Simulation model of concentrated colloidal nanoparticulate flows

Rheology of bi-disperse dense fiber suspensions

While significant progress has been made in the modeling and simulation of uniform fiber suspensions, no existing model has been validated for industrially-relevant concentrated suspensions containing fibers of multiple aspect ratios. In the present work, we investigate bi-disperse suspensions with two fiber populations in varying aspect ratios in a steady shear flow using direct numerical simulations. Moreover, we measure the suspension viscosity by creating a controlled length bidispersity for nylon fibers suspended in a Newtonian fluid. The results showed good agreement between the experimentally measured and numerically predicted viscosity for bi-disperse suspensions. The ratio between the aspect ratio of large to small fibers (size ratio) and the volume fraction of large fibers (composition) in bi-disperse systems strongly affected the rheological behavior of the suspension. The increment of relative viscosity associated with size ratio and composition can be explained by the decrease in the maximum flowable limit or jamming volume fraction. Moreover, the relative viscosity of bi-disperse suspensions collapses, when plotted against the reduced volume fraction, demonstrating the controlling influence of the jamming fraction in bi-disperse fiber suspensions.

Smoothed profile method for direct numerical simulations of hydrodynamically interacting particles

A general method is presented for computing the motions of hydrodynamically interacting particles in various kinds of host fluids for arbitrary Reynolds numbers. The method follows the standard procedure for performing direct numerical simulations (DNS) of particulate systems, where the Navier-Stokes equation must be solved consistently with the motion of the rigid particles, which defines the temporal boundary conditions to be satisfied by the Navier-Stokes equation. The smoothed profile (SP) method provides an efficient numerical scheme for coupling the continuum fluid mechanics with the dispersed moving particles, which are allowed to have arbitrary shapes. In this method, the sharp boundaries between solid particles and the host fluid are replaced with a smeared out thin shell (interfacial) region, which can be accurately resolved on a fixed Cartesian grid utilizing a SP function with a finite thickness. The accuracy of the SP method is illustrated by comparison with known exact results. In the present paper, the high degree of versatility of the SP method is demonstrated by considering several types of active and passive particle suspensions.

Thermal transport phenomena in nanoparticle suspensions

Nanoparticle suspensions in liquids have received great attention, as they may offer an approach to enhance thermophysical properties of base fluids. A good variety of applications in engineering and biomedicine has been investigated with the aim of exploiting the above potential. However, the multiscale nature of nanosuspensions raises several issues in defining a comprehensive modelling framework, incorporating relevant molecular details and much larger scale phenomena, such as particle aggregation and their dynamics. The objectives of the present topical review is to report and discuss the main heat and mass transport phenomena ruling macroscopic behaviour of nanosuspensions, arising from molecular details. Relevant experimental results are included and properly put in the context of recent observations and theoretical studies, which solved long-standing debates about thermophysical properties enhancement. Major transport phenomena are discussed and in-depth analysis is carried out for highlighting the role of geometrical (nanoparticle shape, size, aggregation, concentration), chemical (pH, surfactants, functionalization) and physical parameters (temperature, density). We finally overview several computational techniques available at different scales with the aim of drawing the attention on the need for truly multiscale predictive models. This may help the development of next-generation nanoparticle suspensions and their rational use in thermal applications.

Mesoscale modeling of colloidal suspensions with adsorbing solutes

We construct a mesoscale model of colloidal suspensions that contain solutes reversibly adsorbing onto the colloidal particle surfaces. The present model describes the coupled dynamics of the colloidal particles, the host fluid, and the solutes through the Newton-Euler equations of motion, the hydrodynamic equations, and the advection-diffusion equation, respectively. The solute adsorption is modeled through a square-well potential, which represents a short-range attractive interaction between a particle and a solute molecule. The present model is formulated to be solved through direct numerical simulations. Some numerical results are presented to validate the simulations. The present model enables investigations of solute adsorption effects in the presence of a fluid flow and an inhomogeneous solute concentration distribution.

Mesoscale models of dispersions stabilized by surfactants and colloids

In this paper we discuss and give an outlook on numerical models describing dispersions, stabilized by surfactants and colloidal particles. Examples of these dispersions are foams and emulsions. In particular, we focus on the potential of the diffuse interface models based on a free energy approach, which describe dispersions with the surface-active agent soluble in one of the bulk phases. The free energy approach renders thermodynamic consistent models with realistic sorption isotherms and adsorption kinetics. The free energy approach is attractive because of its ability to describe highly complex dispersions, such as emulsions stabilized by ionic surfactants, or surfactant mixtures and dispersions with surfactant micelles. We have classified existing numerical methods into classes, using either a Eulerian or a Lagrangian representation for fluid and for the surfactant/colloid. A Eulerian representation gives a more coarse-grained, mean field description of the surface-active agent, while a Lagrangian representation can deal with steric effects and larger complexity concerning geometry and (amphiphilic) wetting properties of colloids and surfactants. However, the similarity between the description of wetting properties of both Eulerian and Lagrangian models allows for the development of hybrid Eulerian/Lagrangian models having advantages of both representations.

Effect of hydrodynamic interactions on rapid Brownian coagulation of colloidal dispersions

The rate of rapid Brownian coagulation is investigated for dispersions of spherical particles with particle volume fractions ranging from Øp = 0.003 to 0.1 by the direct numerical simulation method. This method explicitly considers hydrodynamic interactions (HIs) between particles by simultaneously solving for the motions of the dispersed particles and the host fluid. In the dilute limit, the rate of rapid Brownian coagulation decreases to approximately 0.3-0.5 times the theoretical Smoluchowski rate. We compare this result with results of previously reported experiments and theoretical predictions and find a strong correlation between them. This demonstrates that HIs between particles significantly reduce the coagulation rate. Moreover, the volume fraction dependence of the coagulation rate indicates that the coagulation rate increases with increasing volume fraction. At high particle volume fractions, the initial coagulation stage is affected by heterogeneous coagulation process before the steady state is reached.

A direct numerical simulation method for complex modulus of particle dispersions

We report an extension of the smoothed profile method (SPM) (Y. Nakayama, K. Kim, and R. Yamamoto, Eur. Phys. J. E 26, 361 (2008)), a direct numerical simulation method for calculating the complex modulus of the dispersion of particles, in which we introduce a temporally oscillatory external force into the system. The validity of the method was examined by evaluating the storage G'(ω) and loss G"(ω) moduli of a system composed of identical spherical particles dispersed in an incompressible Newtonian host fluid at volume fractions of Φ = 0 , 0.41, 0.46, and 0.51. The moduli were evaluated at several frequencies of shear flow; the shear flow used here has a zigzag profile, as is consistent with the usual periodic boundary conditions. The simulation results were compared with several experiments for colloidal dispersions of spherical particles.

Direct numerical simulations for non-Newtonian rheology of concentrated particle dispersions

The non-Newtonian behavior of a monodisperse concentrated dispersion of spherical particles was investigated using a direct numerical simulation method, which takes into account hydrodynamic interactions and thermal fluctuations accurately. Simulations were performed under steady shear flow with periodic boundary conditions in the three directions. The apparent shear viscosity of the dispersions was calculated at volume fractions ranging from 0.31 to 0.56. Shear-thinning behavior was clearly observed at high volume fractions. The low- and high-limiting viscosities were then estimated from the apparent viscosity by fitting these data into a semiempirical formula. Furthermore, the short-time motions were examined for Brownian particles fluctuating in concentrated dispersions, for which the fluid inertia plays an important role. The mean square displacement was monitored in the vorticity direction at several different Peclet numbers and volume fractions so that the particle diffusion coefficient is determined from the long-time behavior of the mean square displacement. Finally, the relationship between the non-Newtonian viscosity of the dispersions and the structural relaxation of the dispersed Brownian particles is examined.

Short-time motion of Brownian particles in a shear flow

The short-time motion of Brownian particles in an incompressible Newtonian fluid under shear, in which the fluid inertia becomes important, was investigated by direct numerical simulation of particulate flows. Three-dimensional simulations were performed, wherein external forces were introduced to approximately form Couette flows throughout the entire system with periodic boundary conditions. In order to examine the validity of the method, the mean-square displacement of a single spherical particle in a simple shear flow was calculated, and these results were compared with a hydrodynamic analytical solution that includes the effects of the fluid inertia. Finally, the dynamical behavior of a monodisperse dispersion composed of repulsive spherical particles was examined on short-time scales, and the shear-induced diffusion coefficients were measured for several volume fractions up to 0.50.