Background In gas--solid fluidization, it is often common to have a wide size distribution of particles present in the system. During fluidization the smaller particles may be entrained from the fluidization column. Sometimes it is useful to know the maximum particle size that would be elutriated from the system. In order to do this the equation for the terminal velocity can be used as shown below.
u_{t} =√ (4/3 dp (ρ_{p} − ρ_{f})g)/ρ_{f}C_{D}
where
u_{t} is the terminal velocity (m/s)
d_{p} is the particle diameter (m)
ρ_{p} is the particle density (kg/m3)
ρ_{f} is the fluid density (kg/m3)
g is the gravitational constant (9.81 m/s2)
C_{D} is the drag coefficient.
According to Haider and Levenspiel (1989) a single correlation for the drag coefficient for all flow regimes and non--spherical particles is described as follows.
CD = 24/(Re)_{p} [1+ (8.1716e^{−4.0655Φ} )(Re)_{p}^{0.0964+0.5565Φ}]+(73.69(e^{−5.0748}^{Φ })(Re)_{p})/((Re)_{p} + 5.378e^{6.2122Φ})
Where
Φ is the particle sphericity
(Re)_{p} is the particle Reynolds Number
(Re)_{p} is defined as
(Re)_{p} = u_{t}d_{p}ρ_{f}/μ
Where
μ is the fluid viscosity (kg/m^{-s})
Task
The task for this assignment is to solve for the particle diameter (d_{P}), in μm, at different terminal gas velocities (u_{t}) between 0 and 1 m/s. The solution should be solved in Microsoft Excel using VBA. The solution should be flexible and robust enough that different parameters (e.g. particle density, sphericity) could be easily changed and a new solution is automatically find outd. The root finding method should also be able to be easily adapted to handle different nonlinear problems.
For this problem the following parameters will be used.
ρ_{p} 950 kg/m^{3 }
Φ 0.77
ρ_{f} 1.184 kg/m^{3}
μ 1.85×10^{-5} kg/m^{-s}