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_fC_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^−5.0748Φ )(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_td_pρ_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/m³

Φ    0.77

ρ_f      1.184           kg/m³

μ       1.85×10^-5    kg/m^-s