  We aim to study the formation and evolution of solar spicules by means of
numerical simulations of the solar atmosphere. With the use of newly developed
JOANNA code, we numerically solve two-fluid (for ions + electrons and neutrals)
equations in 2D Cartesian geometry. We follow the evolution of a spicule
triggered by the time-dependent signal in ion and neutral components of gas
pressure launched in the upper chromosphere. We use the potential magnetic
field, which evolves self-consistently, but mainly plays a passive role in the
dynamics. Our numerical results reveal that the signal is steepened into a
shock that propagates upward into the corona. The chromospheric cold and dense
plasma lags behind this shock and rises into the corona with a mean speed of
20-25 km s$^{-1}$. The formed spicule exhibits the upflow/downfall of plasma
during its total lifetime of around 3-4 minutes, and it follows the typical
characteristics of a classical spicule, which is modeled by
magnetohydrodynamics. The simulated spicule consists of a dense and cold core
that is dominated by neutrals. The general dynamics of ion and neutral spicules
are very similar to each other. Minor differences in those dynamics result in
different widths of both spicules with increasing rarefaction of the ion
spicule in time.
