Shape design for stabilizing microparticles in inertial microfluidic flows

Abstract

Design of microparticles which stabilize at the centerline of a channel flow when part of a dilute suspension is examined numerically for moderate Reynolds numbers (10 ≤ Re ≤ 80). This problem is motivated by the need for design of shaped particle carriers for use in next generation cell cytometry devices. Stability metrics for particles with arbitrary shapes are formulated based on linear-stability theory. Particle shape is parametrized by a compact, Non-Uniform Rational B-Spline (NURBS)-based representation. Shape-design is posed as an optimization problem and solved using adaptive Bayesian optimization. We focus on designing particles for maximal stability at the channel-centerline robust to perturbations. Our results indicate that centerline-focusing particles are families of characteristic "fish"/"bottle"/"dumbbell"-like shapes, exhibiting fore-aft asymmetry. A parametric exploration is then performed to identify stable particle-designs at different k's (particle chord-to-channel width ratio) and Re's (0.1 ≤ k ≤ 0.4, 10 ≤ Re ≤ 80). Particles at high-k's and Re's are highly stabilized when compared to those at low-k's and Re's. A comparison of the modified dumbbell designs from the current framework also shows better performance to perturbations in Fluid-Structure Interaction (FSI) when compared to the rod-disk model-dumbbell reported previously (Uspal & Doyle, 2014) for low-Re Hele-Shaw flow. We identify a basin of attraction around the centerline, within which any arbitrary release results in rotationally stable centerline-focusing. We find that this basin spans larger release-angle-ranges and lateral locations (tending to the channel width) for narrower channels. This effectively standardizes the notion of global focusing using the current stability-paradigm in narrow channels, which eliminates the need for an independent design for global-focusing in such configurations. The framework detailed in this work is illustrated for 2D cases and is generalizable to stability in 3D flow-fields. The current formulation is agnostic to Re and particle/channel geometry which indicates substantial potential for integration with imaging flow-cytometry tools and microfluidic biosensing-assays.

The influence of cell elastic modulus on inertial positions in Poiseuille microflows

“…It has also previously been shown, both computationally and experimentally, that the shape of rigid particles can influence their migration patterns in a microchannel (43)(44)(45)(46). It is quite likely that it will similarly affect deformable particles such as cells.…”

“…Adherent MCF-7 cells appear rounded in shape, whereas MDA-MB-231 cells are more elongated in one direction and therefore spindle-shaped. It has been hypothesized that deformable particles suspended in flow experience stresses that can cause it to change its shape (14,47), and therefore, it may also affect the cells' inertial positions; however, some of the above studies have shown that centerline-focusing particles typically have fore-aft asymmetry characteristics, similar to ''fish'' or ''bottle''-like shapes (45), which MDA-MB-231 cells also possess when adherent. Interestingly, other studies have found that the direction of lateral migration of a deformable droplet in a ferrofluid depends on the orientation of the droplet because of uniform magnetic fields at different directions (48).…”

A comprehensive review on non-active micro-pumps for microfluidic platforms

“…Another technique utilizes the microfluidic device's hydrodynamic properties to reduce fluctuation of flow [24], such as inertia migration [25], Dean flow [26], hydrophoresis [27], and viscoelastic [28]. The combinations of hydrodynamic forces also progressively attracted attention among the recorded passive schemes.…”