  Context: Photospheric flows create a network of often mixed-polarity magnetic
field in the quiet Sun, where small-scale eruptions and network flares are
commonly seen. Aims: The aim of this paper is (1) to describe the
characteristics of the flows that lead to these energy releases, (2) to
quantify the energy build up due to photospheric flows acting on the magnetic
field, and (3) to assess its contribution to the energy of small-scale,
short-lived X-ray flares in the quiet Sun. Methods: We used photospheric and
X-ray data from the SoHO and Hinode spacecraft combined with tracking
algorithms to analyse the evolution of five network flares. The energy of the
X-ray emitting thermal plasma is compared with an estimate of the energy built
up due to converging and sheared flux. Results: Quiet-Sun network flares occur
above sites of converging opposite-polarity magnetic flux that are often found
on the outskirts of network cell junctions, sometimes with observable
vortex-like motion. In all studied flares the thermal energy was more than an
order of magnitude higher than the magnetic free energy of the converging flux
model. The energy in the sheared field was always higher than in the converging
flux but still lower than the thermal energy. Conclusions: X-ray network flares
occur at sites of magnetic energy dissipation. The energy is probably built up
by supergranular flows causing systematic shearing of the magnetic field. This
process appears more efficient near the junction of the network lanes. Since
this work relies on 11 case studies, our results call for a follow-up
statistical analysis to test our hypothesis throughout the quiet Sun.
