Brownian noise effects on magnetic focusing of prolate and oblate spheroids in channel flow

TL;DR

This study explores how Brownian noise influences magnetic focusing of spheroids in channel flow, revealing counterintuitive effects like defocusing at high magnetic field strengths and mapping different focusing regimes.

Contribution

It introduces a numerical and theoretical framework to analyze noise effects on magnetic spheroid focusing, including a new probabilistic model for strong-field behavior.

Findings

Brownian noise causes defocusing at high magnetic fields.

Focusing regimes depend on field strength and tilt angle.

A probabilistic model explains noise-induced phenomena.

Abstract

We investigate Brownian noise effects on magnetic focusing of prolate and oblate spheroids carrying permanent magnetic dipoles in channel (Poiseuille) flow subject to a uniform magnetic field. The focusing is effected by the low-Reynolds-number wall-induced hydrodynamic lift which can be tuned via tilt angle of the field relative to the flow direction. This mechanism is incorporated in a steady-state Smoluchowski equation that we solve numerically to analyze the noise effects through the joint position-orientation probability distribution function of spheroids within the channel. The results feature partial and complete pinning of spheroidal orientation as the field strength is increased and reveal remarkable and even counterintuitive noise-induced phenomena (specifically due to translational particle diffusivity) deep into the strong-field regime. These include field-induced defocusing, or lateral broadening of the focused spheroidal layer, upon strengthening the field. We map out focusing `phase' diagrams based on the field strength and tilt angle to illustrate different regimes of behavior including centered focusing and defocusing in transverse field, and off-centered focusing in tilted fields. The latter encompasses two subregimes of optimal and shouldered focusing where spheroidal density profiles across the channel width display either an isolated off-centered peak or a skewed peak with a pronounced shoulder stretching toward the channel center. We corroborate our results by analyzing stability of deterministic fixed points and a reduced one-dimensional probabilistic theory which we introduce to semiquantitatively explain noise-induced behavior of pinned spheroids under strong fields. We also elucidate the implications of our results for efficient shape-based sorting of magnetic spheroids.