Crooks Fluctuation Theorem for Single Polymer Dynamics in Time-Dependent Flows: Understanding Viscoelastic Hysteresis

Nonequilibrium work relations have fundamentally advanced our understanding of molecular processes. In recent years, fluctuation theorems have been extensively applied to understand transitions between equilibrium steady-states, commonly described by simple control parameters such as molecular extension of a protein or polymer chain stretched by an external force in a quiescent fluid. Despite recent progress, far less is understood regarding the application of fluctuation theorems to processes involving nonequilibrium steady-states such as those described by polymer stretching dynamics in nonequilibrium fluid flows. In this work, we apply the Crooks fluctuation theorem to understand the nonequilibrium thermodynamics of dilute polymer solutions in flow. We directly determine the nonequilibrium free energy for single polymer molecules in flow using a combination of single molecule experiments and Brownian dynamics simulations. We further develop a time-dependent extensional flow protocol that allows for probing viscoelastic hysteresis over a wide range of flow strengths. Using this framework, we define quantities that uniquely characterize the coil-stretch transition for polymer chains in flow. Overall, generalized fluctuation theorems provide a powerful framework to understand polymer dynamics under far-from-equilibrium conditions.

A Thin-Film Lubrication Model for Biofilm Expansion Under Strong Adhesion

Understanding microbial biofilm growth is important to public health, because biofilms are a leading cause of persistent clinical infections. In this paper, we develop a thin-film model for microbial biofilm growth on a solid substratum to which it adheres strongly. We model biofilms as two-phase viscous fluid mixtures of living cells and extracellular fluid. The model tracks the movement, depletion, and uptake of nutrients explicitly, and incorporates cell proliferation via a nutrient-dependent source term. Notably, our thin-film reduction is two-dimensional and includes the vertical dependence of cell volume fraction. Numerical solutions show that this vertical dependence is weak for biologically-feasible parameters, reinforcing results from previous models in which this dependence was neglected. We exploit this weak dependence by writing and solving a simplified one-dimensional model that is computationally more efficient than the full model. We use both the one and two-dimensional models to predict how model parameters affect expansion speed and biofilm thickness. This analysis reveals that expansion speed depends on cell proliferation, nutrient availability, cell-cell adhesion on the upper surface, and slip on the biofilm-substratum interface. Our numerical solutions provide a means to qualitatively distinguish between the extensional flow and lubrication regimes, and quantitative predictions that can be tested in future experiments.

Rheo-NMR Investigations of Flow and Alignment in Complex Fluids

<p>This thesis reports the use of Rheo-NMR, that is, a class of techniques within the realm of magnetic resonance which are both confirmatory and complementary to rheometric experiments on materials which can best be classified as complex fluids. The physical properties of such fluids are both hybrid and, in general, vaguely defined. In displaying characteristics attributable to both ideal fluids and elastic solids, the term `complex fluid', in a very real sense, epitomises all the fluids with which every human deals with (and is comprised of) daily. With a multitude of potential candidates for further research then, here we confine ourselves to fluids of molecules and aggregates which are either linear polymers or at least maintain the curvilinear one-dimensional topology of linear polymers. Magnetic resonance is an ideal research tool in this regard, as it is in many respects a rather statistical and insensitive tool from a signal-to-samplevolume perspective, precisely the regime in which the dynamics of a macroscopic collection of macromolecules is relevant. Material deformation is the mechanism upon which rheological measurement depends, and the first research presented here reports on a numerical simulation of the NMR signal of sheared polymer melts. Proton NMR relaxation times of such melts have previously been measured experimentally and found to depend on the shear rate applied by a horizontal Couette geometry, presumably due to the alignment of the mean-field boundaries of the space in which the polymer may reside, known as the polymer tube. The restrictions forming the tube are the other polymers in the bulk, around which an exemplar polymer molecule must meander. In diffusing through this tube, whose direction between entanglements is random in equilibrium, at any time, the return-to-origin correlation for a single spin returning to its locally anisotropic environment generates the least NMR transverse relaxation, as the sum contribution from all tube segments is random. When a deformation-related transformation matrix is applied to the coordinates of entanglements in the polymer, tube segments are no longer isotropically distributed, and an enhanced relaxation process results. Here we present the results of a numerical simulation of this procedure, based on the earlier model of Ball, Callaghan and Samulski, in addition to measurements of the transverse NMR relaxation by Cormier. Not only does it demonstrate qualitative agreement, the NMR signal can be simulated quantitavely or conversely, the size of several key polymer physics parameters can be found through fitting to the NMR signal. Proton NMR spectroscopy is inherently simpler than deuteron NMR spectroscopy, in which the nucleus of interest is quadrupolar. However, a large section of this thesis deals with the structures and response of worm-like micellar structures in solution, for which alignment data cannot reasonably be measured with the proton alone. The most used sample in this thesis is that of the BASF nonionic block copolymer Pluronic P105 in aqueous solution (5% w/w), and a small amount of 1-phenylethanol is required to stabilise cylindrical micellar structures. 1-phenylethanol is a small molecule perfectly suited to act also as a deuterated probe molecule to observe alignment, as it resides in the core of the micelle. By using a variety of Rheo-NMR techniques, such as velocimetry, spatially resolved spectroscopy, and diffusometry, many different flow and alignment behaviours were observed for this solution in Couette flow. Following the measured temperature-dependent viscosity of the P105 solution, which shows an elevated viscosity in a temperature region 15K wide centred at 297 K, we use temperature and applied shear rate as independent variables in our experiments, first identifying spectral features through diffusometry, and then observing a range of behaviours including shear-banding and quadrupolar splitting indicating alignment. Finally we present some experimental work performed in the extensional flow geometry known as the semi-hyperbolic converging die. Extensional flow, inherently, is a transient and nite procedure, and such a geometry is designed to produce a constant extension rate along the axis of its constricting pipe, which, compared to the mill geometries, improves the volume and time over which extension occurs. We investigate the flow and alignment measuring capabilities of Rheo-NMR in this geometry.</p>

Rheo-NMR Investigations of Flow and Alignment in Complex Fluids

<p>This thesis reports the use of Rheo-NMR, that is, a class of techniques within the realm of magnetic resonance which are both confirmatory and complementary to rheometric experiments on materials which can best be classified as complex fluids. The physical properties of such fluids are both hybrid and, in general, vaguely defined. In displaying characteristics attributable to both ideal fluids and elastic solids, the term `complex fluid', in a very real sense, epitomises all the fluids with which every human deals with (and is comprised of) daily. With a multitude of potential candidates for further research then, here we confine ourselves to fluids of molecules and aggregates which are either linear polymers or at least maintain the curvilinear one-dimensional topology of linear polymers. Magnetic resonance is an ideal research tool in this regard, as it is in many respects a rather statistical and insensitive tool from a signal-to-samplevolume perspective, precisely the regime in which the dynamics of a macroscopic collection of macromolecules is relevant. Material deformation is the mechanism upon which rheological measurement depends, and the first research presented here reports on a numerical simulation of the NMR signal of sheared polymer melts. Proton NMR relaxation times of such melts have previously been measured experimentally and found to depend on the shear rate applied by a horizontal Couette geometry, presumably due to the alignment of the mean-field boundaries of the space in which the polymer may reside, known as the polymer tube. The restrictions forming the tube are the other polymers in the bulk, around which an exemplar polymer molecule must meander. In diffusing through this tube, whose direction between entanglements is random in equilibrium, at any time, the return-to-origin correlation for a single spin returning to its locally anisotropic environment generates the least NMR transverse relaxation, as the sum contribution from all tube segments is random. When a deformation-related transformation matrix is applied to the coordinates of entanglements in the polymer, tube segments are no longer isotropically distributed, and an enhanced relaxation process results. Here we present the results of a numerical simulation of this procedure, based on the earlier model of Ball, Callaghan and Samulski, in addition to measurements of the transverse NMR relaxation by Cormier. Not only does it demonstrate qualitative agreement, the NMR signal can be simulated quantitavely or conversely, the size of several key polymer physics parameters can be found through fitting to the NMR signal. Proton NMR spectroscopy is inherently simpler than deuteron NMR spectroscopy, in which the nucleus of interest is quadrupolar. However, a large section of this thesis deals with the structures and response of worm-like micellar structures in solution, for which alignment data cannot reasonably be measured with the proton alone. The most used sample in this thesis is that of the BASF nonionic block copolymer Pluronic P105 in aqueous solution (5% w/w), and a small amount of 1-phenylethanol is required to stabilise cylindrical micellar structures. 1-phenylethanol is a small molecule perfectly suited to act also as a deuterated probe molecule to observe alignment, as it resides in the core of the micelle. By using a variety of Rheo-NMR techniques, such as velocimetry, spatially resolved spectroscopy, and diffusometry, many different flow and alignment behaviours were observed for this solution in Couette flow. Following the measured temperature-dependent viscosity of the P105 solution, which shows an elevated viscosity in a temperature region 15K wide centred at 297 K, we use temperature and applied shear rate as independent variables in our experiments, first identifying spectral features through diffusometry, and then observing a range of behaviours including shear-banding and quadrupolar splitting indicating alignment. Finally we present some experimental work performed in the extensional flow geometry known as the semi-hyperbolic converging die. Extensional flow, inherently, is a transient and nite procedure, and such a geometry is designed to produce a constant extension rate along the axis of its constricting pipe, which, compared to the mill geometries, improves the volume and time over which extension occurs. We investigate the flow and alignment measuring capabilities of Rheo-NMR in this geometry.</p>

Vesicle dynamics in large amplitude oscillatory extensional flow

Although the behaviour of fluid-filled vesicles in steady flows has been extensively studied, far less is understood regarding the shape dynamics of vesicles in time-dependent oscillatory flows. Here, we investigate the nonlinear dynamics of vesicles in large amplitude oscillatory extensional (LAOE) flows using both experiments and boundary integral (BI) simulations. Our results characterize the transient membrane deformations, dynamical regimes and stress response of vesicles in LAOE in terms of reduced volume (vesicle asphericity), capillary number ( ${Ca}$ , dimensionless flow strength) and Deborah number ( ${De}$ , dimensionless flow frequency). Results from single vesicle experiments are found to be in good agreement with BI simulations across a wide range of parameters. Our results reveal three distinct dynamical regimes based on vesicle deformation: pulsating, reorienting and symmetrical regimes. We construct phase diagrams characterizing the transition of vesicle shapes between pulsating, reorienting and symmetrical regimes within the two-dimensional Pipkin space defined by ${De}$ and ${Ca}$ . Contrary to observations on clean Newtonian droplets, vesicles do not reach a maximum length twice per strain rate cycle in the reorienting and pulsating regimes. The distinct dynamics observed in each regime result from a competition between the flow frequency, flow time scale and membrane deformation time scale. By calculating the particle stresslet, we quantify the nonlinear relationship between average vesicle stress and strain rate. Additionally, we present results on tubular vesicles that undergo shape transformation over several strain cycles. Broadly, our work provides new information regarding the transient dynamics of vesicles in time-dependent flows that directly informs bulk suspension rheology.

Numerical Simulation of Fluid Flow and Mixing Dynamics inside Planetary Roller Extruders

In this contribution, the fluid flow and mixing dynamics inside planetary roller extruders are simulated using the finite element method (FEM) and the mesh superposition technique (MST). Three-dimensional configurations with planetary spindles of varying number and geometry of planetary spindles were created to analyse the influence of the spindle configuration and the rotational speed on the process behavior. Therefore, pressure gradients, flow velocities and directions, shear rates, the mixing index and residence time distributions were evaluated. The distributive and dispersive mixing efficiencies varied depending on the planetary spindle configuration, and these configurations thus suit different processing tasks. In comparison to the standard planetary spindles, the TT3 spindles, with their incomplete toothing, and the knob spindles, with their double transversal helical toothing, showed intense axial and radial mixing. In general, the mixing performance of the planetary roller extruder is explained by a high rate of extensional flow and frequent changes in flow type. The reported numerical approach allows, for the first time, a comprehensive observation of the process behavior of planetary roller extruders.

Towards a universal shear correction factor in filament stretching rheometry

Filament stretching rheometry is a prominent experimental method to determine rheological properties in extensional flow whereby the separating plates determine the extension rate. In literature, several correction factors that can compensate for the errors introduced by the shear contribution near the plates have been introduced and validated in the linear viscoelastic regime. In this work, a systematic analysis is conducted to determine if a material-independent correction factor can be found for non-linear viscoelastic polymers. To this end, a finite element model is presented to describe the flow and resulting stresses in the filament stretching rheometer. The model incorporates non-linear viscoelasticity and a radius-based controller for the plate speed is added to mimic the typical extensional flow in filament stretching rheometry. The model is validated by comparing force simulations with analytical solutions. The effects of the end-plates on the extensional flow and resulting force measurements are investigated, and a modification of the shear correction factor is proposed for the non-linear viscoelastic flow regime. This shows good agreement with simulations performed at multiple initial aspect ratios and strain rates and is shown to be valid for a range of polymers with non-linear rheological behaviour.