title: Broadband computational rheology for material characterisation
Creators: name: Smith, Matthew George
Publisher: name: University of Glasgow
Year: 2024

description: Rheology is a wide-reaching field whose applications are underpinned by a prior knowledge of the ‘viscoelastic’ properties of (complex) materials generally employed across industries such as oil and gas, food processing, cosmetics, and biophysics; the latter being the main focus of this thesis. Biomedical studies often only have access to small sample volumes, which make conventional bulk rheology techniques unsuitable for their characterization, this has led to the development of a new field called microrheology, where new techniques can characterise the viscoelastic properties of complex fluids by using only a few microlitres of a sample volume. As a branch of rheology, microrheology utilises the same underpinning principles and aims to calculate a material’s properties, including the complex shear modulus, which in turn describes how the material behaves.

The following thesis is aimed at investigating the use of microrheology with optical tweezers in a series of papers exploring different areas within the field of microrheology. Each paper targets certain gaps within the field and as such this thesis is fairly broad reaching touching on algorithm development, machine learning and shear flow analysis.

Chapter 2 presents the work “i-RheoFT: Fourier transforming sampled functions without artefacts”, and introduces an open access MATLAB code, “i-RheoFT”, which can evaluate the Fourier transform of any generic time-dependent function with a finite number of data points. I-RheoFT could be of particular interest and use to those who study sampled or time-averaged functions. The paper investigates three experimental parameters employing i-RheoFT: (i) the density of initial experimental data points that describe the signal, (ii) the interpolation function used to perform virtual oversampling of the signal, which is required for accurate evaluation of the Fourier transform, and (iii) the effect that signal noise has on the Fourier transform. As the chapter shows, a high number of initial data points or a high signal-to-noise ratio corresponds to a good performance for each interpolation function used. Alternatively, a low number of initial points or signal-to-noise ratio corresponds to poor performance across each interpolation function used. As one would expect, there exists a threshold, for both the signal-to-noise and the number of initial points, at which the performance becomes acceptable and has been identified in both cases in the chapter. More recently further development of this work has led to the creation of two open source applications [1, 2] available for download, these aim to compute the complex shear modulus from bulk rheology and atomic force microscopy measurements respectively. Moreover, since its publication this work has been used in three studies [3–5], two of which feature the author of this thesis as a co-author.

Chapter 3 examines the claim that linear microrheology with optical tweezers should not be used for the study of living systems due to the variation between the time required to collect statistically valid data and the mutational time of the studied living system. This work is a first step at enhancing conventional statistical mechanics analysis of particle trajectories, captured using microrheology with optical tweezers, by exploiting machine learning techniques to reduce the current measurement time from tens of minutes down to as little as one second. The chapter describes how computer simulated trajectories, of Newtonian fluids with viscosities spanning three decades, have been used to corroborate the requirement for sufficiently long measurements to offer a good estimation of the fluid viscosity using conventional analytical techniques. In addition, the work provides a method for estimating the measurement time of a microrheology with optical tweezers experiment, based on the relative viscosity of the fluid being analysed to produce an uncertainty as low as 1%. Furthermore, this chapter presents a machine learning algorithm that can predict the viscosity of both simulated and real trajectories, carrying an error as low as ∼ 0.3%, using only one second of data. It is believed that with this machine learning enhancement, microrheology with optical tweezers will become a powerful tool for studies involving living systems.

Chapter 4 presents an investigation into flow induced self-assembly (FISA) of particles suspended in a viscoelastic shear thinning fluid subjected to simple shear flow. This phenomena is currently not fully understood and little has been done in literature so far to investigate the possible effects of the shear-induced elastic instability. In this work, a bespoke cone and plate shear cell is used to provide new insights on the FISA dynamics. In particular, we have fine tuned the applied shear rates to investigate the chaining phenomenon of micron-sized spherical particles suspended into a viscoelastic fluid characterised by a distinct onset of elastic instability. This has allowed us to reveal three phenomena never reported in literature before, i.e.: (I) the onset of the elastic instability is strongly correlated with an enhancement of FISA; (II) particle chains break apart when a constant shear is applied for ‘sufficiently’ long-time (i.e. much longer than the fluids’ longest relaxation time). This latter point correlates well with the outcomes of parallel superposition shear measurements, which (III) reveal a fading of the elastic component of the suspending fluid during continuous shear flows.