bubble size, uniform body force, Reynolds and capillary numbers - has been
carried out using numerical simulations based on the Finite Element Method,
solving the full steady Navier-Stokes equations and its asymptotic counterpart
for the limits of small Reynolds and/or capillary numbers.
