In this paper, an engineered slow-light photonic crystal waveguide (PCW) has been designed and analyzed to serve as a high-sensitivity liquid sensing device at mid-infrared wavelengths of approximately \(3.8 ~\mu m\) . In particular, effort is made to engineer the structural parameters to reach a high group index ( \(n_{g} = 190\) ) with a large bandwidth, which can enhance the interaction between the guided modes and the analyzed sample. To determine the performance of the sensor, the sensitivity of this specific engineered slow-light PCW was estimated by calculating the shift in the upper band edge of the output transmission spectrum. The results showed that the sensitivity of a designed slow-light PCW followed by modifications in the structure parameter yielded a 265 nm shift in the wavelength position of the upper band edge, indicating a sensitivity of more than 600 nm per refractive index unit (RIU). These results show a route towards realizing high-sensitivity mid-infrared liquid sensors for integrated photonics, and prompt further research into the rich physics of such structures.