Hydrodynamic Drag on Fractal Aggregates

Results of this section are based on MVE method—-mainly because of its high accuracy and because it allows for insight into the velocity field of aggregates. The truncation level was set to L = 2 in order to study aggregates with up to 1000 primary particles. According to Fig. 4.15, that means an error of less than 0.1 %. 

In Fig. 4.16, comparison is made between a hexagonal close-packed (hep) and a DLCA aggregate (N = 150). The direction of flow is normal to the projection area, while particles are at rest. Velocities are normalised by the velocity u°° of the undisturbed flow. The colour maps show the velocity component in the direction of flow the undisturbed flow is shown as dark red, zero values are indicated with light green, and the particles are depicted in deep blue. 

Based on the solution of the velocity field, the force and torque acting on the aggregates can be calculated and the hydrodynamic equivalent diameters for translation (xh,t) and rotation (xi -) can be derived. They scale with the aggregate mass via a power law that reflects the stmctural properties of the aggregate. That means, while for hep aggregates the aggregate mass (N) is proportional to the third power of Xh, there is a fractal-tike relationship for DLCA aggregates with a hydrodynamic dimension 4i close to the fiactal dimension (Fig. 4.17, left cf. discussion to Kirkwood-Riseman theory on pp. 164). This fractal relationship 

Once the functional relationship between the hydrodynamic diameters and the aggregate mass is known, one can establish simple models for the average dynamic properties (e.g. for the settling velocity) of suspensions containing aggregates. However, while the aggregate mass is well defined for numeric aggregates, it is difficult to measure in real-life experiments. It is more likely that the radius of 

It can be seen that the Kirkwood-Riseman theory considerably underestimates the hydrodynamic size (by approx. 10 %) even for large clusters. This probably results from ignoring the hydrodynamic many-body interactions within the aggregate, which are more pronounced the more compact the aggregate structure is. On the other hand, the simple correlation by Hess et al. considerably overestimates the hydrodynamic radius. This is because they assume a smooth radial density distribution ip r) r ), which ignores the anisotropy and local density variations of real CCA-formed aggregates. 

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