Page 226 - IJB-9-4

International Journal of Bioprinting Simulation-based comparative analysis of nozzles for bioprinting

15 kPa that we used, as the inlet pressure. Since lower inlet imperfections, such as fabrication failures or surface finish,
pressure means lower volumetric flow and lower shear of the actual nozzle or conical tip. In particular, the frame
stress, the results presented in the work by Liu et al. are not showing the drop at t = 100% for the experimental test of
directly comparable to ours for the same reasons. the Nozzle shows an extruded strand that is not perfectly
vertical despite that the Nozzle was perfectly positioned.
3.4. Experimental tests This deviation might be caused by a possible fabrication
The experimental test was performed to analyze the failure of the inner geometry of the Nozzle that cannot be
strand during the first drop formation. Since drops are easily observed.
formed at different time for the Cone and Nozzle in the
pneumatic μ-extrusion processes, measurement times Looking at the average errors and the results obtained
[47]
were established at 25, 50, 75, and 100% of the time needed by Liravi et al. , it can be concluded that our simulations
to generate the drop. Exact times are given in Table 1. recreate the geometry of the extruded strand with an
acceptable error. Additionally, Liravi et al. concluded that
[47]
The measurement results as well as the relative error if the external geometry of the extruded bioink is similar
between measurements can be seen in Table 2. to the experimental tests, assuming the errors, the model
All relative errors are similar to the results obtained by can predict the falling drop and the suitable combination
Liravi et al. . Additionally, relative errors from Table 2 of inner parameters. With this in mind, values of pressure,
[47]
show a similar evolution along time for Cone and Nozzle. velocity and shear stress obtained in the simulation would
Specifically, height error increases from 6% to 21% and be similar to the actual values, which are difficult to be
from 3% to 27% for Cone and Nozzle, respectively. The experimentally measured without modifying the actual
width error trend is exactly the opposite one, as error flow and therefore the value itself.
decreases when the time increases. It might be expected According to the experimental errors, our results can
that simplifications assumed for these simulations are the be regarded as an approximation of the real values of
main cause of these errors. a material using a new geometry of the extruder head.

Figure 9 shows the frames and simulation images of the Thus, our simulations can guarantee acceptable and
previous measurement times for both geometries. In the similar bioprinting inner parameters values with less
experimental frames, an initial accumulation of material is computational cost than the required for more precise and
produced both in the Cone and Nozzle, which is provoked complex simulations.
by a rolling up of the bioink when extrusion starts. However, the 2D axis-symmetrical approximation
This real behavior is not simulated because the current might be insufficient to obtain more precise values of these
simplified geometry does not include any manufacturing studied inner parameters. This approximation simplifies
the geometry assuming that the material behavior is
equal in its revolution. Taking this into account, further
Table 1. Measurement times for each geometry in the modifications in the simulations and the rheological data
pneumatic simulations of the bioink might be necessary to reduce the error. Taking

Cone (s) Nozzle (s) this into account, it would be necessary to comparatively
t = 25% 1.715 0.145 study the current simulations and more complex ones.
t = 50% 3.430 0.293 This way we can assure that the error in the simplified
simulations is acceptable and they can be used in future
t = 75% 5.145 0.439 works when modifications in the geometry and/or the
t = 100% 6.860 0.586 material rheological data are requested.

Table 2. Experimental (Exp) and simulation (Sim) average measurements of maximum height (h) and width (w) in millimeters with
the relative error (Err) (%) of the extruded strand in pneumatic simulations

Cone Exp Cone Sim Cone Err Nozzle Exp Nozzle Sim Nozzle Err
h, w (mm) h, w (mm) h, w (%) h, w (mm) h, w (mm) h, w (%)
t = 25% 3.32, 0.67 3.52, 0.60 5.99, 10.53 3.47, 0.87 3.36, 0.72 3.01, 17.26
t = 50% 7.59, 0.64 6.53, 0.62 14.00, 3.33 7.29, 0.82 6.35, 0.74 12.80, 9.62
t = 75% 13.35, 0.66 10.34, 0.65 22.53, 2.67 11.92, 0.81 9.67, 0.73 18.86, 9.87
t = 100% 24.86, 0.70 19.68, 0.68 20.85, 2.29 20.44, 0.79 14.84, 0.72 27.42, 7.32
Average error – – 12.85, 4.70 – – 15.52, 11.02

Volume 9 Issue 4 (2023) 218 https://doi.org/10.18063/ijb.730