  Multiple experiments on active systems consider oriented active suspensions
on substrates or in chambers confined along one direction. The theories of
polar and apolar phases in such geometries were considered in A. Maitra et al,
arXiv 1901.01069 and A. Maitra et al., PNAS 115, 6934 (2018) respectively.
However, the presence of quenched random disorder due to the substrate cannot
be completely eliminated in many experimental contexts possibly masking the
predictions from those theories. In this paper, I consider the effect of
quenched orientational disorder on the phase behaviour of both polar and apolar
suspensions on substrates. I show that polar suspensions have long-range order
in two dimensions with anomalous number fluctuations, while their apolar
counterparts have only short-range order, albeit with a correlation length that
can increase with activity, and even more violent number fluctuations than
active nematics without quenched disorder. These results should be of value in
interpreting experiments on active suspensions on substrates with random
disorder.
