3 Physical background
Figure 3.6: The idea behind far eld models. (A) An organism swims by a certain
motion of each surface element, which leads to a complex arrangement
of many forces (in a continuous stress distribution) that act on the uid.
When viewed from the far eld the complex force distribution is `smoothed
out' and only those contributions remain that lead to the slowest ow decay.
If the contribution with the slowest decay is a force quadrupole, i.e., both
the monopole (force) and dipole (strain and torque) vanish, the same far
eld can be obtained from a characteristic arrangement of just three point
forces (B). Less forces are not sucient to cancel the monopole and dipole,
while more forces are not necessary to represent the characteristic far eld
of such a swimmer.
will not inuence their trajectories, since they are spherically symmetric. However, for
active particles the local vorticity will rotate their swimming direction and can thus
inuence their trajectories.
3.4 Integral and far-eld representation of Stokes ows
As mentioned before, self-propelled organisms actuate their body in a certain (periodic)
way in order to continuously move forward. Close to the organism the ow can be very
complex depending on the specic movement, which can vary signicantly between
dierent swimmers. However, when zooming out towards the far eld, less detailed
features can be seen and the ow generally simplies to characteristic patterns, which
are given by the lowest moments of the force distribution on the boundary (gures
3.5 and 3.6). The far eld ow does not look the same for all swimmers, but we can
distinguish dierent swimming modes according to the ow eld at large distance,
with respect to how the forces are distributed. Quantities that can be extracted from
far eld approximations of ows are the magnitudes and arrangement of the main
propulsion forces, the characteristic ow pattern and the decay of the ow speed with
increasing distance from the swimmer. Many microorganisms are exposed to owsensing
predators and they aim to keep their disturbance zones small. For this purpose
a fast decay of the created ows with distance is advantageous Kirboe et al., 2014;
Visser, 2007; Tiselius and Jonsson, 1997.