Читать книгу The Rheology Handbook - Thomas Mezger - Страница 28

With dp = 1 µm = 10-6 m, and η = 100 mPas (e. g. water containing a thickener, measured at

γ ̇ = 0.01 s-1), and with the same values for ρp and ρfl as above in Example (3a), results: v = approx. 8.2 ⋅ 10-9 m/s (or v = 0.7 mm per day). With h = 0.1 µm results: γ ̇ = 0.08 s-1 approximately.

Note 1: Calculation of a too high settling velocity if interactions are ignored

Stokes’ sedimentation formula only considers a single particle sinking, undisturbed on a straight path. Therefore, relatively high shear rate values are calculated. These values do not mirror the real behavior of most dispersions, since usually interactions are occurring. The layer thickness h is hardly determinable. We know from colloid science: It depends on the strength of the ionic charge on the particle surface, and on the ionic concentration of the dispersion fluid (interaction potential, zeta-potential) [2.28] [2.29]. Due to ionic adsorption, a diffuse double layer of ions can be found on the particle surface. For this reason, in reality the result is usually a considerably lower settling velocity. Therefore, and since the shear rate within the sheared layer is not constant: It is difficult to estimate the corresponding shear rate values occurring with sedimentation processes.

Note 2: Particle size of colloid dispersions, and nano-particles

In literature, as medium diameters of colloid particles are mentioned different specifications: between 10-9 m and 10-6 m (or 1 nm to 1 µm) [2.14] [2.25], or between 10-9 m and 10-7 m (or 1 nm to 100 nm) [2.13], or between 10-8 m and 10-6 m (or 10 nm to 1 µm) [2.26]. In ISO 80004-1 of 2015 is stated: Nano-scaled particles are in the range of approximately 1 nm to 100 nm [2.27]. Due to Brownian motion, the nano-particles usually are remaining in a suspended state and do not tend to sedimentation. Above all, the limiting value of the settling particle size depends on the density difference of particles and dispersing fluid.

End of the Cleverly section