Capsule equilibrium positions near channel center in Poiseuille flow

Abstract A fundamental question in microfluidics is how capsules migrate laterally in microchannels. Because of formidable challenges in physics, no study has investigated capsule migration near the channel center at a wide range of Capillary numbers and Reynolds numbers. To fill this significant knowledge gap, we developed a 2D mathematical model, based on the front tracking method, to investigate the lateral migration of capsules near the channel center. The trajectory, shape, deformation, equilibrium position of capsules were studied at various capsule Capillary numbers ( Ca  = 0.005–0.6) and Reynolds numbers ( Re  = 1–20). At high Reynolds numbers and Capillary numbers ( Ca > 1.694 Re - 1.068 ), the equilibrium positions were at the channel center; whereas, at low Reynolds numbers and Capillary numbers, they were between the channel center and the wall. A region near the channel center where no capsule can equilibrate within the studied range of Reynolds numbers and Capillary numbers was discovered for the first time. This region of non-equilibrium position has never been identified in either 3D or 2D simulations, though it is unclear this region will exist in 3D simulations. We deciphered the underlying mechanism for this novel region as outlined below: First, both the lateral velocity and the resultant lift force increased. Second, the shape of capsule transformed from an ellipse to a bullet. Third, the relative velocity at the top of the capsule changed from the direction towards the channel outlet to the direction towards the inlet. Fourth, the velocity difference between the top and the bottom of the capsule decreased. Finally, the high pressure region on the top windward disappeared. This study has advanced our understanding of the fluid mechanics of capsule migration in microchannel.