Diffusion and Settling of Aggregates

Any motion of colloidal particles is driven by volume forces (e.g. gravity), stochastic Brownian forces and hydrodynamic forces. The latter act on the particles surface and can be calculated via flie hydrodynamic stress tensor II  

This relationship is fundamental for the calculation of hydrodynamic properties of colloidal objects (e.g. the terminal settling velocity of small spheres). The factor 6ntja is called friction coefiicient its reciprocal is the hydrodynamic mobility fiy.  

This may be understood by regarding the total flow field. In the region between the two particles, the external flow field is screened considerably (i.e. the velocities are smaller than in the far field) and the local shear rates are lowered accordingly (cf. Fig. 4.14). As a result, the momentum flux from the fluid phase to the particles is not as high as for two completely separated particles. 

The analytical approach of Happel and Brenner provides first insight into the physics of the hydrodynamic interaction between particles. However, it fails in 

Once the total velocity field inside an aggregate is known, the drag on each particle can be computed with Eq. (4.65) and the total drag acting on the aggregate 

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