Download 151-0902-00 Micro- and Nano-Particle (MNP) Technology FS09

Particle Technology Laboratory
Prof. Sotiris E. Pratsinis
Sonneggstrasse 3, ML F13, ETH Zentrum
Tel.: +41-44-632 25 10
http://www.ptl.ethz.ch
151-0902-00 Micro- and Nano-Particle (MNP) Technology FS17
Exercise 6: Forces on Single Particles
Problem 1
The dynamic viscosity f and the density ρf of a fluid can be determined by
measuring the stationary settling velocities of two spherical particles of different sizes
in this fluid. The first particle has a diameter of 10-3 m and a density of 1.18 g/cm3.
The second particle has a diameter of 10-2 m and a density of 4.00 g/cm3. The first
particle settles in the Stokes’ regime with a velocity of 10-3 m/s. The second particle
settles in the Newton regime with a velocity of 0.89 m/s. Calculate the dynamic
viscosity f and the density ρf of the fluid.
Problem 2
Carbon black agglomerates with mobility, dm , and primary particle diameter, dp , of
750 and 25 nm, respectively, are filled into a silo at a height of 2 m. In the continuum
regime, their number of primary particles, np , is related to dm and dp by (Dastanpour
& Rogak, 2016):
1.92

dm 
1
np  

4.4
 0.85  0.03g,p
dp 

where g,p = 1.3 is the geometric standard deviation of the primary particle diameter.
a) In the absence of coagulation, how long will it take until all carbon black
agglomerates have settled?
b) Agglomerates with monodisperse primary particles will settle faster or slower
than those with g,p = 1.3?
c) What is the error in the settling time calculation assuming carbon black
spheres of the same dm ?
Data:
Viscosity of air (25°C): 1.861×10-5 Pa s
Carbon black density: 1.8 g/cm3
1
Reference:
Dastanpour R, Rogak SN. The effect of primary particle polydispersity on the
morphology and mobility diameter of the fractal agglomerates in different flow
regimes, J. Aerosol Sci. 2017; 94: 22-32.
Problem 3
The steady state settling velocity (terminal velocity) of a particle can be utilized to
determine its diameter. A sphere of density 2500 kg/m3 falls freely under gravity in a
fluid of density 700 kg/m3 and viscosity 0.5×10-3 Pa s and reaches a settling velocity
of 0.15 m/s.
a) Calculate the diameter of the sphere.
b) What would be the edge length of a cube of the same material falling in the same
fluid at the same steady state settling velocity?
Problem 4
Spray drying is commonly used in the food or chemical industry for the production of
easily soluble, powdered products such as instant coffee, detergents or
pharmaceutics. In spray drying a slurry (suspension) is atomized into a flow of hot
gas (Figure 1). The liquid evaporates from the droplets leaving solid particles at the
outlet of the drying chamber. The drying time is governed by heat- and mass transfer
processes, which depend on the relative velocity between the gas and the droplets.
Along with the settling velocity of the droplets it determines the height of the drying
chamber.
Figure 1. Example of a spray drying
unit with cyclone separator product
powder recovery.
www.malvern.co.uk/.
a) The atomizer of the spray dryer breaks the feed suspension into fine droplets
and thereby enlarges the surface area enabling fast drying. Calculate the
surface area of 1L slurry that is sprayed into spherical 50 m droplets.
b) The atomizer generates polydisperse droplets. The droplet size distribution
changes during the drying process when converting droplets into particles as
shown in Figure 2. The droplet size distribution results in a distribution of the
steady-state settling velocity, which has to be accounted for in the design of
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Passage P
the unit. Estimate the range of settling velocities, by calculating the settling
velocity of entering droplets with a size corresponding to the 10 and 90%
passage.
Outlet
(Particles)
Inlet
(Droplets)
Figure 2: Droplet size distribution in the spray dryer.
Data:
Gas temperature: 300 °C, viscosity Gas (300 °C) = 29.3×10-6 m2/s,
Gas density Gas (300 °C) = 0.924 kg/m3
Droplet density ≈ density of water: w = 1000 kg/m3
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