Enhanced pinch flow fractionation using inertial streamline crossing

Abstract

In this work, we study the influence of inertia on the dynamics of neutrally buoyant spherical microbeads of varying diameter in a Pinch Flow Fractionation device. To that aim, we monitor their trajectory over an unprecedented wide range of flow rates and flow rate ratios. Our experimental results are supplemented by a depth-averaged 2D-model where the flow is described using the Navier-Stokes equation coupled with the shallow channel approximation and where particles trajectories are computed from Newton's second law of motion with a particle tracing model. Above a certain flow rate, we show that particles inertia enables them to cross streamlines in response to an abrupt change of direction. These streamline crossing events combined with the increasing effect of the inertial lift forces drive particles to deviate from the inertialess trajectory. The amplitude of the resulting inertial deviation increases both with the particles diameter and the total flow rate before reaching a plateau. Consequently, based on our numerical and experimental results, we determine the optimal flow conditions to shift the particles distribution to significantly enhance their size-based separation.

Shear-enhanced sorting of ovoid and filamentous bacterial cells using pinch flow fractionation

“…We notice a small shift of their equilibrium position towards the centre of the channel over Re π = 32, which might be induced by their inertia becoming strong enough to enable them to cross streamlines over a short distance at the pinch outlet. 44 In line with what we observed at the pinch outlet, the distance between the 10 μm diameter spherical particles and the lateral wall increases with the flow rate. However, they are much closer to the wall in the expansion than small filamentous cells when Re π ≤ 4 although their positions are almost identical at the pinch outlet under the same flow conditions.…”

“…At the pinch outlet, the positions of the particles remain mainly constant as Re π increases, except for 5 μm diameter particles, where Y π becomes larger at Re π = 16 due to the wall-induced lift force. 44 The 5 μm diameter particles travel further away from the wall of the pinched segment than the 3 μm diameter particles. Ovoid cells are the closest to the wall independently from Re π .…”

“…The trajectories of the spherical particles are extracted from the results obtained in our previous study. 44…”

“…However, we previously demonstrated that the effect of the resulting deformations on the flow rate was negligible in our device, even at Re π = 128. 44 The ratio between the flow rate of the solution carrying the particles Q 1 and flow rate of the sheath flow Q 2 is Q 1 / Q 2 = 1/30, with Q 1 + Q 2 = Q . This value is small enough to ensure a narrow alignment of the cells against the wall of the pinch while allowing both an acceptable throughput and a direct comparison of cells trajectories with the trajectories of the spherical particles extracted from our previous study 44 under identical flow conditions.…”

“…44 The ratio between the flow rate of the solution carrying the particles Q 1 and flow rate of the sheath flow Q 2 is Q 1 / Q 2 = 1/30, with Q 1 + Q 2 = Q . This value is small enough to ensure a narrow alignment of the cells against the wall of the pinch while allowing both an acceptable throughput and a direct comparison of cells trajectories with the trajectories of the spherical particles extracted from our previous study 44 under identical flow conditions. The two solutions are injected into the device by two high-precision syringe-pumps (Nemesys, Cetoni).…”