Modeling the Transition between Localized and Extended Deposition in Flow Networks through Packings of Glass Beads

TL;DR

This paper presents a theoretical and computational study of particle deposition in microfluidic networks, revealing a phase transition between localized and uniform deposition driven by pressure and shear stress thresholds.

Contribution

The study introduces a mathematical model and agent-based simulations to explain the transition in deposition patterns, connecting experimental observations with analytical phase transition analysis.

Findings

Deposition shifts from localized to uniform with increasing pressure.

Two distinct phases of deposition are identified and characterized.

An analogy to one-dimensional aggregation models explains the phase transition.

Abstract

We use a theoretical model to explore how fluid dynamics, in particular, the pressure gradient and wall shear stress in a channel, affect the deposition of particles flowing in a microfluidic network. Experiments on transport of colloidal particles in pressure-driven systems of packed beads have shown that at lower pressure drop, particles deposit locally at the inlet, while at higher pressure drop, they deposit uniformly along the direction of flow. We develop a mathematical model and use agent-based simulations to capture these essential qualitative features observed in experiments. We explore the deposition profile over a two-dimensional phase diagram defined in terms of the pressure and shear stress threshold, and show that two distinct phases exist. We explain this apparent phase transition by drawing an analogy to simple one-dimensional models of aggregation in which the phase transition is calculated analytically.