Calculating the motion of highly confined, arbitrary-shaped particles in Hele-Shaw channels

TL;DR

This paper presents a fast, effective method combining theory, simulations, and experiments to predict the motion of arbitrarily shaped, confined particles in microfluidic channels, validated with experiments on dumbbell-shaped particles.

Contribution

It introduces a quasi-two-dimensional modeling approach using the Brinkman equation for efficient prediction of particle trajectories in confined microchannels, validated with experimental data.

Findings

Reorientation time of dumbbell particles has a minimum at a specific size ratio.

The proposed model is two orders of magnitude faster than 3D simulations.

Experimental results confirm the model's accuracy in predicting particle motion.

Abstract

We combine theory, numerical calculations, and experiments to accurately predict the motion of anisotropic particles in shallow microfluidic channels, in which the particles are strongly confined in the vertical direction. We formulate an effective quasi-two-dimensional description of the Stokes flow around the particle via the Brinkman equation, which can be solved in a time that is two orders of magnitude faster than the three-dimensional problem. The computational speedup enables us to calculate the full trajectories of particles in the channel. To test our scheme, we study the motion of dumbbell-shaped particles that are produced in a microfluidic channel using `continuous flow lithography'. Contrary to what was reported in earlier work (Uspal et al., Nature communications 4 (2013)), we find that the reorientation time of a dumbbell particle in an external flow exhibits a minimum as a function of its disk size ratio. This finding is in excellent agreement with new experiments, thus confirming the predictive power of our scheme.