Orientation Dynamics of Elongated Particles in Viscous Converging-Diverging Flows

Neutrally buoyant, ellipsoidal particles in unidirectional flows at zero Reynolds number follow streamlines and perform tumbling motions. In more complex geometries, such as converging-diverging channels, rigid elongated particles exhibit a markedly different behavior: they align parallel to the flow before the constriction and reorient perpendicular to the flow direction after the constriction.

To rationalize this diverse phenomenology, we combine analytical methods and particle-based simulations to study particle motion in non-unidirectional viscous flows. By solving the Stokes equation perturbatively, we derive an analytical expression for the velocity field in a converging-diverging channel. This enables us to determine whether the fluid locally rotates or aligns the particle, depending on particle shape and the rotational and extensional flow components.

Our findings reveal that zones of tumbling and stable orientations can coexist within the same channel, unveiling rich behaviors as both particle and channel shapes vary. These results are supported by preliminary microfluidic experiments. Our approach is not limited to the presented geometry but can be readily adapted to other regular-shaped channels, providing a robust framework to predict particle motion in various flow environments.