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Nomenclature

CD Drag coefficient

cn Coefficients in size distribution function series expansion

Dp Diffusivity, m2/s

dp Particle diameter, m

Emni Coefficients in moment equations for FSE

F Function in drag model

f Number density function

f Dimensionless number density function

Fmni Coefficients in moment equations for FSE

G Growth rate, kg/m3-s

h Net rate of introduction of new particles in PBE i Moment order

K Constant in growth rate law

M Number of terms in truncated series expansion approximating particle size distribution and number of moments in simulation No Initial number of particles in Gaussian-like distribution

P Legendre polynomials

Re Reynolds number

Rep Particle Reynolds number

S Source term in PBE

T Dimensionless time

t Time, s

vk k-phase velocity, m/s

vp Particulate phase velocity, m/s

x External coordinate vector in PBE

Greek Symbols

в Aggregation kernel

в0 Aggregation constant

ekj Drag coefficient between k phase and j phase ek Volume fraction of k phase

Pi ith moment of number density function

pk 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

pk k-phase density, kg/m3

и Model parameter Gaussian-like distribution

Tk k-phase stress tensor, N/m2

Tp Particle relaxation time, s

Фп Trial function associated with Legendre polynomials

 
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