Modeling the Flow Behavior and Flow Rate of Medium Viscosity Alginate for Scaffold Fabrication with a Three-Dimensional Bioplotter
3.5 Results and model equation verification
3.5.4 Combined effect of needle diameter and temperature on flow rate
In real applications, various dispensing pressures, needle diameters, and temperatures are used for the biofabrication of alginate scaffolds with rapid prototyping techniques. In this study, two different dispensing pressures (20 and 30 kPa) were maintained to study the flow rate of alginate under the collective influence of various needle diameters (0.2, 0.25, 0.41, and 0.61 mm) and temperatures (25, 35, 45, and 55 °C).
Good agreement between model predictions and experimental data was observed for dispensing pressures of 20 and 30 kPa (Table 3.5). However, model prediction is more accurate at a dispensing pressure of 20 kPa (R2 = 0.99, MAPE = 11.61%) versus 30 kPa (R2 = 0.98, MAPE = 12.35%) (Figs. 3.11 (b) and 3.11 (e)). The residuals demonstrate a random distribution pattern representative of an unbiased predictability of the flow rate model equation (Figs. 3.11 (c) and 3.11 (f)). At the same dispensing temperature and pressure, alginate flow rate increases with increasing needle diameter. At the same needle diameter and dispensing pressure, flow rate increases with temperature. The higher temperatures (35, 45, and 55 °C) and dispensing pressure (30 kPa) cause more deviations between model predictions and measured data compared to the lower temperature (25 °C) and dispensing pressure (20 kPa) (Figs. 3.11 (a) and 3.11 (d)). The deviations between model predictions and experimental results at different needle diameters and operating temperatures could be due to the combined effect of various considerations. For example, wall slip could take place in the cone and plate rheometric arrangement during alginate viscosity measurements [48, 49]. Because the flow behavior model was developed without considering the effect of wall slip in the rheometer, the predicted flow behavior parameters (K, τ0, and n) would introduce error into the flow rate model. Further, the increase of needle diameter and wall shear stress results in reduced slip flow for the shear-thinning (yield pseudoplastic) fluid (alginate), and thus influences the deviations between experimental results and model predictions [48,50]. Errors were also introduced into the flow rate model predictions because surface parameters of the needle (e.g., polarity, electric charge, wettability, and roughness), which affect wall slip [48, 51], were not considered. Consequently, the error in the slip flow model further increases the uncertainty and difficulties in the prediction of total flow rate, as wall slip augments turbulence and instabilities in the fluid flow through the dispensing needle [52].
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Fig. 3.11 Model-predicted versus experimental mass flow rate of alginate (2% w/v) through a tapered needle with varying exit diameters (0.2, 0.25, 0.41, and 0.61mm) at different temperatures (25, 35, 45, and 55 °C) and dispensing pressures of (a) 20 and (d) 30 kPa;
comparison (with diagonal line of equality) of measured and predicted flow rates at dispensing pressures of (b) 20 and (e) 30 kPa; and distribution of residual prediction errors of flow rates at
dispensing pressures of (c) 20 and (f) 30kPa 3.6 Conclusions
The present study developed model equations to predict the flow behavior and flow rate of alginate for 3D bioplotting. Experimental rheological data for alginate (1–4%) at four different temperatures (25, 35, 45, and 55 °C) were presented. Experiments to characterize the flow behavior of alginate suggest that temperature and concentration have a profound effect on the
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consistency index, flow index, and yield stress. The model equations developed to predict flow behavior parameters at any arbitrary alginate concentration and temperature were validated against experimental values. Good agreement with experimental data indicates the ability of the model equations to predict the flow behavior of medium viscosity alginate during scaffold fabrication. Moreover, the flow rate model developed can predict the non-Newtonian flow rate of alginate from a tapered needle with remarkable accuracy and can predict the flow rate of alginate with outstanding precision under the combined effect of various needle diameters and temperatures. In addition, the assumption of the wall slip effect of alginate is reasonable because the flow behavior curve of medium viscosity alginate follows the shear-thinning (yield pseudoplastic) pattern of a Hershel–Bulkley fluid.
80 3.7 References
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