Investigation of thermoplastic melt flow and dimensionless groups in 3D bioplotting

We investigate the key 3D bioplotting processing parameters, including needle diameter and dispensing pressure, on the shear rates, shear stresses, pressure drops, and swell ratios of extruded miscible polycaprolactone (PCL) blends having a range of viscosities. Assuming simple capillary flow, we construct flow curves and we estimate that the shear stresses inside the needle of the bioplotter range from 2500 to 20,000 Pa and the corresponding shear rates from 2 to 25 s⁻¹, depending upon the viscosity of the blend. We further identify relevant dimensionless numbers that reflect the material rheological properties and processing conditions; these include the capillary number (Ca), Bond number (Bo), Weissenberg number (Wi), and elasticity number (El). At most processing conditions Ca > 1, whereas Bo < 1, suggesting that viscous forces dominated surface forces, except for needle diameters below 0.2 mm, where the flow approached micro-fluidic conditions. While Wi was below 1 at all conditions, El increased significantly with decreasing needle diameter. High El numbers at a needle internal diameter of 0.2 mm were associated with extrudate swell ratios above 2. Based on these results, we define ranges of operation in 3D bioplotting, which can serve as guidelines for process design. Even though this work is specific on the particular bioplotting equipment, the methodology described herein can be applied on any type of micro-extrusion equipment.