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The computational modeling of complex fluids systems like suspensions presents a significant challenge, largely because it is difficult to track the boundary between a fluid and a solid phase. Recently, a new computational method called dissipative particle dynamics (DPD) has shown great promise for modeling such systems [18-20].
We have carried out extensive simulations to validate the DPD approach for modeling suspensions. For example, our rheology codes recover the Einstein prediction of the intrinsic viscosity for the case of a very dilute suspension of spheres. We have also tested our algorithms for the case of a dense suspension of monosize spheres. While there is no accepted theory for predicting the rheological properties of such suspensions, we have found good agreement with experimental data [21, 22]. Figure 4 shows the reduced viscosity vs. Peclet number for different solid fractions. The Peclet number describes the competition between hydrodynamic forces due to shear and Brownian motion. For Pe > 1, hydrodynamic forces dominate, while Brownian forces dominate for Pe < 1. In most problems of interest to the aggregate industry, the Peclet number is much bigger than 1, so that hydrodynamic forces dominate. Experimental data are also included in Fig. 4 from studies of silica particles [23]. Note the good agreement over a wide range of solid fractions. The experimental and computational uncertainties are given in the caption of Fig. 4.
Figure 4: Log-log plot of experimental and computational viscosities
vs. Peclet number. The particle volume fraction is denoted as
. The lines represent experimental data from
sheared suspensions of silica particles (dashed line
=0.60, solid line
=0.48, dotted line
=0.44) and the points correspond to data
from the DPD simulation (plus signs
=0.60, open circles
=0.50, filled squares
=0.46, and filled triangles
=0.40). Note that there are no experimental data to compare to the
=0.50 computational data. The experimental uncertainties are approximately
10 %, and there is approximately 5 % uncertainty in the computational results
(due to statistical uncertainty).
While our initial studies have focused on validating our DPD-based algorithms for the case of the flow of suspensions composed of uniform shaped objects (e.g. single size sphere and ellipsoids), we have begun to study the role particle size distribution plays in controlling the rheological properties of suspensions. Figure 5 shows a multi-size spherical aggregate system where the aggregates are approximately consistent with an ASTM coarse aggregate specification [24]. We are also applying the DPD code to studying the rheological properties of realistic shaped particles based on tomographic images of concrete, as in Fig. 1 above. Once the tomographic image has been processed with the burning algorithm to identify each particle, the individual digitized aggregate images can be used as templates to construct a set of rigid body inclusions that may be input into the DPD-based rheology code. Studies of such systems are currently being pursued.
Figure 5: A multi-size spherical aggregate system where the aggregate PSD is approximately consistent with an ASTM C33 coarse aggregate specification. The picture is from the dissipative particle dynamics unit cell.