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In this study, we focus on a black hole immersed in a cosmological Chaplygin-like dark fluid (CDF), characterized by the equation of state $p=-B/\rho$ and an additional parameter $q$ influencing the energy density of the fluid. We investigate the geodesic structure, shadow, and optical appearance of such a black hole. Through analysis on the effective potential and the epicyclic frequencies, it is found that the existence of innermost/outermost stable circular orbits for a timelike particle is governed by the CDF parameters. The behaviors of the orbital conserved quantities and Keplerian frequency are also examined. Due to the existence of pseudo-cosmological horizon, the determination of the shadow radius depends significantly on the position of the observer. By placing the static observer at an approximately flat position between the event and pseudo-cosmological horizons, we constrain the CDF parameters using EHT observations. We investigate the effect of CDF on the shadows and optical images of the black hole, surrounded by various profiles of accretions. For the thin disk accretion, the light trajectories are categorized into direct emission, lensing ring, and photon ring based on impact parameters. Due to the existence of outermost stable circular orbits, outer edges could exist in the direct and lensing ring images. The observed brightness is mainly due to direct emission, with a minor contribution from the lensing ring, while the contribution from the photon ring is negligible due to extreme demagnetization. In the case of spherical accretion, we consider both static and infalling accretion models. The images obtained under infalling accretion are slightly darker than those under static accretion, attributed to the Doppler effect. Throughout the study, we analyze the influence of the parameters $B$ and $q$ on the results., Comment: 35 pages, 15 figures. Discussions added

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., Comment: 19 pages, 12 figures. PRD accepted version. arXiv admin note: text overlap with arXiv:2012.13271, arXiv:1407.0011 by other authors