  Assuming that the interchange convection of magnetic flux elements is the
physical cause for the existence of filamentary penumbrae in sunspots, we
investigate the behavior of an individual fibril embedded in the deep penumbra.
The fibril is approximated by a thin magnetic flux tube which evolves
dynamically in the environment given by the global magnetostatic model of a
sunspot.
  Our simulation shows that the flux tube, initially positioned at the
penumbra--quiet Sun boundary in the model, will rise through its deep penumbra
developing a flow along the tube that points upward beneath the photosphere,
and radially outward above the photosphere. Our results suggest that a bright
filament may be formed by an extended tail of a penumbral grain. Such filaments
are optically thick, hotter than the surroundings, and elevated above a darker
background. An upflow in penumbral grains bends horizontally outwards above the
photosphere and gradually cools down due to radiative losses leading to a tail
that gradually darkens. The plasma flow inside the flux tube then becomes
transparent and the tube constitutes a thin elevated flow channel, that can
reproduce the observed features of the Evershed effect. We present also a new
acceleration mechanism for the Evershed flow. It is demonstrated that a local
surplus of gas pressure develops inside the tube as it rises through the
specific (superadiabatic and magnetized) penumbral background. The resulting
gradient of the gas pressure can drive the flow along the tube.
