  Supposing the existence of Dark Fluid with a Chaplygin-like equation of state
$p=-B/\rho$ (CDF) as a cosmic background, we obtain a static
spherically-symmetric black hole (BH) solution to the Einstein gravitational
equations. We study the $P-V$ critical behavior of AdS BH surrounded by the CDF
in the extended phase space where the cosmological constant appears as
pressure, and our results show the existence of the Van der Waals like
small/large BH phase transition. Also, it is found that such a BH displays a
first-order low/high-$\Phi$ BH phase transition and admits the same criticality
with van der Waals liquid/gas system in the non-extended phase space, where the
normalization factor $q$ is considered as a thermodynamic variable, while the
cosmological constant being fixed. In both $P-V$ and the newly proposed
$q-\Phi$ phase spaces, we calculate the BH equations of state and then
numerically study the corresponding critical quantities. Moreover, the critical
exponents are derived and the results show the universal class of the scaling
behavior of thermodynamic quantities near criticality. Finally, we study the
shadow thermodynamics of AdS BHs surrounded by the CDF. We find that, there
exists a positive correlation between the shadow radius and the event horizon
radius in our case. By analyzing the temperature and heat capacity curves under
the shadow context, we discover that the shadow radius can replace the event
horizon radius to demonstrate the BH phase transition process, and the changes
of the shadow radius can serve as order parameters for the small/large BH phase
transition, indicating that the shadow radius could give us a glimpse into the
BH phase structure from the observational point of view.
