Page 433 - IJB-9-2

International Journal of Bioprinting Shear-thinning and bioprinting parameters

2.4. Domains and boundary conditions 3. Results and discussion

The model considers two domains. The first refers to the Alginate-based hydrogels were prepared with CaCl
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union of the syringe and the nozzle where the biomaterial cross-linking agent with varied alginate concentrations
is located, and the second to the outside of the nozzle in the (Table 1). The samples were light yellowish and transparent
extrusion zone. in appearance. Numerous samples of hydrogels were
The characteristic parameters of the materials were used, and preliminary tests were carried out varying
configured in the selected domains. In that of the syringe the composition and proportions of CaCl and alginate.
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and the nozzle, the corresponding densities and rheological In some cases, the hydrogels did not show significant
parameters were specified, and in the second domain, differences in their rheological behavior. Therefore, for
the conditions of the air. The rheological parameters the benefit of a better representative and computational
were obtained through rheological characterization clarity, the results of the hydrogels that offered the most
tests and a fit to the Newtonian power-law (Equation I), relevant results are shown.
where k and n are the model’s rheological parameters, 3.1. Rheological characterization
representing the flow consistency and flow behavior
indices, respectively. The steady-state flow curves showed the alginate-based
hydrogels to present shear rate dependence and thinning
In addition, the edges of the geometries corresponding behavior characteristic of shear-thinning fluids. All three
to the system input, output, walls, and the initial interface viscosity curves showed similar trends (Figure 2), but the
were defined in the boundary conditions. apparent viscosity increased with increasing proportion of
alginate.
2.5. Meshing
By way of example, Figure 3 shows a plot of shear
A 2D triangular-type mesh was created for the model stress versus shear rate for the 4% alginate sample. One
simulations, opting for adaptive meshing since this type sees that the hydrogels show a markedly shear-thinning
allows for higher resolution results in the extrusion zone evolution conforming to a Newtonian power-law. From
of the biomaterial and coarser meshing for the zones, the corresponding fit, one can determine the parameters,
where no measurable or precision results are required, thus that is, the consistency index, k, and the behavior index,
reducing the simulation’s computational load.
n, that characterize the fluid’s viscosity behavior. These,
2.6. Simulation together with the datum corresponding to the density of
the hydrogels, constitute the values representative of the
Numerous simulations were carried out for the different behavior of the materials used in the simulation.
materials, varying the system’s inlet pressure, which
corresponds to the pressure exerted by the bioprinter on The flow consistency index, k, increased and the flow
the biomaterial. The pressure range used was from 400 kPa behavior index, n, decreased with increasing percentage of
to 1200 kPa, reflecting very different results for the various
biomaterials studied.
These simulations provided such results as the
volumetric fraction of fluid in extrusion. At low pressures,
there occurs detachment of a droplet, contrary to the
case at high pressures. For this reason, the inlet pressure
corresponding to reaching the droplet detachment limit
was evaluated for each biomaterial.

Dispensing head displacement speed is another
bioprinter’s variable that needs to be controlled, since
the faster the movement, the thinner the deposited
line of printing, and vice versa. To this end, once the
pressures are defined and set, the extrusion time with
which the samples result in a similar geometry, that is,
reaching a certain thickness or level, is obtained. It will
thus be possible to determine how rapidly or slowly each
material is extruded, and this can be related to the head’s Figure 2. Viscosity versus shear rate of the 3.5%, 4%, and 5% (w/v)
displacement speed. alginate-based hydrogels, which contain 3.5% CaCl each.
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Volume 9 Issue 2 (2023) 425 https://doi.org/10.18063/ijb.687