Kinetic Theory Microstructure Modeling in Concentrated Suspensions

When suspensions involving rigid rods become too concentrated, standard dilute theories fail to describe their behavior. Rich microstructures involving complex clusters are observed, and no model allows describing its kinematics and rheological effects. In previous works the authors propose a first attempt to describe such clusters from a micromechanical model, but neither its validity nor the rheological effects were addressed. Later, authors applied this model for fitting the rheological measurements in concentrated suspensions of carbon nanotubes (CNTs) by assuming a rheo-thinning behavior at the constitutive law level. However, three major issues were never addressed until now: (i) the validation of the micromechanical model by direct numerical simulation; (ii) the establishment of a general enough multi-scale kinetic theory description, taking into account interaction, diffusion and elastic effects; and (iii) proposing a numerical technique able to solve the kinetic theory description. This paper focuses on these three major issues, proving the validity of the micromechanical model, establishing a multi-scale kinetic theory description and, then, solving it by using an advanced and efficient separated representation of the cluster distribution function. These three aspects, never until now addressed in the past, constitute the main originality and the major contribution of the present paper

Deterministic solution of the kinetic theory model of colloidal suspensions of structureless particles

A direct modeling of colloidal suspensions consists of calculating trajectories of all suspended objects. Due to the large time computing and the large cost involved in such calculations, we consider in this paper another route. Colloidal suspensions are described on a mesoscopic level by a distribution function whose time evolution is governed by a Fokker–Plancklike equation. The difficulty encountered on this route is the high dimensionality of the space in which the distribution function is defined. A novel strategy is used to solve numerically the Fokker–Planck equation circumventing the curse of dimensionality issue. Rheological and morphological predictions of the model that includes both direct and hydrodynamic interactions are presented in different flows

Shear-induced self-diffusion of inertial particles in a viscous fluid

We propose a theoretical prediction of the self-diffusion tensor of inertial particles embedded in a viscous fluid. The derivation of the model is based on the kinetic theory for granular media including the effects of finite particle inertia and drag. The self-diffusion coefficients are expressed in terms of the components of the kinetic stress tensor in a general formulation. The model is valid from dilute to dense suspensions and its accuracy is verified in a pure shear flow. The theoretical prediction is compared to simulations of discrete particle trajectories assuming Stokes drag and binary collisions. We show that the prediction of the self-diffusion tensor is accurate provided that the kinetic stress components are correctly predicted

One and two-fiber orientation kinetic theories of fiber suspensions

http://dx.doi.org/10.1016/j.jnnfm.2012.10.009The morphology influencing rheological properties of suspensions of rigid spheres constitutes the flow induced collective ordering of the spheres characterized by two or more sphere distribution functions. When the rigid spheres are replaced by rigid fibers, the collective order in the position of the spheres is replaced by the flow induced orientation of the fibers that suffices to be characterized by one-fiber orientation distribution function. A flow induced collective ordering of fibers (both in position and orientation), that can only be characterized by two or more fiber distribution functions, can still however constitute an important part of the morphology. We show that two types of interaction among fibers, one being the Onsager-type topological interaction entering the free energy and the other the hydrodynamics interaction entering the dissipative part of the time evolution, give indeed rise to a collective order in the orientation influencing the rheology of fiber suspensions

Deterministic solution of the kinetic theory model of colloidal suspensions of structureless particles

A direct modeling of colloidal suspensions consists of calculating trajectories of all suspended objects. Due to the large time computing and the large cost involved in such calculations, we consider in this paper another route. Colloidal suspensions are described on a mesoscopic level by a distribution function whose time evolution is governed by a Fokker–Plancklike equation. The difficulty encountered on this route is the high dimensionality of the space in which the distribution function is defined. A novel strategy is used to solve numerically the Fokker–Planck equation circumventing the curse of dimensionality issue. Rheological and morphological predictions of the model that includes both direct and hydrodynamic interactions are presented in different flows

Kinetic Theory Models

Discrete techniques (MD or BD), despite their conceptual simplicity, are very often too expensive from the computational point of view. Kinetic theory approaches seem, in many cases, a suitable compromise between the accuracy of finer descriptions and the computational efficiency of macroscopic descriptions. In this chapter, we revisit some kinetic theory models. Even if there is a common rationale for deriving the different models, in order to emphasize their physical contents, we will follow a diversity of alternative routes to derive them

Turbulent channel flow of dense suspensions of neutrally-buoyant spheres

Dense particle suspensions are widely encountered in many applications and in environmental flows. While many previous studies investigate their rheological properties in laminar flows, little is known on the behaviour of these suspensions in the turbulent/inertial regime. The present study aims to fill this gap by investigating the turbulent flow of a Newtonian fluid laden with solid neutrally-buoyant spheres at relatively high volume fractions in a plane channel. Direct Numerical Simulation are performed in the range of volume fractions Phi=0-0.2 with an Immersed Boundary Method used to account for the dispersed phase. The results show that the mean velocity profiles are significantly altered by the presence of a solid phase with a decrease of the von Karman constant in the log-law. The overall drag is found to increase with the volume fraction, more than one would expect just considering the increase of the system viscosity due to the presence of the particles. At the highest volume fraction here investigated, Phi=0.2, the velocity fluctuation intensities and the Reynolds shear stress are found to decrease. The analysis of the mean momentum balance shows that the particle-induced stresses govern the dynamics at high Phi and are the main responsible of the overall drag increase. In the dense limit, we therefore find a decrease of the turbulence activity and a growth of the particle induced stress, where the latter dominates for the Reynolds numbers considered here.Comment: Journal of Fluid Mechanics, 201

Shape evolution of 3D periodic structure fabricated by direct-write assembly of concentrated colloidal gels

Scope and Method of Study: 3D periodic structures were fabricated by direct-write assembly of concentrated colloidal gels with self-supporting features. The rheological behavior of the gel was characterized in linear viscoelastic regions. The flow behavior of the gel was modeled by using structural kinetics theory. Based on this model, the dynamic extrusion process of the gel was simulated by incorporating slip wall boundary conditions. A viscoelastic catenary model was developed to describe span shape and compare the results to previous results that used a simple elastic beam theory. The shape evolution (i.e., spanning behavior) of spanning filaments observed was related to shear stress conditions and a limited set of rheological parameters.Findings and Conclusions: The rate and magnitude of microstructure change within a colloidal gel ink are crucial factors for shape evolution of 3D structures assembled by direct write techniques. The events that set the equilibrium shape of 3D structure occur within the initial few seconds after deposition and gels microstructure recovery within this period is critical to geometric fidelity. The shape evolution of 3D structures may be predicted by knowledge of the rheological behavior of the colloidal gel in shear loading. Rheological behavior can be related to the structural recovery time of the colloidal gel and this may be measured with a series of equilibrium flow measurements. Successful completion of this research advances science-based ink design methods and optimization of deposition variables. Better control of shape evolution will lead to improvements in advanced applications such as photonic band gap structures, artificial bone structures, and metal-ceramic composites. The improved connections between time-dependent shear behavior and shape evolution in an extrusion process will also impact other industries (e.g., clay extrusion for catalytic converter substrates) and improve industrial productivity through better paste design. Although the current work is limited to colloidal gels, the knowledge gained here may be easily extended to other complex ink systems such as partially melted thermoplastic polymers and metals

Tuning Interparticle Hydrogen Bonding in Shear-Jamming Suspensions: Kinetic Effects and Consequences for Tribology and Rheology

The shear-jamming of dense suspensions can be strongly affected by molecular-scale interactions between particles, e.g. by chemically controlling their propensity for hydrogen bonding. However, hydrogen bonding not only enhances interparticle friction, a critical parameter for shear jamming, but also introduces (reversible) adhesion, whose interplay with friction in shear-jamming systems has so far remained unclear. Here, we present atomic force microscopy studies to assess interparticle adhesion, its relationship to friction, and how these attributes are influenced by urea, a molecule that interferes with hydrogen bonding. We characterize the kinetics of this process with nuclear magnetic resonance, relating it to the time dependence of the macroscopic flow behavior with rheological measurements. We find that time-dependent urea sorption reduces friction and adhesion, causing a shift in the shear-jamming onset. These results extend our mechanistic understanding of chemical effects on the nature of shear jamming, promising new avenues for fundamental studies and applications alike