Made from biomaterials, tissue scaffolds are three-dimensional (3D) constructs with highly interconnected pore networks for facilitating cell growth and flow transport of nutrients and metabolic waste. To fabricate the scaffolds with complex structures, dispensing-based rapid prototyping technique has been employed recently. In such a fabrication process, the flow rate of biomaterial dispensed is of importance since it directly contributes to the pore size and porosity of the scaffold fabricated. However, the modeling of the flow rate has proven to be a challenging task due to its complexity. This paper presents the development of a model for the flow rate in the scaffold fabrication process based on the fundamentals of fluid mechanics. To verify the effectiveness of the developed model, experiments were carried out, in which the chitosan solution (2% w/v) in acetic acid was used for dispensing under different applied pressures ($50kPa$, $100kPa$, $150kPa$, $200kPa$, and $250kPa$) and needle heater temperatures ($25°C$, $35°C$, $50°C$, and $65°C$). The measured flow rates were used to identify the flow behavior of the solution and were compared to the predictions from the developed model to illustrate the model effectiveness. Based on the developed model, simulations were carried out to identify the effects of the needle size and the flow behavior on the flow rate in the scaffold fabrication process. The developed model was also applied to determine the dispensing conditions for fabricating 3D scaffolds from a 50% chitosan-hydroxyapatite colloidal gel. As an example, a scaffold fabricated with a well-controlled internal structure of diameters of $610±43μm$ and pore sizes of $850±75μm$ in the horizontal plane and of $430±50μm$ in the vertical direction is presented in this paper to illustrate the promise of the developed model as applied to the 3D scaffold fabrication.

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