Multi-material bioprinting is a promising technique that enables the fabrication of complex heterogeneous constructs with tailored mechanical and biological properties for tissue engineering. Recently, the bioprinting process with a helical static mixer has been shown feasible to print fibers from multiple biomaterials. However, much remains undiscovered regarding the mixing of transient streams and the control of composition gradients during the printing process. This study investigates the mixing of biomaterials, aimed at improving the spatial resolution of composition gradients along the fiber longitudinal direction. Computational Fluid Dynamics (CFD) was utilized to investigate the flow and mixing of precursor streams with results used in redesigning the bioprinting head for improved performance. Rheological studies were performed to characterize the flow behaviour of biomaterials; the obtained results were to examine the mixing of biomaterials and the transition time (or time needed between flow rate changes at the inlets and the corresponding change in fiber composition) with the help of CFD simulations. Our results demonstrated that the redesigned bioprinting head was able to completely mix biomaterials and that the transition time could be regulated or reduced by advancing inlet flow rate changes, thereby enhancing the spatial resolution of composition gradients by 17-30% as examined in our case study presented in this paper. Also, it has been illustrated that adjusting the toolpath can further improve resolution in composition gradient printing. Overall, this study reveals the science behind multi-material bioprinting and provide means to improve the design of bioprinting head for improved spatial resolution of composition gradients.