Conditional stability of particle alignment in finite-Reynolds-number channel flow

Abstract

Finite-size neutrally buoyant particles in a channel flow are known to accumulate at specific equilibrium positions or spots in the channel cross-section if the flow inertia is finite at the particle scale. Experiments in different conduit geometries have shown that while reaching equilibrium locations, particles tend also to align regularly in the streamwise direction. In this paper, the Force Coupling Method was used to numerically investigate the inertia-induced particle alignment, using square channel geometry. The method was first shown to be suitable to capture the quasisteady lift force that leads to particle cross-streamline migration in channel flow. Then the particle alignment in the flow direction was investigated by calculating the particle relative trajectories as a function of flow inertia and of the ratio between the particle size and channel hydraulic diameter. The flow streamlines were examined around the freely rotating particles at equilibrium, revealing stable small-scale vortices between aligned particles. The streamwise inter-particle spacing between aligned particles at equilibrium was calculated and compared to available experimental data in square channel flow (Gao et al. Microfluidics and Nanofluidics 21, 154 (2017)). The new result highlighted by our numerical simulations is that the inter-particle spacing is unconditionally stable only for a limited number of aligned particles in a single train, the threshold number being dependent on the confinement (particle-to-channel size ratio) and on the Reynolds number. For instance, when the particle Reynolds number is ≈ 1 and the particle-to-channel height size ratio is ≈ 0.1, the maximum number of stable aligned particles per train is equal to 3. This agrees with statistics realized on the experiments of (Gao et al. Microfluidics and Nanofluidics 21, 154 (2017)). It is argued that when several particles are hydrodynamically connected moving as a unique structure (the train) with a steady streamwise velocity, large-scale hydrodynamic perturbations induced at the train scale prohibit small-scale vortex connection between the leading and second particles, forcing the leading particle to leave the train. arXiv:1810.08670v1 [physics.flu-dyn]

Particle pairs and trains in inertial microfluidics

“…However, early experiments [5] and most recent 2D simulations [23] report an increase of particle spacing over time in agreement with our own findings [25]. Some experiments report that for increasing Reynolds number the axial spacing between the particles decreases [22,28] even to the value of cross-streamline pairs [6]. However, other experiments report an increase of the spacing in linear trains with increasing Re, while the spacing decreases in staggered trains [29].…”

“…The separation of the leading particle from the rest of the train was also reported in simulations by Gupta et al [28]. They also mention stable trains up to a certain cluster size, an effect the authors name conditional stability.…”

“…Linear particle trains flowing on the same streamline have been observed both in experiments [6,22] and simulations [28]. Typically, they have an axial particle spacing about twice the distance measured for staggered trains.…”

“…In the range of Re ≈ 1 to 4 recent experiments observe that the spacing is independent of the flow velocity and that the smallest channel dimension determines the axial spacing between pairs [30]. Finally, simulations using a force coupling method report that trains are only stable up to lengths of 2 to 4 particles depending on the confinement ratio and the particle Reynolds number [28].…”

“…This is especially relevant for Re ≈ 100, where the secondary flow around a single larger particle (a/w = 0.4) becomes so strong that it influences the particle-wall interactions [29]. A detailed review of the effect of particle size suggests that for a small confinement ratio a/w 0.1 the particles move closer together with increasing Reynolds number [17,22,28] while for larger particles the separation seems to increase [5,29].…”