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PAT > Equations > Flashcards

Equations Flashcards

1
Q

Van der waals force (adhesion force)

A

F(ad)=(A*Rp)/6x^2

A=Hamakar constant (7.2*10^-20)
Rp=radius of particle
x= Gap between particles

** When distance is small force is high**

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2
Q

Gravity force

A

F(gr)=4/3piRp^3*rho

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3
Q

Forces due to liquid bridges

A

F(s)=2piy*Dp

y= surface tension
Dp=Particle diameter

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4
Q

Breakage equations (3)

A
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5
Q

Ribbon tensile strength

A

tensile strength= 3FG/2wt^2

F= force
G= gap between beams
W=ribbon width
t=thickness

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6
Q

pressing force

A

Pmax=2Rf/WDF

Rf= pressing force
W=width of roll
D= roll diameter
f=force factor
Pmax = peak pressure

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7
Q

Hardness

A

H=Fmax/Ap(Hc)

Fmax = max force
Ap(Hc) = projected contact area
Hc indentor contact depeth at Hmax

Hmax=Hc+Hf
Hmax = total distance
Hf = distance after loading
Hc = sinking depth

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8
Q

Granule size distribution

A

Y=1-exp(-x/xo)^n

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9
Q

Gravitational force

A

Fg=(d^3pi/6)rho*g

d= diameter
rho=particle density

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10
Q

buoyancy force

A

Fb=(d^3pi/6)rho*g

rho=particel density

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11
Q

drag force

A
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12
Q

carmen kozey

A

pressure drop=180((1-e)^2/e^3)((viscU)/(d^2rho))

e=voidage
visc = visccity
U=velocity

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13
Q

min fluidisation velocity (baeyan and geldart correlation)

A

look at notes but used when particle size <100Um

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14
Q

min fluidsation velocity (Wen and Yu)

A

look at notes but use when particle size>100Um

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15
Q

archemedies number

A

Ar=(pf(pp-pf)gd^3)/visc*2

pp=particle density
pf=fluid density
visc= viscocity

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16
Q

Bed density

A

Pb=(1-e)pp
e=voidage
pp= particle density

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17
Q

moisture content

A

X=xw/1+xw
Xw=x/1-x

x=dry basis
xw = wet basis

18
Q

relative humidty

A

RH=p/ps

P
p=PY/0.622+Y

y=absolute humidity
P=total pressure
p = vapour pressure
ps = saturation pressure

19
Q

Convective heat flux

A

Q”=H(ts-Tinf)

h= proportanity constant
ts= surface temp
tinf= fluid temp

20
Q

Constant drying rate

A

X0-X=(rhoFgCpg(Tgi-Tgo))/(Mslambda)t

rho= gas density
Fg= gas vol flowrate
Cpg=specific heat of gas
t= drying time
Ms=mass of solids
lambda= latent heat

21
Q

constant drying time

A

T=(M/AR)(xf-xi)

M= mass of dry material
A= area
R= drying rate

22
Q

Falling rate time (linear)

A

t=(m/a)(Xcr/Rcr)ln(Xin/Xfin)

xcr = critical moisture content
m= mass of dry material
a=area
Rcr = crticial drying rate

23
Q

Falling rate time (parabolic)

A

t=(m/a)(Xcr/Rcr)ln(Xin/Xfin)+(m/a)(1/a)ln((a+bXfin)Xcr/((a+bXcr)Xfin)

xcr = critical moisture content
m= mass of dry material
a=area
Rcr = crticial drying rate

24
Q

Falling rate time (Linear+ parabolic)

A

t=(m/a)(Xcr/Rcr)ln(Xin/Xfin)+(m/a)(1/a)ln((a+bXfin)Xcr/((a+bXcr)Xfin)

xcr = critical moisture content
m= mass of dry material
a=area
Rcr = crticial drying rate

25
Q

dimensionless fragmentation number

A

Fa= applied stress/ agglomerate strength

rate of extent of dispersion increases with fragmentation number
Fa<1 then no dispersion
Fa>1 then agglomerates begin to erode

26
Q

tensile strength for collision dispersion

A

tensile strength is when particles collide with each other or boundary

tensile strength = 2/3* rhoPDp(Vi/delta T)

rhoP= particle density
Dp=particle dimater
vi= impact velocity
delta T= impact time

27
Q

dispersion efficency

A

defined as particle size distribution of dispersed particles and primary particles

look at equation in notes

28
Q

imbibition rate

A

imbibition rate = (7Dpe^2y^lvcos())/(75udagg^2(1-e))

e=voidage
y^lv = surface tension between liquid and vapour
* = contact angle
u- fluid viscocity
Dagg= agglomerate diameter

29
Q

stagnant conditions
- mass
- particle radius
- dissolution time

A

m=Kl(4piRp^2)*(Cs-Cb)

Rp= particle radius
Cs= saturation conc
Cb= bulk conc

assumptions
- conc at the surface is the saturation conc
Cs»Cn dissolution under sink conditions

Rp^2=Rp0^2= (2DlCs)/rhoP)*t

RP0 is radius when dissolution is finished

Td= (- rhoPRp0)/(2Dl*Cs)

30
Q

non zero velocity
- slip velcocity for laminar flow

A

stagnant conditions give no dependence to flow field and implies rate is independent of stirrer speed

slip velcocity can be approximated for laminar flow as slip increase mass transfer coefficent increases

** look at laminar slip equation in notes**

31
Q

volume fraction of particles that dissolve at time t

A

t*=1-(ri^3)/(ri0^3)

32
Q

total fraction of powder dissolved

A

t=Vit

Vi= inital volume fraction
t*= volume fraction of particles dissolved at time t

33
Q

weight fraction in saturated phase?

A

Fsat=(Ctot-Ccr)/ (Csat-Ccr)

34
Q

weight fraction in crystalline phase phase?

A

Fcr=(Ctot-Csat)/(Ccr-Csat)

35
Q

gibbs free energy

crtiical radius and crticial gibbs

A

delta G= 4pir^2y-4/3pir^3(deltaU/Vm)

r= crystal cluser radius
y= interfacail free energy
delta U=chemical potential difference per solute molecule in the fluid and in the solid
Vm= molecular volume

r=(2yVm)/(delta U)
delta G=(16piy^3Vm^2)/(3deltaU^2)

36
Q

driving force from solution (crystalisation)

A

delta U= KT*ln(C/Cs)

37
Q

driving force from melt (crystallisation)

A

delta U= delta Hm*deltaT/Tm
Tm= crystaliisation temp

38
Q

rate of formation of 3D nuclei

A

J=Aexp(-delta G*/KbT)

39
Q

limear growth rate (growth rate of a face in the direction normal to the face

A

v=dl/dt

growth is a kinetic phemomen driven by superaturation that is determined by thermodynamic data

40
Q

mass deposition rate (crystal growth kinetics)

A

Kgm=3alpha/betarho*Kgl

kgl= linear growth rate
alpha and beta = volume and area shape factors

for spheres and cubes
Kgm=rho*v
v= mean lineat growth velocity

kgm and kgl are both temperature dependent and fit arrenhius

PAT (2 decks)

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