While some analytical solutions describing the rheological properties of simple suspensions exist (e.g., for very dilute suspensions), understanding the flow of more complex suspensions like cement-based materials−dense suspensions and suspensions composed of particles with different shapes or particles that interact−remains a challenge. A major difficulty in modeling complex fluids like suspensions is the tracking of boundaries between the fluid and solid phases. Recently, promising new computational method called dissipative particle dynamics (DPD)21 has been developed for modeling complex fluid systems. Indeed, DPD may have advantages over other computational fluid dynamics methods because it can describe moving boundaries without requiring regridding of the computational domain.
On the surface, DPD looks similar to molecular dynamics algorithm, 23 where particles, subject to interatomic forces, move according to Newton´s laws. However, the particles in DPD are not atomistic but instead are a mesoscopic representation of the suspension. The interactions between the particles are described by three classes of forces: conservative, dissipative, and random. The conservative force is central force, derivable from some potential. The dissipative force is proportional to the difference in velocity between particles and acts to slow down their relative motion, producing a viscous effect. The random force (usually based on a Gaussian random noise) helps reproduce the temperature of the system while producing a viscous effect. Finally, it has been shown that DPD equations can account for hydrodynamic behavior consistent with the Navier-Stokes equations.24 , 25 To model a rigid-body inclusion in fluid, a subset of the DPD particles are initially assigned a location in space such that they approximate the shape of the object.26 The motion of these particles is then constrained so that their relative positions never change. The total force and torque are determined from the DPD particle interactions, and the rigid body moves according to the Euler equations.
Cement-based materials are usually composed of particles with a broad shape and size distribution. Figure 4 shows some typical examples. Figure 4a is a system polydisperse spheres that could correspond to a concrete composed of riverbed aggregates, which are usually rounder and smoother than most aggregates. Figure 4b is based on realistic images of aggregates acquired by x-ray microtomography of crushed aggregate. The tomographic images of aggregates can be analyzed their geometrical properties by constructing a spherical harmonic representation their shape.27 Once the aggregate images are incorporated into the code, we can determine the viscosity of the total system relative to the matrix fluid viscosity for given shear rate.
Figure 4. Example of concrete systems: (a) system of polydisperse spheres, corresponding to a concrete composed of riverbed aggregates, which are usually rounder and smoother than most aggregates; (b) model based on three-dimensional images of realistically shaped particles, acquired by x-ray microtomography of crushed aggregates.
So far, we have found good agreement with experimental studies of the plastic viscosity of fresh concrete having an aggregate composition similar to that used in the simulations28 (Figure 5).
Figure 5. Comparison of relative plastic-viscosity values from a simulation of coarse aggregate gradings and experimental measurements using different concrete rheometers. In the figure, Grad. #1, #2, and #3 correspond to gradations of spherical aggregates used in the computer simulation. BML is a coaxial concrete rheometer, IBB is a vane concrete rheometer, and "beads in paste" corresponds to measurements of monosized glass beads in a cement paste using a parallel plate rheometer. The solid line is included as a guide for the eye.28