  We discuss the flow field and propulsion velocity of active droplets, which
are driven by body forces residing on a rigid gel. The latter is modelled as a
porous medium which gives rise to permeation forces. In the simplest model, the
Brinkman equation, the porous medium is characterised by a single length scale
$\ell$ --the square root of the permeability. We compute the flow fields inside
and outside of the droplet as well as the energy dissipation as a function of
$\ell$. We furthermore show that there are optimal gel fractions, giving rise
to maximal linear and rotational velocities. In the limit $\ell\to\infty$,
corresponding to a very dilute gel, we recover Stokes flow. The opposite limit,
$\ell\to 0$, corresponding to a space filling gel, is singular and not
equivalent to Darcy's equation, which cannot account for self-propulsion.
