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

Effect of liquid volume fraction and shear rate on rheological properties and microstructure formation in ternary particle/oil/water dispersion systems under shear flow: two-dimensional direct numerical simulation

We numerically studied the rheological properties and microstructure formation under shear flow in a ternary particle/oil/water dispersion system. Our numerical simulation method was based on a phase-field model for capturing a free interface, the discrete element method for tracking particle motion, the immersed boundary method for calculating fluid-particle interactions, and a wetting model that assigns an order parameter to the solid surface according to the wettability. The effects of the water-phase volume fraction and shear rate on the microstructure and apparent viscosity were investigated. When the water-phase volume fraction was low, a pendular state was formed, and with an increase in the water-phase volume fraction, the state transitioned into a co-continuous state and a Pickering emulsion. This change in the microstructure state is qualitatively consistent with the results of previous experimental studies. In the pendular state, the viscosity increased with an increase in the water-phase volume fraction. This was due to the development of a network structure connected by liquid bridges, and the increase in the coordination number was quantitatively confirmed. In the case of the pendular state, significant shear thinning was observed, but in the case of the Pickering emulsion, no significant shear thinning was observed. It is concluded that this is due to the difference in the manner in which the microstructure changes with the shear rate. This is the first study to numerically demonstrate the microstructure formation of a ternary dispersion under shear flow and its correlation with the apparent viscosity.

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.

Effects of viscoelasticity on shear-thickening in dilute suspensions in a viscoelastic fluid

We investigate previously unclarified effects of fluid elasticity on shear-thickening in dilute suspensions in an Oldroyd-B viscoelastic fluid using a novel direct numerical simulation based on the smoothed profile method. Fluid elasticity is determined by the Weissenberg number Wi and by viscosity ratio 1 - β = ηp/(ηs + ηp) which measures the coupling between the polymer stress and flow: ηp and ηs are the polymer and solvent viscosity, respectively. As 1 - β increases, while the stresslet does not change significantly compared to that in the β → 1 limit, the growth rate of the normalized polymer stress with Wi was suppressed. Analysis of flow and conformation dynamics around a particle for different β reveals that at large 1 - β, polymer stress modulates flow, leading to suppression of polymer stretch. This effect of β on polymer stress development indicates complex coupling between fluid elasticity and flow, and is essential to understand the rheology and hydrodynamic interactions in suspensions in viscoelastic media.

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.

Shear rheology of hard-sphere, dispersed, and aggregated suspensions, and filler-matrix composites

This paper reviews the shear rheology of suspensions of microscopic particles. The nature of interparticle forces determines the microstructure, and hence the deformation and flow behavior of suspensions. Consequently, suspensions were classified according to the resulting microstructure: hard-spheres, stabilized, or aggregated particles. This study begins with the most simple case: flowing suspensions of inert, rigid, monomodal spherical particles (called hard-spheres), at low shear rates. Even for inert particles, we reviewed the effect of several factors that produce deviations from this ideal case, namely: shear rate, particle shape, particle size distribution, and particle deformability. Then we moved to suspensions of colloidal particles, where interparticle forces play a significant role. First we studied the case of dispersed or stabilized suspensions (colloidal dispersions), where long range repulsive forces keep particles separated, leading to a crystalline order. Second we studied the more common case of aggregated or flocculated suspensions, where net attractive forces lead to the formation of fractal clusters. Above the gelation concentration (which depends on the magnitude of the attractive forces), clusters are interconnected into a network, forming a gel. We differentiate between weak and strong aggregation, which may lead to weak or strong gels, respectively. Finally, we reviewed the case of filler/matrix composite suspensions or gels, where rigid or viscoelastic particles (fillers) are dispersed in a continuous viscoelastic material (matrix), usually a gel. For each type of suspension, predictive curves of fundamental rheological properties (viscosity, yield stress, elastic and complex moduli) vs. particle volume fraction and shear rate were obtained from theoretical or empirical models and sound experimental data, covering ranges of practical interest.

Brownian dynamics of a self-propelled particle in shear flow

Brownian dynamics of a self-propelled particle in linear shear flow is studied analytically by solving the Langevin equation and in simulation. The particle has a constant propagation speed along a fluctuating orientation and is additionally subjected to a constant torque. In two spatial dimensions, the mean trajectory and the mean square displacement (MSD) are calculated as functions of time t analytically. In general, the mean trajectories are cycloids that are modified by finite temperature effects. With regard to the MSD, different regimes are identified where the MSD scales with t(ν) with ν=0,1,2,3,4. In particular, an accelerated (ν=4) motion emerges if the particle is self-propelled along the gradient direction of the shear flow.

Implementation of Lees-Edwards periodic boundary conditions for direct numerical simulations of particle dispersions under shear flow

A general methodology is presented to perform direct numerical simulations of particle dispersions in a shear flow with Lees-Edwards periodic boundary conditions. The Navier-Stokes equation is solved in oblique coordinates to resolve the incompatibility of the fluid motions with the sheared geometry, and the force coupling between colloidal particles and the host fluid is imposed by using a smoothed profile method. The validity of the method is carefully examined by comparing the present numerical results with experimental viscosity data for particle dispersions in a wide range of volume fractions and shear rates including nonlinear shear-thinning regimes.

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.