  The plasma dynamics at frequencies comparable with collisional frequency
between various species has to be described in multi-fluid framework, where
collisional interaction between particles is an important ingredient. In our
study we will assume that charged particles are strongly coupled, meaning that
they form a single fluid that interacts with neutrals, therefore we will employ
a two-fluid model. Here we aim to investigate the evolutionary equation of slow
sausage waves propagating in a gravitationally stratified flux tube in the
two-fluid solar atmosphere in a strongly ionised limit using an initial value
analysis. Due to the collisional interaction between massive particles (ions
and neutrals) the governing equations are coupled. Solutions are sought in the
strongly ionised limit and the density ratio between neutrals and charged
particles is a small parameter. This limit is relevant to the upper part of the
chromosphere. Our results show that slow sausage waves associated with charged
particles propagate such that their possible frequency is affected by a cut-off
due to the gravitational stratification. contrast, for neutral acoustic waves
the cut-off value applies on their wavelength and only small wavelength waves
are able to propagate. Slow modes associated to neutrals are driven by the
collisional coupling with ions.
