  The interaction of dust grains originating from the local interstellar cloud
with the environment inside the heliosphere is investigated. As a consequence
of this interaction the spatial distribution of interstellar dust grains
changes with time. Since dust grains are charged in the interplanetary plasma
and radiation environment, the interaction of small grains with the heliosphere
is dominated by their coupling to the solar wind magnetic field. The change of
the field polarity with the solar cycle imposes a temporal variation of the
spatial distribution and the flux of small (radius smaller than $0.4 \mu m$)
interstellar dust grains in the Solar System, whereas the flux of large grains
is constant because of their negligible coupling to the solar wind magnetic
field. The flux variation observed by in-situ measurements of the Galileo and
Ulysses spacecraft are reproduced by simulating the interaction of interstellar
grains with charge-to-mass ratios between $0.5 C/kg^{-1}$ and $1.4 C/kg$ with
the interplanetary environment.
