Sedimentation Methods for Determining Particle Sizes

Mechanics

Feb 21, 2014 (4 years and 2 months ago)

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Sedimentation Methods for Determining Particle Sizes

Rely on Stokes’ Law

Sphere of diameter D falling through viscous fluid reaches a terminal
velocity, which depends on the bouyant weight of the sphere, the sphere
diameter, and the fluid viscosity (for R
e

< 1)

Thus, a sphere of diameter D will fall distance h in time t
D:

where


is the fluid viscosity,
g
s

is the unit weight (=
r
g) of the sphere
material, and
g
w

is the unit weight of water

This is the basis of the “pipette” method of determining the sizes of fine
soils

easy to explain, but requires high precision

Also the basis of the “hydrometer” method

more complex to explain, but
simpler to do

2
w
s
D
D
h
18
t
g

g

Pipette Method

Mix 50g of dry soil in 1 litre of
water, and put into 1 litre graduated
cylinder. Shake thoroughly so that
soil is evenly dispersed in the water

Any

10 ml volume of the water will
contain 0.5g of soil

Set on bench

allow to start settling

At pre
-
determined times, use pipette
to take 10 ml sample from exactly
100 mm below the surface of the

Dry the sample, and weigh the dry
soil

So how can this be used to work out
particle size distribution?

10 ml pipette

100 mm

t
D2

t
D1

h

Coarse spheres (D1)

Fine spheres (D2)

2
w
s
2
D
2
w
s
1
D
2
w
s
D
2
D
h
18
t
1
D
h
18
t
D
h
18
t
g

g

g

g

g

g

t
D2

t
D1

h

Coarse spheres (D1)

Fine spheres (D2)

2
w
s
2
D
2
w
s
1
D
2
w
s
D
2
D
h
18
t
1
D
h
18
t
D
h
18
t
g

g

g

g

g

g

t
D2

h

Spheres (D1 & D2)

t
D1

Before t
D1
, particles D1 are at same
concentration at height h as in
original sample

After t
D1
, but before t
D2
, particles
D1 are missing, but particles D2 are
in their original concentration

After t
D2
, none of either D1 or D2
particles present

To find percentage of particles finer
than D1, take sample just after t
D1

2
w
s
2
D
2
w
s
1
D
2
w
s
D
2
D
h
18
t
1
D
h
18
t
D
h
18
t
g

g

g

g

g

g

t
D2

h

Spheres (D1 & D2)

t
D1

Before t
D1
, particles D1 are at same
concentration at height h as in
original sample

After t
D1
, but before t
D2
, particles
D1 are missing, but particles D2 are
in their original concentration

After t
D2
, none of either D1 or D2
particles present

To find percentage of particles finer
than D1, take sample just after t
D1

2
w
s
2
D
2
w
s
1
D
2
w
s
D
2
D
h
18
t
1
D
h
18
t
D
h
18
t
g

g

g

g

g

g

Continuous distribution

Choosing a time for taking a sample is
like choosing a sieve size . Thus, to find
percentage finer than 20
m
m, take sample
at depth 100 mm at time 4.57 minutes.

Dry the sample; weigh the dry soil.

Weight of soil in this 10 ml sample is
same as weight of material finer than 20
mm in 10 ml of original sample.

Say 50 g of soil per litre

i.e. 0.5 g per 10
ml in original sample

Say 0.3 g of soil in sample taken at 4.57
minutes

Thus, % finer than 20
m
m is

0.3/0.5 = 60%

hours

7.62

minutes

457

longer
10

is

time
equivalent

m,

2
For
minutes

4.57

seconds

274
10
20
81
.
9
4
.
26
1
.
0
10
1
18
t
m)

(0.1

mm

100

h
(water)

kN/m

81
.
9
soils
many
for

kN/m

4
.
26
C
20

@

kPa.s

10
1
D
h
18
t
2
2
6
6
m
20
2
w
2
s
6
w
2
w
s
D

m

g

g

g

g

m

Spheres of quartz settling in water
10
20
1.13
2
3
4
5
7
1 day
10 hours
10
100
1,000
10,000
100,000
0
10
20
30
40
50
60
70
80
90
100
110
Sphere Diameter (

m)
Time to settle 100 mm (sec.) .
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Reynold's Number
Settling time
Reynolds Number
Stoke's Law only valid for Reynold's Number < 1. From below,
only valid for D < 100
m

)
Pa.s
k

10
1
(

fluid

the

of

viscosity

dynamic

is

diameter

is

D
velocity

is

v
)
t/m

1
(

fluid

the

of

density

is

where

vD
R
:
)
R
(
Number

s
Reynold'
6
w
3
w
e
e

r
r

r

Equipment for Hydrometer Test

Hydrometer measures the average density of the fluid (at about the depth to the
centre of the bulb. This reduces as coarser material settles

hydrometer
“samples” the density at different times (like the pipette in a sense)