Anomalous diffusion for mass transport phenomena II: Subdiffusion in polydimethylsiloxane (PDMS)

TL;DR

This paper investigates subdiffusive mass transport in PDMS, revealing anomalous diffusion behavior modeled by fractional diffusion, which impacts microfluidic device performance and chemical interactions.

Contribution

It demonstrates that diffusion in PDMS is anomalous and models it using stretched-time fractional diffusion, providing new transport parameters for various dyes.

Findings

Diffusion in PDMS is subdiffusive and nonlinear.

Anomalous diffusion can be modeled with fractional diffusion.

Transport parameters vary with dye and device conditions.

Abstract

Polydimethylsiloxane (PDMS) is a glassy polymer widely used in biomedical engineering, namely in microfluidics applications. However, PDMS is known to interact with hydrophobic chemicals. This interaction is exacerbated at the scale of microfluidics, making careful modeling of in-device concentrations vital for PDMS-based microfluidic devices. While it has been previously reported that many chemicals diffuse through PDMS, here we report that diffusion in PDMS is anomalous, i.e. characterized by nonlinear, subdiffusive mean-squared displacements (MSD). We show that this anomalous diffusion can be modeled in the framework of stretched-time fractional diffusion, and report the transport parameters for a set of fluorescent tracer dyes. Depending on the device geometry and protocol, this anomalous behavior may have a significant impact, specifically in regards to cross-talk between microfluidic channels.