Equations

Question 1

Van der waals force (adhesion force)

Answer 1

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**

Question 2

Gravity force

Answer 2

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

Question 3

Forces due to liquid bridges

Answer 3

F(s)=2piy*Dp

y= surface tension
Dp=Particle diameter

Question 4

Breakage equations (3)

Question 5

Ribbon tensile strength

Answer 5

tensile strength= 3FG/2wt^2

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

Question 6

pressing force

Answer 6

Pmax=2Rf/WDF

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

Question 7

Hardness

Answer 7

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

Question 8

Granule size distribution

Answer 8

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

Question 9

Gravitational force

Answer 9

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

d= diameter
rho=particle density

Question 10

buoyancy force

Answer 10

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

rho=particel density

Question 11

drag force

Question 12

carmen kozey

Answer 12

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

e=voidage
visc = visccity
U=velocity

Question 13

min fluidisation velocity (baeyan and geldart correlation)

Answer 13

look at notes but used when particle size <100Um

Question 14

min fluidsation velocity (Wen and Yu)

Answer 14

look at notes but use when particle size>100Um

Question 15

archemedies number

Answer 15

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

pp=particle density
pf=fluid density
visc= viscocity

Question 16

Bed density

Answer 16

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

Question 17

moisture content

Answer 17

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

x=dry basis
xw = wet basis

Question 18

relative humidty

Answer 18

RH=p/ps

P
p=PY/0.622+Y

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

Question 19

Convective heat flux

Answer 19

Q”=H(ts-Tinf)

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

Question 20

Constant drying rate

Answer 20

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

Question 21

constant drying time

Answer 21

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

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

Question 22

Falling rate time (linear)

Answer 22

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

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

Question 23

Falling rate time (parabolic)

Answer 23

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

Question 24

Falling rate time (Linear+ parabolic)

Answer 24

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

Question 25

dimensionless fragmentation number

Answer 25

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

Question 26

tensile strength for collision dispersion

Answer 26

tensile strength is when particles collide with each other or boundary tensile strength = 2/3* rhoP*Dp*(Vi/delta T) rhoP= particle density Dp=particle dimater vi= impact velocity delta T= impact time

Question 27

dispersion efficency

Answer 27

defined as particle size distribution of dispersed particles and primary particles look at equation in notes

Question 28

imbibition rate

Answer 28

imbibition rate = (7*Dp*e^2*y^lv*cos(*))/(75*u*dagg^2*(1-e)) e=voidage y^lv = surface tension between liquid and vapour * = contact angle u- fluid viscocity Dagg= agglomerate diameter

Question 29

stagnant conditions - mass - particle radius - dissolution time

Answer 29

m=Kl(4*pi*Rp^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= (2*Dl*Cs)/rhoP)*t RP0 is radius when dissolution is finished Td= (- rhoP*Rp0)/(2*Dl*Cs)

Question 30

non zero velocity - slip velcocity for laminar flow

Answer 30

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**

Question 31

volume fraction of particles that dissolve at time t

Answer 31

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

Question 32

total fraction of powder dissolved

Answer 32

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

Question 33

weight fraction in saturated phase?

Answer 33

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

Question 34

weight fraction in crystalline phase phase?

Answer 34

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

Question 35

gibbs free energy crtiical radius and crticial gibbs

Answer 35

delta G= 4*pi*r^2*y-4/3*pi*r^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*=(2*y*Vm)/(delta U) delta G*=(16*pi*y^3*Vm^2)/(3*deltaU^2)

Question 36

driving force from solution (crystalisation)

Answer 36

delta U= KT*ln(C/Cs)

Question 37

driving force from melt (crystallisation)

Answer 37

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

Question 38

rate of formation of 3D nuclei

Answer 38

J=A*exp*(-delta G*/KbT)

Question 39

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

Answer 39

v=dl/dt growth is a kinetic phemomen driven by superaturation that is determined by thermodynamic data

Question 40

mass deposition rate (crystal growth kinetics)

Answer 40

Kgm=3*alpha/beta*rho*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