# Oriented suspension mechanics with applications to flow linear dichrosim spectroscopy and pathogen detection

## TL;DR

This paper develops a model for flow linear dichroism in suspension-based pathogen detection, showing how channel dimensions and flow oscillations influence particle alignment and signal sensitivity.

## Contribution

It introduces a coupled Fokker-Planck and flow model for oriented suspension mechanics, optimizing parameters for enhanced linear dichroism signals in pathogen detection.

## Key findings

- Increasing channel depth significantly improves the dichroism signal.
- Oscillating flow can achieve similar alignment to steady flow at certain frequencies.
- Optimal channel depth and pressure maximize particle alignment.

## Abstract

Flow linear dichroism is a biophysical spectroscopic technique that exploits the shear-induced alignment of elongated particles in suspension. Motivated by the broad aim of optimising the sensitivity of this technique, and more specifically by a handheld synthetic biotechnology prototype for waterborne-pathogen detection, a model of steady and oscillating pressure-driven channel flow and orientation dynamics of a suspension of slender microscopic fibres is developed. The model couples the Fokker-Planck equation for Brownian suspensions with the narrow channel flow equations, the latter modified to incorporate mechanical anisotropy induced by the particles. The linear dichroism signal is estimated through integrating the perpendicular components of the distribution function via an appropriate formula which takes the bi-axial nature of the orientation into account. For the specific application of pathogen detection via binding of M13 bacteriophage, it is found that increases in the channel depth are more significant in improving the linear dichroism signal than increases in the channel width. Increasing channel depth to $2~$mm and pressure gradient to $5 \times 10^4~$Pa/m essentially maximises the alignment. Oscillating flow can produce nearly equal alignment to steady flow at appropriate frequencies, which has significant potential practical value in the analysis of small sample volumes.