Post on 24-Dec-2015
A process used to separate or concentrate materials suspended in a liquid medium.
Centrifugation separates on the basis of the particle size and density difference between the liquid and solid phases.
the effect of gravity on particles (including macromolecules) in suspension.
Two particles of different masses will settle in a tube at different rates in response to gravity.
Centrifugal force is used to increase this settling rate in an instrument called a centrifuge.
Centrifuges are devices used in a variety of scientific and technical applications
The centrifugal force generated is proportional to the rotation rate of the rotor (in rpm) and the distance between the rotor center and the centrifuge tube.
Settling: acceleration from gravity (Fg) Centrifuge:
acceleration from centrifugal force (Fc) circular motion and acceleration occurred
from centrifugal force
ac = acceleration from centrifugal force (m/s2)
r = radial distance (m) ω = angular velocity (rad/s)
2rac
The centrifugal force, Fc acting on an object of mass m, rotating in a circular path of radius R, at an angular velocity of ω is :
(1)
and
(2)
where N = rotational speed (rpm) ω= an angular velocity (rad s-1)
2mRFc
3060
2 NN
- The steady state velocity of particles mo ving in a streamline flow under the actio
n of an accelerating force
Where vt=terminal velicity of partical; ρs and ρl = density of solid and liquid ; r = distance of the particle from center of rotation;µ = viscosity of liquid.
18
)( 2pls
t
Dgvfrom
18
)( 22pls
t
Drv
Time taken by the particle to move though the liquid layer is called residence time (tr).
dt
drVt
18
)( 22 rDv ppt
18
)(22 pprD
dt
dr
)(
ln18
18
)(ln
18
)(1
22
22
0
22
1
pp
i
o
r
rpp
i
o
tpp
r
r
D
rr
t
tD
r
r
dtD
drr
o
i
flow rate (Q)
i
o
ppio
pp
i
o
io
r
rr
DbrrQ
D
r
rbrr
t
VQ
ln18
)()(
)(
ln18
)(
2222
22
22
ri = inside radius (m)
ro = outside radius (m) b = height of centrifuge(m) µ = viscosity (Pa.s) ω = an angular velocity (rad s-1) ρp = density of solid (kg/m3) ρ = density of liquid (kg/m3) Dp= diameter of particle(m)
Figure 1 Liquid centrifuge
(a) Pressure difference
Consider a thin differential cylinder, of thickness dr and height b as shown in Fig .1(a ): the differential centrifugal force across the thickness dr is given by equation (1):
dFc = (dm)r2
where dFc is the differential force acro ss the cylinder wall, dm is the mass of
the differential cylinder, is the angul ar velocity of the cylinder and r is the
radius of the cylinder.
dm = 2πρrbdr
where is the density of the liquid and b is the height of the cylinder . The area over which the force dFc act s i s 2πrb , so that:
dFc /2πrb = dP =ρ 2rdr
where dP is the differential pressure across the wall of the differential cylinder.
To find the differential pressure in a centrifuge, between radius r1 and r2, the equation for dP can be integrated, letting the pressure at radius r1 be P1 and that at r2 be P2, and so
P2 - P1 = ρω2 (r2
2 - r12)/2 (3)
Equation (3) shows the radial variation
in pressure across the centrifuge.
Figure 1 Liquid centrifuge
(b)neutral zone
ρAω2 (rn2 - r1
2)/2 = ρB ω2(rn2– r2
2)/2
rn2 = (ρAr1
2 - ρBr22) / (ρA - ρB) (4)
where ρA is the density of the heavier liquid
ρB is the density of the lighter liquid
Equation (4) shows that as the discharge radius for the heavier liquid is made smaller, then the radius of the neutral zone must also decrease
FIG. 2 Liquid centrifuges: (a) conical bowl
In liquid/liquid separation centrifuges, conical plates are arranged as illustrated in Fig. 2(a) and these give smoother flow and better separation.
Whereas liquid phases can easily be removed from a centrifuge, solids present much more of a problem.
FIG. 3 Liquid/solid centrifuges (a) telescoping bowl, (b) horizontal bowl, scroll discharge
FIG. 3 Liquid/solid centrifuges (c) nozzle
(c)
One method of handling solids from continuous feed is to employ telescoping action in the bowl, sections of the bowl moving over one another and conveying the solids that have accumulated towards the outlet, as illustrated in Fig. 3(a).
The horizontal bowl with scroll discharge, centrifuge, as illustrated in Fig.3(b) can discharge continuously. In this machine, the horizontal collection scroll (or screw) rotates inside the conical-ended bowl of the machine and conveys the solids with it, whilst the liquid discharges over an overflow towards the centre of the machine and at the opposite end to the solid discharge.
Another method of handling solids is to provide nozzles on the circumference of the centrifuge bowl as illustrated in Fig. 3(c). These nozzles may be opened at intervals to discharge accumulated solids together with some of the heavy liquid.
Find centrifugation time tr of a particle d=1mm. In a centrifuge
Given
.25.0
.20.0
/1000
/1100
.101.8
995
3
3
4
mR
mR
mkg
mkg
sPa
RPMN
o
i
f
P
Ri
Ro
srad
N
/20.10460
995260
2
Find ω
sec1025.3
1000110020.104001.0
)20.0/25.0ln(101.818
)/ln(18
3
22
4
22
r
r
fp
ior
t
t
d
rrt
Find time
tr of particle d=1mm. in centrifuge≥3.25x10-3sec
A bowl centrifuge is used to break an oil-in-water emulsion. Determine the radius of the neutral zone in order to position the feed pipe correctly. (Assume that the density of the continuous phase is 1000 kg/m3 and the density of the oil is 870 kg/m3. the outlet radius from the centrifuge are 3 cm and 4.5 cm).
Solution
mr
r
r
n
n
n
098.0130
783.0025.2
8701000
)03.0(870)045.0(1000 222
Beer with a specific gravity of 1.042 and a viscosity of 1.04x10-3 N s/m2 contains 1.5% solids which
have a density of 1160kg/m3. It is clarified at a rate of 240 l/h in a bowl centrifuge which has and
operating volume of 0.09 m3 and a speed of 10000 rev/min. The bowl has a diameter of 5.5 cm and is fitted with a 4 cm outlet. Calculate the effect on feed rate of an increase in bowl speed to 15000
rev/min and the minimum particle size that can be removed at the higher speed.
Solution Initial flow rate
new flow rate
)/ln(18
)60/2( 221
1io
fp
rr
DNVQ
)/ln(18
)60/2( 222
2io
fp
rr
DNVQ
As all conditions except the bowl speed remain the same,
Therefore, Q2 = 0.15 l/s
2
22
21
22
1
2
)60/10000142.32(
)60/15000142.32(
)3600/240(
)60/2(
)60/2(
Q
N
N
Q
Q
mD
VN
rrQD
fp
io
8.61062.2
1020.1
09.0)10421160()60/15000142.32(
)]02.0/0275.0ln(1040.118[15.0
)()60/2(
)]/ln(18[
7
3
2
3
22
22