Polymers have been successfully deployed in the oil&gas industry in various field implementations, including mobility control in waterflood, flow divergence, and well conformance control. However, lab and field applications of polymer injections often encounter polymer-induced formation damage related to pore-throat clogging from polymer entrapments, leading to permeability reduction. This phenomenon manifests as a loss of injectivity, which can diminish the recovery performance. The first principles of polymer interaction with porous rocks are poorly understood. In this work, we use microfluidics to assess formation damage induced by polymer flood. Microfluidic techniques offer convenient tools to observe polymer flow behavior and transport mechanisms through porous media. The microfluidic chips were designed to mimic the pore-size distribution of oil-bearing conventional reservoir rocks, with pore-throats ranging from 1 to 10 µm. The proposed fabrication techniques enabled us to transfer the design onto a silicon wafer substrate, through photolithography. The constructed microfluidic chip, conceptually known as "Reservoir-on-a-Chip", served as a two-dimensional flow proxy. With this technique, we overcome the inherent complexity of the three-dimensional aspects of porous rocks to study the transport mechanisms occurring at the pore-scale. We performed various experiments to assess the mechanisms of polymer-rock interaction. The polymer flow behavior was compared to that of the water-flood baseline. Our observations showed that prolonged injection of polymer solutions could clog pore-throats of sizes larger than the measured mean polymer-coil size, which is consistent with lab and field observations. This finding highlights a major limitation in some polymer screening workflows in the industry that suggest selecting the candidate polymers based solely on their molecular size and the size distribution of the rock pore-throats. This work emphasizes the need for careful core-flood experiments to assess polymer entrapment mechanisms and their implication on short- and long-term injectivity.