Lake environments - Environmental Sedimentology - page 126

lake volume and the water discharge to or from
the lake ( Q ):

may appear. It is important to note the differ-
ence between the settling velocity ( v in cm s −1 )
and the sedimentation rate ( R sed in L s −1 ).
Stokes' law expresses the settling velocity ( v ) as:

T = V / Q

(( d w - d p · g · d 2 )/(18 ·

The value of Q can be derived from time-series
of measurements, or be given as a mean monthly
value, or as a mean yearly value. In the latter
case, T is generally referred to as the theoretical
lake-water retention time.
The concentration in the lake water may then
be expressed as:

v = μ · Ø )

where v is the settling velocity (usually in
cm s −1 or m month −1 ), d p is the particle density
(usually in g dw cm −3 ), d w is the density of the
lake water (often set to 1 g ww cm −3 ), g is the
acceleration due to gravity (980.6 cm s −1 ), d is
the particle diameter (in m, cm or mm), is the

coefficient of absolute viscosity (obtained from
standard tables; 0.01 poise at 20°C) and Ø is
the coefficient of form resistance (set to 1 for
spheres; Hutchinson 1967).
Stokes' law (Stokes 1851) is depicted in
Fig. 4.13. The behaviour of material that follows
Stokes' law (i.e. particles with a diameter between
about 0.01 and 0.0001 cm) differs from that of
the coarser fraction material and from that
of still finer material. The sedimentological
behaviour of the material is closely linked to the
grain size of the individual particles (Einstein
1950; Allen 1970). The sedimentological beha-
viour of the very fine materials is governed by
Brownian motion. These latter particles are so
small that they will not settle individually, but
will do so if they form larger flocs or aggregates
that are dense enough to settle according to
Stokes' law (Kranck 1973, 1979; Lick et al. 1992).
The cohesive materials that follow Stokes' law are
very important, because they have a great affinity
for pollutants (Fig. 4.7). This group includes
many types of detritus, humic substances and
plankton. All play significant roles in aquatic
ecosystems (Salomons & Förstner 1984).
The settling velocity ( v ) of a given particle,
aggregate or particulate pollutant, and its dis-
tribution in a lake, depends on the density, size
and form of the particle (and on the hydro-
dynamics of the flow of water in the lake). If
the particle density, d p , is close to 1, if the form
factor, Ø , is large and if the diameter, d , is
small, the settling velocity, v , and the sedimenta-
tion rate, R sed , may be very slow. If R sed is close
to 0, the particle or aggregate is conservative in

μ

C = ( Q · C in + M S · R res )/( Q + V · R res · PF )

This expression for the lake concentration is
fundamental in lake science and management.
When Vollenweider (1968) presented his first
loading model for lake eutrophication (phos-
phorus), it meant a breakthrough not 'just' for
lake management but also for lake modelling.
Vollenweider simplified the mass-balance model
first by omitting seasonal variations and instead
gave the annual budget. He also omitted different
nutrients and different forms of the nutrients,
and instead made the calculations for total
phosphorus. In addition, he disregarded inter-
nal loading (the M S · R res term in the given equa-
tion) and simplified the sedimentation term
( M S · R sed · PF , which he approximated to √ T ).

This gave the famous Vollenweider model:

C = C in /(1 +√ T )

It is evident that substances with large R sed
values settle rapidly, near the point of discharge,
and that substances with small R sed values may
be distributed over much larger areas. For most
substances, it is important to determine or pre-
dict the R sed value, which is related to the settling
velocity, v ( v z · R sed , where z is the distance

through which the particle sinks in the given
time interval). The settling velocity, v , is gener-
ally given in centimetres per second or metres per
year. Given R sed or v , one can model or predict
where high and low concentrations are likely to
appear in water and sediments. This is the key to
predicting where high and low ecological effects

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