  We use active Brownian model to study effective pressure produced by active
fluids on a fixed permeable inclusion whose interior and exterior regions are
characterized by different particle motilities. We consider both rectangular
and disklike inclusions and investigate the role of mismatching
interior/exterior motility in the osmotic-like (effective) pressure which is
exerted by active particles on the enclosing membrane of the inclusions. We
find two different traits in the regimes of small and large motility strengths.
In the former case, active pressure is sensitive to initial conditions. Given
an initial condition where active particles are homogeneously distributed in
the environment, active pressure is found to be higher in the region with
higher motility. By contrast, in the regime of strong motility, active pressure
is nonsensitive to initial conditions and is found to be higher in the region
with lower motility. This difference arises from the ability of active
particles to go through the membrane enclosure. In the weak motility regime,
active particles are unable to permeate through the membrane, maintaining the
same concentration inside and outside the inclusion as established by initial
conditions; hence, expectedly, active pressure is higher in the region of
higher motility strength. In the strong motility regime, active particles
accumulate preferentially in the region of lower motility strength where they
produce a respectively higher active pressure.

Soft Condensed Matter;Statistical Mechanics;Biological Physics;Computational Physics