Anomalous diffusion in an electrolyte saturated paper matrix

TL;DR

This paper investigates the anomalously high effective diffusivity of dye molecules in electrolyte-saturated paper, revealing its dependence on pH and salt concentration, and proposes a theory based on electrostatic interactions.

Contribution

It introduces a simple theoretical model explaining enhanced diffusion in porous electrolyte-saturated paper due to electrostatic interactions.

Findings

Effective diffusivity exceeds free solution diffusivity by several orders of magnitude.

Diffusivity depends significantly on pH and salt concentration.

Electrostatic interactions at porous interfaces influence dye diffusion.

Abstract

Diffusion of colored dye on water saturated paper substrates has been traditionally exploited with great skill by renowned water color artists. The same physics finds more recent practical applications in paper based diagnostic devices deploying chemicals that react with a bodily fluid yielding colorimetric signals for disease detection. During spontaneous imbibition through the tortuous pathways of a porous electrolyte saturated paper matrix, a dye molecule undergoes diffusion in a complex network of pores. The advancing front forms a strongly correlated interface that propagates diffusively but with an enhanced effective diffusivity. We measure this effective diffusivity and show that it is several orders of magnitude greater than the free solution diffusivity and has a significant dependence on the solution pH and salt concentration in the background electrolyte. We attribute this to electrically mediated interfacial interactions between the ionic species in the liquid dye and spontaneous surface charges developed at porous interfaces, and introduce a simple theory to explain this phenomenon.