5
Bacteria and Marine Biogeochemistry
174
5.2.1
Hydrodynamics
of Low Reynolds Numbers
Water movement on a large scale is characterized
by inertial flows and turbulence. These are the
dominant mechanisms of transport and mixing, yet
they are inefficient in bringing substrates to the
microorganisms living in the water. This is
because the fundamental property required for
turbulence, namely the inertial forces associated
with mass, plays no role for very small masses, or
at very small scales, relative to the viscosity or
internal friction of the fluid. In the microscale, time
is insignificant for the movement of water, particles or organisms and only instantaneous forces
are important. Furthermore, fluid flow is rather
simple and predictable, the water sticking to any
solid surface and adjacent water volumes slipping
past it in a smooth pattern of laminar flow. The
transition from laminar to turbulent flow depends
on the scale and the flow velocity and is described by the dimensionless Reynolds number,
Re, which expresses the ratio between inertial and
viscous forces affecting the fluid or the particle
considered:
Re = uL/ν
(5.6)
where u is the velocity, L is the characteristic
dimension of the water parcel or particle, and ν is
the kinematic viscosity of the seawater (ca. 0.01
cm
2
s
-1
at 20°C). The transition from low (<1) to
high Reynolds numbers for swimming organisms,
for sinking particles, or for hydrodynamics in
general lies in the size range of 0.1-1 mm.
5.2.2
Diffusion at Small Scale
Diffusion is a random movement of molecules due
to collision with water molecules which leads to a
net displacement over time, a ‘random walk’.
When a large number of molecules is considered,
the mean deviation, L (more precisely: the root
mean square of deviations), from the starting
position is described by a simple but very
important equation, which holds the secret of
diffusion:
Dt
L
2
=
(5.7)
where D is the diffusion coefficient and t is the
time. This equation says that the distance molecules are likely to travel by diffusion increases
only with the square root of time, not with time
itself as in the locomotion of objects and fluids
which we generally know from our macroworld.
Expressed in a different way, the time needed for
diffusion increases with the square of the
distance:
Fig. 5.3 Relationships between size, diffusion time and Reynolds number. Representative organisms of the different
scales and their length and biomass are indicated. The diffusion times were calculated for small solutes with a
molecular diffusion coefficient of 10
-5 cm
2 s
–1 . The Reynolds numbers were calculated for organisms swimming at a
speed typical for their size or for water parcels of similar size and moving at similar speed.
Bacteria and Marine Biogeochemistry
174
5.2.1
Hydrodynamics
of Low Reynolds Numbers
Water movement on a large scale is characterized
by inertial flows and turbulence. These are the
dominant mechanisms of transport and mixing, yet
they are inefficient in bringing substrates to the
microorganisms living in the water. This is
because the fundamental property required for
turbulence, namely the inertial forces associated
with mass, plays no role for very small masses, or
at very small scales, relative to the viscosity or
internal friction of the fluid. In the microscale, time
is insignificant for the movement of water, particles or organisms and only instantaneous forces
are important. Furthermore, fluid flow is rather
simple and predictable, the water sticking to any
solid surface and adjacent water volumes slipping
past it in a smooth pattern of laminar flow. The
transition from laminar to turbulent flow depends
on the scale and the flow velocity and is described by the dimensionless Reynolds number,
Re, which expresses the ratio between inertial and
viscous forces affecting the fluid or the particle
considered:
Re = uL/ν
(5.6)
where u is the velocity, L is the characteristic
dimension of the water parcel or particle, and ν is
the kinematic viscosity of the seawater (ca. 0.01
cm
2
s
-1
at 20°C). The transition from low (<1) to
high Reynolds numbers for swimming organisms,
for sinking particles, or for hydrodynamics in
general lies in the size range of 0.1-1 mm.
5.2.2
Diffusion at Small Scale
Diffusion is a random movement of molecules due
to collision with water molecules which leads to a
net displacement over time, a ‘random walk’.
When a large number of molecules is considered,
the mean deviation, L (more precisely: the root
mean square of deviations), from the starting
position is described by a simple but very
important equation, which holds the secret of
diffusion:
Dt
L
2
=
(5.7)
where D is the diffusion coefficient and t is the
time. This equation says that the distance molecules are likely to travel by diffusion increases
only with the square root of time, not with time
itself as in the locomotion of objects and fluids
which we generally know from our macroworld.
Expressed in a different way, the time needed for
diffusion increases with the square of the
distance:
Fig. 5.3 Relationships between size, diffusion time and Reynolds number. Representative organisms of the different
scales and their length and biomass are indicated. The diffusion times were calculated for small solutes with a
molecular diffusion coefficient of 10
-5 cm
2 s
–1 . The Reynolds numbers were calculated for organisms swimming at a
speed typical for their size or for water parcels of similar size and moving at similar speed.