Tham khảo tài liệu 'hydrodynamics advanced topics part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 256 Hydrodynamics - Advanced Topics hydrodynamic force which depends on the aggregate size and its permeability. The use of hydrodynamic radius which is the radius of an impermeable sphere of the same mass Fig. 4. Graphical representation of the mass-radius relation for asphaltene aggregates. having the same dynamic properties instead of the aggregate radius makes it possible to neglect the internal permeability. For an aggregate of hydrodynamic radius r composed of i IiB primary particles of radius a the force balance is Using the mass-hydrodynamic radius relations for blob and aggregate Eqs. 9 10 one gets 2 íl-l DÍBl-l DB 15 u where u - pS-PfW 16 70 is the Stokes falling velocity of primary particle. Alternatively using the expression for the hydrodynamic radius changed by the presence of blobs Eq. 12 one obtains u ua 17 If the blobs of the fractal dimension different from that of the aggregate are not present D Db and r0 r the corresponding dependences reduce to the following relations Hydrodynamic Properties of Aggregates with Complex structure 257 Mo jl-l D Ua 18 19 characteristic for fractal aggregates with one-level structure. Hence the following formulae 20 u _r_0 u r 21 describe the free settling velocity of aggregates with mixed statistics. 5. Intrinsic viscosity of macromolecular coils and the thermal blob mass A macromolecular coil in a solution is modeled as an aggregate with mixed statistics consisting of I thermal blobs of Dg 2 each containing ig solid monomers of radius a and mass Ma. To calculate the intrinsic viscosity 22 one has to define the mass concentration c of a macromolecular solution analyzed. The mass concentration in the coil represented by the equivalent impermeable sphere can be calculated as the product of the total number of non-porous monomers IiB multiplied by their mass 41 3ĩĩả and divided by the hydrodynamic volume of the coil 413ĩĩr3 . This concentration multiplied by the volume fraction of equivalent aggregates p gives the .
