  In the absence of an initial seed, the Biermann battery term of a non-ideal
induction equation acts as a source that generates weak magnetic fields. These
fields are then amplified via a dynamo mechanism. The Kelvin-Helmholtz
instability is a fluid phenomenon that takes place in many astrophysical
scenarios and can trigger the action of the Biermann battery and dynamo
processes. We aim to investigate the effect that the ionisation degree of the
plasma and the interaction between the charged and neutral species have on the
generation and amplification of magnetic fields during the different stages of
the instability. We use the two-fluid model implemented in the numerical code
Mancha-2F. We perform 2D simulations starting from a configuration with no
initial magnetic field and which is unstable due to a velocity shear. We vary
the ionisation degree of the plasma and we analyse the role that the different
collisional terms included in the equations of the model play on the evolution
of the instability and the generation of magnetic field. We find that when no
collisional coupling is considered between the two fluids, the effect of the
Biermann battery mechanism does not depend on the ionisation degree. However,
when elastic collisions are taken into account, the generation of magnetic
field is increased as the ionisation degree is reduced. This behaviour is
slightly enhanced if the process of charge-exchange is also considered. We also
find a dependence on the total density of the plasma related to the dependence
on the coupling degree between the two fluids. As the total density is
increased, the results from the two-fluid model converge to the predictions of
single-fluid models.
