Bubble dynamics in microchannels: inertial and capillary migration forces

This work focuses on the dynamics of a train of unconfined bubbles flowing in a microchannel. We investigate the transverse position of the 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, the inertial migration force plays a crucial role in determining the transverse equilibrium position of the bubbles. Besides 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 a rigid bubble interface. The resulting migration force may balance external body forces, if present, such as buoyancy, centrifugal 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 with 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 their asymptotic counterparts for the limits of small Reynolds and/or capillary numbers.