**7. Discussion**

Covering the aggregate with spheres of a given size, one defines the blobs which are the units in which the monomers present in aggregates are grouped. Changing the size of the spheres we can increase or decrease the blob size. If the blobs have the same structure as the whole aggregate, the aggregate is the self-similar object.

Otherwise the object is a structure of mixed statistics with the hydrodynamic properties described in this chapter. There were analyzed aggregates containing monosized blobs of a given fractal dimension. The blobs of asphaltene aggregates are dense, probably of fractal dimension close to three. The thermal blobs - the constituents of polymer coils - have constant fractal dimension of two, independently of the thermodynamic quality of the solvent and hence the coil fractal dimension.

The determination of the hydrodynamic radius of hydrodynamic blobs in fractal aggregates, despite the same fractal structure as for the whole aggregate, serves to estimate the size of large pores through the fluid can flow. It makes it possible to model the fluid flow through the aggregate in terms of both the continuum and slip regimes.

## **8. References**

Brinkman, H. C. (1947). A calculation of the viscosity and the sedimentation velocity for solutions of large chain molecules taking into account the hampered flow of the solvent through each chain molecule. *Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, Vol.* 50, (1947), pp. 618-625, 821, ISSN: 0920-2250

1 1.612 *continuum*

 

*<sup>f</sup> k k <sup>k</sup> f a*

in which the monomer size should be replaced by the hydrodynamic blob radius rising such as the growing aggregate. So large differences in permeabilities at the beginning diminish when the aggregate mass increases and disappear when the aggregate size greatly exceeds

Calculated mobility radius *rm* , representing impermeable aggregate in the slip regime, is smaller than the hydrodynamic one because of higher permeability and tends to the hydrodynamic size when the difference in permeabilities becomes negligible. At an early stage of the growth of aerosol aggregates it can be approximated as a power of mass (Cai &

Covering the aggregate with spheres of a given size, one defines the blobs which are the units in which the monomers present in aggregates are grouped. Changing the size of the spheres we can increase or decrease the blob size. If the blobs have the same structure as the

Otherwise the object is a structure of mixed statistics with the hydrodynamic properties described in this chapter. There were analyzed aggregates containing monosized blobs of a given fractal dimension. The blobs of asphaltene aggregates are dense, probably of fractal dimension close to three. The thermal blobs - the constituents of polymer coils - have constant fractal dimension of two, independently of the thermodynamic quality of the

The determination of the hydrodynamic radius of hydrodynamic blobs in fractal aggregates, despite the same fractal structure as for the whole aggregate, serves to estimate the size of large pores through the fluid can flow. It makes it possible to model the fluid flow through

Brinkman, H. C. (1947). A calculation of the viscosity and the sedimentation velocity for

solutions of large chain molecules taking into account the hampered flow of the solvent through each chain molecule. *Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, Vol.* 50, (1947), pp. 618-625, 821, ISSN:

coefficient in the slip regime from that valid in the continuum regime (Gmachowski, 2010)

*slip*

in which the number 2.3 greatly differs from the fractal dimension equal to 1.8.

whole aggregate, the aggregate is the self-similar object.

the aggregate in terms of both the continuum and slip regimes.

solvent and hence the coil fractal dimension.

it possible to calculate the permeability

(52)

1/2.3 *r ai <sup>m</sup>* (53)

where 

the gas mean free path.

Sorensen, 1994)

**7. Discussion** 

**8. References** 

0920-2250

 is the gas mean free path. For a given structure of arrangement *a*,

*slip*


**Part 4** 

**Radiation-, Electro-,** 

**Magnetohydrodynamics and Magnetorheology** 

Woodfield, D., & Bickert, G. (2001). An improved permeability model for fractal aggregates settling in creeping flow. *Water Research*, Vol. 35, No. 16, (November 2001), pp. 3801- 3806, ISSN 0043-1354
