# Nomenclature

C_{D} Drag coefficient

c_{n} Coefficients in size distribution function series expansion

D_{p} Diffusivity, m^{2}/s

* d_{p}* Particle diameter, m

* E_{mni}* Coefficients in moment equations for FSE

* F* Function in drag model

* f* Number density function

* f* Dimensionless number density function

* F_{mni}* Coefficients in moment equations for FSE

* G* Growth rate, kg/m

^{3}-s

* h* Net rate of introduction of new particles in PBE

*Moment order*

**i*** K* Constant in growth rate law

* M* Number of terms in truncated series expansion approximating particle size distribution and number of moments in simulation

*Initial number of particles in Gaussian-like distribution*

**N**_{o}* P* Legendre polynomials

* Re* Reynolds number

* Re_{p}* Particle Reynolds number

* S* Source term in PBE

* T* Dimensionless time

* t* Time, s

* v_{k}* k-phase velocity, m/s

* v_{p}* Particulate phase velocity, m/s

x External coordinate vector in PBE

Greek Symbols

* в* Aggregation kernel

* в_{0}* Aggregation constant

* e_{k}j* Drag coefficient between

*phase and*

**k***phase*

**j***Volume fraction of*

**e**_{k}*phase*

**k*** Pi* ith moment of number density function

* p_{k}* k-phase viscosity, kg/m. s

П Second internal coordinate in Smoluchowski equation

- ? Internal coordinate in PBE
- ? Dimensionless internal coordinate in PBE
- ?
_{o}Initial average particle size in Gaussian-like distribution, m

* Г* Gamma function

* p_{k}* k-phase density, kg/m

^{3}

* и* Model parameter Gaussian-like distribution

T_{k} k-phase stress tensor, N/m^{2}

T_{p} Particle relaxation time, s

Ф_{п} Trial function associated with Legendre polynomials