Transport and deposition of weakly inertial particles in closed channel flows at low Reynolds number

An analytical approach is developed to show how particles sparsely distributed in steady and laminar channel flows can be transported for long distances or conversely deposited inside the channel due to the relative importance between the flow-induced drag and gravity forces. More precisely, we establish a rather simple particle trajectory equation which demonstrates that when particles' inertia is negligible, their behavior is characterized by the channel geometry and by a dimensionless number W that relates the ratio of the particles sedimentation terminal velocity to the flow mean velocity. The proposed particle trajectory equation is verified by comparing its predictions to particle tracking numerical simulations taking into account particle inertia and fully resolving equations. The equation is shown to be valid under the conditions that flow inertial effects are limited. Based on this trajectory equation, we build a regime diagram that can predict the behavior of particles entering closed channel flows. This diagram, by relating W to the ratio of the channel mean aperture to its total length, enables to forecast if the particles entering the flow will be either deposited or transported along the channel. The influence of the channel geometry on the particle behavior is then investigated by considering channels with straight and sinusoidal walls. In particular, the effect of the corrugation amplitude, of the asymmetry and of the phase lag between the walls on the extent of the transport and deposition zones is evaluated and verified against numerical experiments. Firstly, it is shown that the regime diagram for straight channels can be used for wavy channels with in-phase walls. Secondly, it is found that increasing the phase lag between the two walls and/or the walls corrugation amplitude leads to an increase of both the transport and sedimentation zones. Finally, it is demonstrated that increasing the lower wall corrugation amplitude relatively to the upper wall corrugation enhances particle transport.