Modelling of colloidal dynamics in complex soft matter systems

This dissertation, divided into three parts and funded by the multinational company Synthomer LTD, is devoted to the modelling of the complex dynamics among colloidal particles in soft matter systems which are influenced by the interplay between Brownian motion, the common denominator among all the projects, and other phenomena such as inter-particle interactions and external fields. Since the Brownian motion and its interplay with shear flow and physico-chemical interactions has a clear impact on the spatial arrangement, also called microstructure, of a colloidal suspension the first part of the thesis focuses on the proposal of a new theoretical framework which analyses the aforementioned feature of diverse dispersions under strongly sheared conditions by analytically solving the 2-Body Smoluchowski equation. The obtained solution is an extension of already existing theories and it is able to recover previous results for hard-spheres fluids under semi-dilute conditions. The new framework has also unveiled a new rich physical behavior by studying the microstructure of two paradigmatic cases of physically relevant interactions, the attractive Lennard-Jones potential and the Debye-Hückel or Yukawa potential for charge-stabilized particles. The Brownian motion is also crucial in determining the aggregation behavior of colloidal particles: the mechanism proposed by Smoluchowski to study the collision rate between Brownian particles and a stationary one is used nowadays to describe the entry and exit of radicals during an emulsion polymerization. The second part of the thesis is then dedicated to the development of a mathematical model which, by using the pseudo-homopolymerization approach, describes the kinetics of this polymerization mode. By using the state-of-the-art models for radical entry and desorption the framework has the ultimate goal of predicting crucial kinetic variables such as the monomers conversions and latex composition throughout the process. The model foresees a series of unknown parameters which have been determined by extensive calibration on three different test cases of increasing complexity: a homo-polymerization of n-BA, a co-polymerization involving n-BA and methyl methacrylate (MMA) and, finally, a ter-polymerization of n-BA with MMA and 2-HydroxyEthyl Methacrylate (2-HEMA); the data for the first two series have been found in the literature, while the data for the ter-polymerization have been provided by Synthomer LTD. The predictive model has been applied to study between the surfactant surface coverage of the particles as well as the total concentration of counterions in the system in order to rationalize the coagulation behavior during the whole polymerization process. The third and final part focuses on a biological system: the self assembly of proteins in vivo. The work is focused on the growth dynamics of a poly-glutamine agglomerate, named aggresome, in a mammalian cell: through a numerical solution of the advection diffusion equation, the macroscopic equivalent of the Smoluchowski equation, it has been possible to disentangle the relative importance of Brownian diffusion and active directed cellular transport in the growth of the amyloid aggresome inside cells, thus unveiling the dominant role of diffusion over active transport

Pair correlation function of charge-stabilized colloidal systems under sheared conditions

The pair correlation function of charge stabilized colloidal particles under strongly sheared conditions is studied using the analytical intermediate asymptotics method recently developed in [L. Banetta and A. Zaccone, Phys. Rev. E 99, 052606 (2019)] to solve the steady-state Smoluchowski equation for medium to high values of the P\'eclet number; the analytical theory works for dilute conditions. A rich physical behaviour is unveiled for the pair correlation function of colloids interacting via the repulsive Yukawa (or Debye-H\"uckel) potential, in both the extensional and compressional sectors of the solid angle. In the compression sector, a peak near contact is due to the advecting action of the flow and decreases upon increasing the coupling strength parameter $\Gamma$ of the Yukawa potential. Upon increasing the screening (Debye) length $\kappa^{-1}$, a secondary peak shows up, at a larger separation distance, slightly less than the Debye length. While this secondary peak grows, the primary peak near contact decreases. The secondary peak is attributed to the competition between the advecting (attractive-like) action of the flow in the compressions sector, and the repulsion due to the electrostatics. In the extensional sectors, a depletion layer (where the pair-correlation function is identically zero) near contact is predicted, the width of which increases upon increasing either $\Gamma$ or $\kappa^{-1}$.Comment: Special issue in honour of Matthias Ballauf

IMPACT OF TURBULENCE MODELING ON FLUID/SOLID HEAT TRANSFER INSIDE INDUSTRIAL AUTOCLAVES

This work is centred on the analysis of the impact of different turbulence modeling approaches on the fluid/solid heat exchange inside a commercial size autoclave. This project proposes itself to be a first step towards the optimization of the turbulent flow inside this kind of machinery to improve the curing treatment of Carbon-Fiber Reinforced Plastics (CFRP). The setup of the CFD simulations includes the presence of a metallic sample object inside the autoclave, where air will be recirculated with velocity, pressure and temperature typically adopted for this type of treatments. The analysis takes advantage of parallel CFD simulations, conducted by using the open-source software openFOAM v2106. Two turbulence models have been adopted: one is the well-known Reynolds-Average Navier-Stokes approach (RANS), which is currently used to model the turbulence inside this type of machinery. The second one is the Delayed Detached Eddy Simulations (DDES), which allows the full resolution of the majority of turbulent scales around the sample object. First, we propose the difference between the local heat flux distribution at the air/solid interface computed by using RANS and DDES, next we analyse the overall heat flux entering the sample object: the resolution of the turbulent scales does not influence the local heat flux only, but also the overall heat flux entering the object; an average increase of 35% is reported when the velocity fluctuations are neglected. Future steps of the research foresee the analysis of the heat flux and temperature distributions on the surface of realistic shapes and common-use CFRP. Afterwards, the autoclave design will be optimized by adding multiple inlets and aerodynamic devices to guarantee a more homogeneous heat flux distribution on the surface of realistic shapes of actual CFRP

Radial distribution function of Lennard-Jones fluids in shear flows from intermediate asymptotics

Determining the microstructure of colloidal suspensions under shear flows has been a challenge for theoreticaland computational methods due to the singularly perturbed boundary-layer nature of the problem. Previousapproaches have been limited to the case of hard-sphere systems and suffer from various limitations in theirapplicability. We present an alternative analytic scheme based on intermediate asymptotics which solves theSmoluchowski diffusion-convection equation including both intermolecular and hydrodynamic interactions. Themethod is able to recover previous results for the hard-sphere fluid and to predict the radial distribution function(rdf) of attractive fluids such as the Lennard-Jones (LJ) fluid. In particular, a new depletion effect is predictedin the rdf of the LJ fluid under shear. This method can be used for the theoretical modeling and understandingof real fluids subjected to flow, with applications ranging from chemical systems to colloids, rheology, plasmas,and atmospherical science

Pair correlation function of charge-stabilized colloidal systems under sheared conditions

Abstract: The pair correlation function of charge stabilized colloidal particles under strongly sheared conditions is studied using the analytical intermediate asymptotics method recently developed in Banetta and Zaccone (Phys. Rev. E 99, 052606 (2019) to solve the steady-state Smoluchowski equation for medium to high values of the Péclet number; the analytical theory works for dilute conditions. A rich physical behaviour is unveiled for the pair correlation function of colloids interacting via the repulsive Yukawa (or Debye-Hückel) potential, in both the extensional and compressional sectors of the solid angle. In the compression sector, a peak near contact is due to the advecting action of the flow and decreases upon increasing the coupling strength parameter Γ of the Yukawa potential. Upon increasing the screening (Debye) length κ− 1, a secondary peak shows up, at a larger separation distance, slightly less than the Debye length. While this secondary peak grows, the primary peak near contact decreases. The secondary peak is attributed to the competition between the advecting (attractive-like) action of the flow in the compressions sector, and the repulsion due to the electrostatics. In the extensional sectors, a depletion layer (where the pair-correlation function is identically zero) near contact is predicted, the width of which increases upon increasing either Γ or κ− 1

Predictive model of polymer reaction kinetics and coagulation behavior in seeded emulsion co- and ter-polymerizations

A mathematical model to describe the emulsion polymerization kinetics of co- and ter-polymerizations is developed. The model is based on the classical Smith-Ewart (SE) equations, within the pseudo-homopolymerization approach, with state-of-the-art models for radical entry and desorption. For co- and ter-polymerizations there are unknown parameters in the model which are related to monomer-specific gel-effect coefficients, that are needed to compute the bimolecular termination reaction rates. The unknown parameters are determined through extensive calibration of the model on literature data for homo- and co-polymerizations of \textit{n}-butyl acrylate (n-BA) and methyl methacrylate (MMA). The so-obtained predictive model is then applied to the modelling of the ter-polymerization of n-BA and MMA with 2-hydroxyethyl methacrylate (2-HEMA) with sodium persulphate (SPR) as initiator: predictions for the time-evolution of particle size and conversion are in excellent agreement with experimental measurements using Dynamic Light Scattering (DLS) and Gas Chromatography (GC), upon tuning the gel-effect coefficient related to 2-HEMA. The developed model is used to quantify the surfactant surface coverage of the particles as well as the total concentration of counterions in the system throughout the entire polymerization process. This key information provides a way to rationalize and control the coagulation behavior during the whole polymerization process

Microscopic theory for the pair correlation function of liquidlike colloidal suspensions under shear flow

We present a theoretical framework to investigate the microscopic structure of concentrated hard-sphere colloidal suspensions under strong shear flows by fully taking into account the boundary-layer structure of convective diffusion. We solve the pair Smoluchowski equation with shear separately in the compressing and extensional sectors of the solid angle, by means of matched asymptotics. A proper, albeit approximate, treatment of the hydrodynamic interactions in the different sectors allows us to construct a potential of mean force containing the effect of the flow field on pair correlations. We insert the obtained pair potential in the Percus-Yevick relation and use the latter as a closure to solve the Ornstein-Zernike integral equation. For a wide range of either the packing fraction $\eta$ and the P\'eclet ($\textrm{Pe}$) number, we compute the pair correlation function and extract scaling laws for its value at contact. For all the considered value of $\textrm{Pe},$ we observe a very good agreement between theoretical findings and numerical results from literature, up to rather large values of $\eta.$ The theory predicts a consistent enhancement of the structure factor $S(k)$ at $k \to 0,$ upon increasing the $\textrm{Pe}$ number. We argue this behaviour may signal the onset of a phase transition from the isotropic phase to a non-uniform one, induced by the external shear flow

Direct observation of heterogeneous formation of amyloid spherulites in real-time by super-resolution microscopy

Real-time super-resolution microscopy analysis reveals the growth kinetics, morphology, and abundance of human insulin amyloid spherulites with different growth pathways.Protein misfolding in the form of fibrils or spherulites is involved in a spectrum of pathological abnormalities. Our current understanding of protein aggregation mechanisms has primarily relied on the use of spectrometric methods to determine the average growth rates and diffraction-limited microscopes with low temporal resolution to observe the large-scale morphologies of intermediates. We developed a REal-time kinetics via binding and Photobleaching LOcalization Microscopy (REPLOM) super-resolution method to directly observe and quantify the existence and abundance of diverse aggregate morphologies of human insulin, below the diffraction limit and extract their heterogeneous growth kinetics. Our results revealed that even the growth of microscopically identical aggregates, e.g., amyloid spherulites, may follow distinct pathways. Specifically, spherulites do not exclusively grow isotropically but, surprisingly, may also grow anisotropically, following similar pathways as reported for minerals and polymers. Combining our technique with machine learning approaches, we associated growth rates to specific morphological transitions and provided energy barriers and the energy landscape at the level of single aggregate morphology. Our unifying framework for the detection and analysis of spherulite growth can be extended to other self-assembled systems characterized by a high degree of heterogeneity, disentangling the broad spectrum of diverse morphologies at the single-molecule level

Live-cell super-resolution microscopy reveals a primary role for diffusion in polyglutamine-driven aggresome assembly.

The mechanisms leading to self-assembly of misfolded proteins into amyloid aggregates have been studied extensively in the test tube under well-controlled conditions. However, to what extent these processes are representative of those in the cellular environment remains unclear. Using super-resolution imaging of live cells, we show here that an amyloidogenic polyglutamine-containing protein first forms small, amorphous aggregate clusters in the cytosol, chiefly by diffusion. Dynamic interactions among these clusters limited their elongation and led to structures with a branched morphology, differing from the predominantly linear fibrils observed in vitro Some of these clusters then assembled via active transport at the microtubule-organizing center and thereby initiated the formation of perinuclear aggresomes. Although it is widely believed that aggresome formation is entirely governed by active transport along microtubules, here we demonstrate, using a combined approach of advanced imaging and mathematical modeling, that diffusion is the principal mechanism driving aggresome expansion. We found that the increasing surface area of the expanding aggresome increases the rate of accretion caused by diffusion of cytosolic aggregates and that this pathway soon dominates aggresome assembly. Our findings lead to a different view of aggresome formation than that proposed previously. We also show that aggresomes mature over time, becoming more compacted as the structure grows. The presence of large perinuclear aggregates profoundly affects the behavior and health of the cell, and our super-resolution imaging results indicate that aggresome formation and development are governed by highly dynamic processes that could be important for the design of potential therapeutic strategies