Geoscience 240 – Lab 3 Shales and Stokes Law
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LAB 3: SHALES AND STOKES’ LAW
In terms of earth history, the fossil record, and understanding primary fluid geochemistry, shales
and other mudrocks are the most important part of the sedimentary record. Coarse grained
clastics, be they from mountain stream fans, beach gravels, landslides or glacial outwash, are
interesting and easy to interpret. Fine grained sediments occur in far more diverse geological
environments and offer much more complete sedimentary records. Among the resources they
comprised of are clay minerals for bricks, ceramics and insulators, organic (kerogen-rich) source
rocks for petroleum, caprocks for hydrocarbon reservoirs and aquicludes for ground water
aquifers.
In terms of fossils, these fine grained mudrocks are the most productive. Terrestrial shales contain
spores and pollen, algal cysts, seeds, leaf impressions, higher plant matter (stems, trunks, roots)
and direct and indirect fossils of animals from worm burrows to ostracodes, sin impressions or
hard body parts like teeth and bones. While coarse grained rocks can be deposited in one storm, or
some other single short lived depositional event, fine grained rocks slowly and faithfully record
cycles from tidal to diurnal (animal daytime activity) to seasonal to long term climate shifts. It is the
slow settling of small amounts of fine particulate matter that produce the highest resolution
records of the Earth.
There are three parts to this lab:

Part 1: Mudrock – Hand Specimens and Thin Sections

Part 2: Stokes Law of Particle Settling

Part 3: Determination of the Viscosity of a Fluid

Part 4: Exploring the Effects of Shape on the Settling of Sedimentary Particles
PART 1: MUDROCK – HAND SPECIMENS AND THIN SECTIONS
Examine several fine grained mud rocks in hand specimen and thin section. Note the scale and
variations in bedding thickness, particle sizes, particle shapes, particle orientations and lithology.
Various questions to consider might be as follows:

What is the matrix; quartz, clay minerals, fine grained iron oxides, carbonates, and/or
organic matter?

Are these components all detrital or are some diagenetic?

How do the textures vary?

Are these rocks well cemented or mainly just compacted?

How much compaction is represented in terms of a percentage of the original be thickness?

What kinds of fossils are present?
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Geoscience 240 – Lab 3 Shales and Stokes Law
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
How do fossils indicate depositional environment?
Take these factor into account and fill out a brief description and write a summary for each of the
four specimens.
1. Tertiary shale – Penticton, British Columbia
2. Graptolitic shale
3. Bituminous or Kerogen rich shale
4. Argillaceous, Ferruginous, Calcareous, Carbonaceous or Siliceous shale (circle which
one you chose)
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Geoscience 240 – Lab 3 Shales and Stokes Law
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PART 2: STOKES LAW OF PARTICLE SETTLING
Note: Read all of the instructions before starting the experiment.
OBJECTIVE
A. Explore Stokes’ Law of Settling
B. Determine the Viscosity of a Fluid
C. Investigate the Effect of Particle Shape on the Settling of Particles
BACKGROUND
Some of the properties of fluid are discussed in the notes “Properties of Fluids”. Review these notes
first.
A knowledge of particle settling is necessary for the solution of many sedimentation problems. It is
clear from the earlier notes that in the “real world” of geoscience there are many variables e.g. fluid
viscosity and velocity; particle size, shape and density. In these experiments we hold some of these
variables constant. For example we may use a stationary fluid and spherical particles, rather than a
turbulent stream with particles of irregular shape.
Note that the hydraulic method is used in determination of particle size for silt and clay. This is
discussed in an appendix.
Note also that the particle shape experiment is instructive in practical problems such as prediction
of the dispersal of solid pollutants from an outfall into a river or estuary.
STOKES LAW THEORY
Consider a small spherical particle settling through a column of still liquid. Initially the particle will
accelerate. Eventually the particle attains a constant velocity called the terminal velocity. At this
velocity the gravitational forces acting downward on the sphere are balanced by the viscous drag
which the fluid exerts on it. The gravitational force Fg downward is given by the equation:
d 3
4
Fg = 3 π (2) ρs g
where d = particle diameter &
ρs = density of particle
The buoyant force Fup is given by the equation:
4
d 3
Fup = 3 π (2) ρf g
where ρf = density of fluid
The fluid drag is a function of the particle projection area (cross section), a drag coefficient and the
drag force per unit area. This gives the drag force
d 2
1
D = π (2) Cd 2 ρV 2
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where Cd = drag coefficient
Geoscience 240 – Lab 3 Shales and Stokes Law
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V = terminal velocity
For low Reynolds number and low particle concentration,
24
CD = R
e
Substituting
Fg =
dVρf
μ
for Re
At the terminal velocity
𝑑 2 𝜌𝐹 𝑉 2
2
CD𝜋 ( 2 )
=
4
𝑑 3
𝜋
(
) 𝑔(𝜌𝑠
3
2
− 𝜌𝐹 )
4 dg(𝜌𝑠 − 𝜌𝐹 )
CD ρF
V2 = 3
Substituting for C
ν2 =
∴𝑉=
4μg(ρs −ρF )dVρF
3ρF 24μ
1 (ρs − ρF )gd2
18
μ
This is a square law of the form
𝑉 = 𝐾𝑑2
where K is a constant
Thus a plot of V against d2 gives a straight line with gradient K which passes through the origin.
The fluid viscosity, “μ” ,can be obtained.
PART 3: DETERMINATION OF THE VISCOSITY OF A FLUID
Apparatus and Materials:

Tall cylinders

Beaker

Castor Oil/Glycerol

Stop watch

Thermometer

Ball bearings
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Geoscience 240 – Lab 3 Shales and Stokes Law
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Magnets

Micrometers

Tweezers
Note: Do not use plasticene or other substances in this experiment.
PROCEDURE AND OBSERVATIONS
1. Use the micrometer to find the diameter of the steel ball bearings that you select. Find the
mass of each ball using the balance. From the mass and diameter find the density.
2. Place your ball bearing into the cylinder filled with castor oil/glycerin. Hold it with tweezers
about 1 cm below the surface of the liquid. There should be no air bubbles attached to the
ball. Release the ball. Time the decent of the ball between the upper and lower marks on
the cylinder.
3. Measure the distance between the marks and calculate “V”.
4. Plot V against d2.
5. Calculate the slope of the graph and then obtain “μ”.
RELEVANCE
Stokes’ Law works accurately for particles of low Reynolds number. In geoscience this corresponds
to silt size and smaller particles of the density of quartz settling in water. Here, flow around the
particle can be considered laminar. For larger particles, turbulence is generated and drag is
increased.
Sediment grains are neither perfectly round nor spherical. For example the descent of shell sands
through a water column will display motions normal to the mean downward velocity vector.
Also, in nature, particles do not settle individually but as a group. Particle interaction and increased
drag result in a decrease in the fall velocity relative to the velocity in a grain-free fluid. In highly
sediment-laden flows such as turbidity currents, settling velocity may be <10% in grain-free fluid.
PART 4: EXPLORING THE EFFECTS OF SHAPE ON THE SETTLING OF
SEDIMENTARY PARTICLES
APPARATUS AND MATERIALS

1 litre cylinder of glycerol

Plasticine
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Geoscience 240 – Lab 3 Shales and Stokes Law
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
Penny or Copper Foil piece of similar size

Stopwatch

Tape measure/ruler
PROCEDURE
1. Cut and weigh the plasticene into masses of about 2.0 to 3.0 g which agree in weight to a few
percent.
2. Shape the pieces into spheres, prolate spheroids, oblate spheroids, hemispheres, disks,
cylinders and concavo-convex lens.
3. Allow the pieces to cool to ambient temperature.
4. Wet each particle with glycerol.
5. Release one particle at a time broadside to the liquid. Note the time take for each shape to
pass between the upper and lower marks.
6. Do the particles vary with particle shape?
7. Which shape has the highest velocity?
8. The concavo-convex lens shape represents bivalve shells. Try releasing them at various
orientations and observe their behavior.
APPENDIX: PARTICLE SIZE ANALYSIS OF SILT AND CLAY
Sedimentation methods based on particle settling velocity may be used to analyze sediment of silt
and clay size. The size parameter measured is called the equivalent diameter. It is the diameter of a
sphere (standardized to the density of quartz) having the same settling velocity as the particle.
The pipette method is used on samples from which sediment coarser than 4μm (0.062mm) has
been removed. Five to fifteen grams of sample is added to distilled water to give a uniform dilute
suspension.
A volume of 20 mL is withdrawn from prescribed depths on a time schedule determined by
calculations based on Stokes’ law. At those times, all particles of a given size will have settled below
that depth, and only finer particles remain in the sample that is withdrawn. The dry weight of these
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Geoscience 240 – Lab 3 Shales and Stokes Law
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samples is used to calculate the grain size distribution of the original sample. The method is mainly
used for sediment in the range 9 μm to 4 μm. See the figure for details.
Insert diagram here
FIGURE 7.4: THE PIPETTE METHOD FOR STUDYING SILT AND CLAY.
a) General setup with pipette and 1 L graduated cylinder.
b) After 20 seconds a 20 mL sample is withdrawn from a depth of 20 cm. Because no
appreciable settling has occurred in this sample, all grain sizes are present in the
proportions found in the original sample. This sample is one-fiftieth of the total volume of
the suspension. If the dry weight of the suspended sediment is 0.195 g, the total weight of
the original sample is 0.195 × 50 = 9.75 g.
c) After 1m 45s, a further 20 mL sample is withdrawn from a depth of 20 cm. By this time all
the particles coarser than 31 μm have settled below the depth of 20 cm. If the dry weight of
this sample is 0.108 g, the weight of the whole sample finer than 31 μm is 0.108 g × 50 =
5.40 g. The total weight of particles in the range 31 – 62 μm is 9.75 g (from “b” above) –
5.40 g = 4.35 g. This is 45% of the total sample. (4.35/9.75).
d) After 6m 58s a 20 mL sample is withdrawn from a depth of 10 cm. If the dry weight of this
sample is 0.073 g, the weight of that part of the sample finer than 15.6 μm is 0.073 × 50 =
3.64 g. The total weight of particles in the range 15.6 to 31 μm is 5.40 g (from “c” above) –
3.64 g = 1.76 g. This is 18% of the total sample (1.76/9.75).
Note: this example is based on data in Folk (1980: 37). The withdrawal times were calculated
using Stokes’ Law (for water at 20 °C and solids with a density of 2.65) in the form
T = D/1500 × A × d2
where T = time in minutes, D = depth in cm, and d = particle diameter in mm. A is a constant which
depends upon the viscosity of the water ( a function of the temperature), the force of gravity, and
the density of the particle.
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