The viscosity versus time graph of a ZnTiO3 sol-gel system can provide valuable insights into its rheological behavior, which is crucial for understanding its processability and applications. However, predicting the exact theoretical behavior of viscosity over time for this specific system may require empirical data or detailed knowledge of the sol-gel synthesis process, as well as the interactions between the solute (ZnTiO3) and solvent (gel).

Typically, the viscosity of a sol-gel system can exhibit complex temporal evolution due to processes such as gelation, aging, and structural rearrangements. Initially, the viscosity may be relatively low as the sol-gel system behaves more like a fluid. However, as gelation occurs, leading to the formation of a three-dimensional network structure, the viscosity typically increases, signifying the transition from a sol to a gel.

The rate and extent of viscosity change over time can be influenced by various factors, including the concentration of precursors, the nature of the solvent and additives, temperature, and pH. Therefore, it's essential to conduct rheological experiments under conditions relevant to the intended application and to analyze the resulting viscosity-time data to understand the underlying mechanisms governing the sol-gel behavior.

To obtain theoretical insights into the viscosity-time relationship of the ZnTiO3 sol-gel system, you may consider consulting existing literature on sol-gel processes, rheology of similar systems, or computational modeling approaches. Additionally, experimental characterization techniques such as dynamic rheology can provide real-time data on viscosity changes, helping to validate theoretical models and refine understanding of the sol-gel system's behavior.