Measuring collective diffusion properties by counting particles in boxes

Fuente: arXiv
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Main Authors: Carter, Adam, Mackay, Eleanor K. R., Sprinkle, Brennan, Thorneywork, Alice L., Marbach, Sophie
Format: Preprint
Published: 2024
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_version_ 1866913755958345728
author Carter, Adam
Mackay, Eleanor K. R.
Sprinkle, Brennan
Thorneywork, Alice L.
Marbach, Sophie
author_facet Carter, Adam
Mackay, Eleanor K. R.
Sprinkle, Brennan
Thorneywork, Alice L.
Marbach, Sophie
contents The collective diffusion coefficient $D_\mathrm{coll}$ is a key quantity for describing the macroscopic transport properties of soft matter systems. However, measuring $D_\mathrm{coll}$ is a fundamental experimental and numerical challenge, as it either relies on nonequilibrium techniques that are hard to interpret or, at equilibrium, on Fourier-based approaches which are fraught with difficulties associated with Fourier transforms. In this work, we investigate the equilibrium diffusive dynamics of a 2D colloidal suspension experimentally and numerically. We use a "Countoscope" technique, which analyses the statistics of particle number counts $N(t)$ in virtual observation boxes of a series of microscopy images at equilibrium, to measure $D_\mathrm{coll}$ for the first time. We validate our results against Fourier-based approaches and establish best practices for measuring $D_\mathrm{coll}$ using fluctuating counts. We show that Fourier techniques yield inaccurate long-range collective measurements because of the non-periodic nature of an experimental image, yet counting exploits this property by using finite observation windows. Finally, we discuss the potential of our method to advance our understanding of collective properties in suspensions, particularly the role of hydrodynamic interactions.
format Preprint
id arxiv_https___arxiv_org_abs_2412_14122
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Measuring collective diffusion properties by counting particles in boxes
Carter, Adam
Mackay, Eleanor K. R.
Sprinkle, Brennan
Thorneywork, Alice L.
Marbach, Sophie
Soft Condensed Matter
Statistical Mechanics
The collective diffusion coefficient $D_\mathrm{coll}$ is a key quantity for describing the macroscopic transport properties of soft matter systems. However, measuring $D_\mathrm{coll}$ is a fundamental experimental and numerical challenge, as it either relies on nonequilibrium techniques that are hard to interpret or, at equilibrium, on Fourier-based approaches which are fraught with difficulties associated with Fourier transforms. In this work, we investigate the equilibrium diffusive dynamics of a 2D colloidal suspension experimentally and numerically. We use a "Countoscope" technique, which analyses the statistics of particle number counts $N(t)$ in virtual observation boxes of a series of microscopy images at equilibrium, to measure $D_\mathrm{coll}$ for the first time. We validate our results against Fourier-based approaches and establish best practices for measuring $D_\mathrm{coll}$ using fluctuating counts. We show that Fourier techniques yield inaccurate long-range collective measurements because of the non-periodic nature of an experimental image, yet counting exploits this property by using finite observation windows. Finally, we discuss the potential of our method to advance our understanding of collective properties in suspensions, particularly the role of hydrodynamic interactions.
title Measuring collective diffusion properties by counting particles in boxes
topic Soft Condensed Matter
Statistical Mechanics
url https://arxiv.org/abs/2412.14122