Analysis of the trajectory of a sphere moving through a geometric constriction

TL;DR

This study numerically investigates how fluid and particle inertia influence the motion of spherical particles through a constriction, revealing effects on particle separation potential in microfluidic applications.

Contribution

It provides new insights into the impact of inertia and geometric constrictions on particle trajectories, informing microfluidic separation techniques.

Findings

Particles attain smaller separations due to inertia and constriction.

Increased inertia leads to larger lateral displacements.

Separation based on density differences is feasible due to inertia effects.

Abstract

We present a numerical study of the effect that fluid and particle inertia have on the motion of suspended spherical particles through a geometric constriction to understand analogous microfluidic settings, such as pinched flow fractionation devices. The particles are driven by a constant force in a quiescent fluid, and the constriction (the pinching gap) corresponds to the space between a plane wall and a second, fixed sphere of the same size (the obstacle). The results show that, due to inertia and/or the presence of a geometric constriction the particles attain smaller separations to the obstacle. We then relate the minimum surface-to-surface separation to the effect that short-range, repulsive non-hydrodynamic interactions (such as solid-solid contact due to surface roughness, electrostatic double layer repulsion, etc.) would have on the particle trajectories. In particular, using a simple hard-core repulsive potential model for such interactions, we infer that the particles would experience larger lateral displacements moving through the pinching gap as inertia increases and/or the aperture of the constriction decreases. Thus, separation of particles based on differences in density is in principle possible, owing to the differences in inertia associated with them. We also discuss the case of significant inertia, in which the presence of a small construction may hinder separation by reducing inertia effects.