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Yang Fluidization, Solids Handling, and Processing

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Coating and Granulation 425

fsur

Fraction of surviving granules

F

Total force

Fvis

Viscous force from Eq. (18)

Fcap

Capillary force from Eq. (19)

Fcoat

Feed rate of coating material (solute only)

g

Acceleration due to gravity

G

Growth rate of particles due to coating

Gc

Critical strain energy release rate

h

Height of wetted powder in a Washburn Test or

 

half separation distance between two particles

 

held in contact by a pendular liquid bridge

ha

Minimum separation distance between two particles

 

due to surface asperities

hb

Height of a fluidized bed

he

Equilibrium height of rise in Eq. (15)

H

Hardness (from indentation test)

k, k1,

Constants in Eqs. (7, 8 and 46)

K, K

 

kg

Thermal conductivity of gas

Kc

Fracture toughness of material

lWear displacement

mMass

MWg

Molecular weight of gas

MWl

Molecular weight of liquid

n

Coefficient in Eq. (46)

nk

Mass distribution of feed or product particles

n(v,t)

Number frequency distribution

N

Total number of granules or number of

 

particle circulations

pl*

Vapor pressure of liquid

ptot

Total pressure of system

P

Applied load in indentation test

N

N

N

kg/s m/s2

kg/s J/m2

m

m m m Pa

W/m·°C

Pa·m1/2

m

kg

kg/kmol

kg/kmol

kg-1

# particles Pa

Pa

N

426 Fluidization, Solids Handling, and Processing

Qk

Rate of feed or product withdrawal

# particles/s

rp

Characteristic length of process zone

 

m

R

Radius of capillary

 

m

S

Saturation or spray rate

 

-

St, St*

Stokes number and critical Stokes number, Eq. (20)

 

-

Sf

Shape Factor in Eqs. (29) and (31)

 

-

t

Time

 

s

Tbulk

Bulk gas temperature

 

°C

Ts

Surface temperature of liquid droplet or minimum

 

°C

 

sintering temperature of a solid

 

TM

Melting point of a solid

 

°C

T

= (Tbulk - Ts)

 

°C

tv

Time for complete evaporation of a liquid droplet

 

s

tcirc

Time elapsed between successive passages of a

 

s

 

particle through the spray zone

 

u

Particle size measure (volume) for coalescing particles

m3

U

Superficial gas velocity

 

m/s

UB

Rise velocity of a bubble

 

m/s

Ui

Impact velocity

 

m/s

Umf

Minimum fluidizing velocity

 

m/s

Uo

Relative velocity of two approaching particles

 

m/s

v

Particle size measure (volume) for coalescing particles

m3

V

Volumetric wear or breakage rate or volumetric flow

 

 

of feed

 

m3/s

Var

Variance

 

 

w*

Critical average granule size capable of rebound

 

 

 

from a collision

 

 

Xtotal

Total mass of coating received by a particle in a

 

kg

 

batch coating operation

 

xc

Critical specimen size, Eq. (35)

 

 

xk

Amount of mass received by a particle in its kth

 

kg

 

passage through the spray zone

 

 

Coating and Granulation

427

y

Liquid loading

 

 

ybulk

Mass fraction of solvent in the bulk

-

 

yd

Mass fraction of solvent in the liquid droplet

-

 

ys

Mass fraction of solvent in gas at the liquid surface

-

 

Y

Yield number, Eq. (28)

-

 

Greek Letters

 

 

α

Thermal diffusivity

m2/s

 

β

Constant in Eq. (34)

-

 

β()

Coalescence kernel, Eq. (40)

-

 

Γ

Shear rate

s-1

 

γ

Surface tension or interfacial energy

N/m

 

δ

Dimensionless bubble spacing

-

 

δc

Effective increase in crack length

m

 

εDimensionless separation of two particles = 2h/a

or powder void fraction, Eq. (26)

θContact angle between liquid and powder compact

λ

Latent heat of vaporization

J/kg

μ

Viscosity

kg/m·s

ρ

Density

kg/m3

σy

True yield stress of material

Pa

σf

Applied fracture stress

Pa

τ

Coating run time

s

τ

Yield strength of wet granule

N/m2

o

 

 

φFilling angle defined in Fig. 22

ϕProbability distribution function

Subscripts

ave

Average value

breakage

Breakage

c

Crystal

428 Fluidization, Solids Handling, and Processing

circ Circulation

dDroplet

eEquilibrium, exit

g

Gas or granule

i

Inlet

I-C

Inertial to coating transition

l

Liquid

max

Maximum value

N-I

Non-inertial to inertial transition

p

Particle

tot

Total

wear

Wear

yy

Denotes stress value in material

Superscripts

C

Coating

fb

Fluid bed

I

Inertial

lv

Liquid-vapor

N

Non-inertial

sv

Solid vapor

sl

Solid-liquid

*Critical value

Coating and Granulation 429

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