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 optimizing the sensitivity of this technique, and more specifically by a hand-held 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 biaxial 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 the channel depth to 2 mm and pressure gradient to 5 × 104 Pa m−1 essentially maximizes 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.
Highlights
Suspensions of particles in liquid or gas are found throughout the natural world and in many industrial processes; including blood, particulate-laden air, algae in open water or in bioconvection experiments, semen samples and industrial applications such as emulsions in food and cosmetics—these examples and more are elaborated in [1,2,3,4,5]
The core idea of flow linear dichroism spectroscopy is that elongated particles undergo shear-induced rotation, which has the effect of concentrating their orientation in the direction of flow
The analyte is mixed with a reagent containing a synthetic biology micrometre-length fibre based on M13 bacteriophage, a filamentous virus known to infect Gram-negative bacteria [13]
Summary
Suspensions of particles in liquid or gas are found throughout the natural world and in many industrial processes; including blood, particulate-laden air, algae in open water or in bioconvection experiments, semen samples and industrial applications such as emulsions in food and cosmetics—these examples and more are elaborated in [1,2,3,4,5]. The application of mathematical modelling to understand and quantify molecular orientation in flow linear dichroism was addressed by McLachlan et al [10], building on classical oriented suspension mechanics [11,12] This manuscript will generalize this work to the significantly more complex problem of a non-homogeneous shear environment of pressure-driven, and potentially time-varying, channel flow, and will focus on a specific technological application. In the related context of suspensions of actively-swimming oriented particles, Pedley & Kessler [22] described a coupled model of orientation distribution, governed by a Fokker–Planck equation, and fluid flow, given by modifications to the Navier– Stokes equations proportional to the ensemble averages of orientation These early studies form the theoretical framework for our model of homogeneous suspensions of semi-rigid M13 bacteriophage via the approximation of elongated, axisymmetric, rigid Brownian rods in the limit of infinite aspect ratio.
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