  We study the binary phase separation in active model B, on a two-dimensional
substrate with inhomogeneous activity. Activity is introduced with a maximum
value at the center of the box and spread as a Bivariate-Gaussian distribution
as we move away from the center. The system is studied for three different
intensities of the distribution. Towards the boundary of the box, activity is
zero or the model is similar to the passive model B. We start from the random
homogeneous distribution of density of particles, the system evolves towards a
structured distribution of density. With time, density starts to phase separate
with maximum density at the center of the box and decreases as we move away
from the center of the box. The width of the density profile at the center
increases as a power law with respect to time and reaches a maximum at a late
time. The power-law exponent increases with an increase in the intensity of the
activity. Hence our result shows the response of density in an active binary
system with respect to the patterned substrate. It can be used to design
devices useful for the trapping and segregation of active particles.
