The quality of graphene sheets significantly depends on the degree of oxidation of graphite and the methods used for synthesis. Therefore, selecting an eco-friendly and cost-effective process is an important step in order to increase the oxidation level. The latest studies show that Taylor-Couette reactors are one of the best options to improve the oxidation level of graphite. Graphene suspensions show shear-thinning behavior, and the emergent flow structures in TC flows significantly influence the oxidation degree. In this study, we investigated the flow patterns of shear-thinning fluids in a TC reactor. The effect of radius ratio, power-law index and the rotating direction of the cylinders on the flow patterns and their critical values is studied experimentally in a Taylor-Couette flow that occurred between concentric cylinders. The Reynolds numbers defined with the wall shear viscosities (Re-i and Re-o) are used for evaluating the critical conditions of various flow structures. The results demonstrate that fluid properties and radius ratio may have significant destabilization effects in forming non-axisymmetric flow patterns and change their critical values. The characteristics of various flow regimes are altered substantially with increasing inner cylinder speed. A strong influence of the rotation direction of the outer cylinder on flow structures and their critical Reynolds numbers has also been revealed in this study. The obtained results also provide a deeper understanding of fluid-suspension interactions in TC reactors. These new findings will help in designing and developing more efficient TC reactors to be used in synthesizing high-quality graphene products.