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CFD Assessment of Extrusion Bioprinting Parameters
defined materials with the density and power-law of the simulations. It was assumed that (a) there was
parameters enlisted in Table 2. no slip between the bioink and the wall of the nozzle
boundary condition of the nozzle wall; (b) the flow of
2.3. Simulations bioink is incompressible, meaning its density is constant;
Steady-state simulations were run in ANSYS Fluent and (c) the flow of the fluid is laminar.
®
with each of the bioinks comprising the fluid domain. 3. Results and discussion
The boundary conditions were set to 0-gauge pressure at
the outlet and six different values for inlet pressure were 3.1. Nozzle geometry
chosen: 0.025 MPa, 0.050 MPa, 0.10 MPa, 0.15 MPa,
0.20 MPa, and 0.25 MPa, similar to values found in the In general, as shown in Figure 2, the tapered conical
literature [20-22] . For the printing speed, multiphase volume nozzle has a lower value for maximum wall shear stress
of fluid transient simulations were run for 1000 timesteps (MWSS) than the conical nozzle, except for a dispensing
with step size of 0.01 s, giving a flowtime of 10 s. The pressure equal to 0.025 MPa for a given outlet diameter.
inlet condition was chosen as a constant mass flow rate The cylindrical nozzle with an outlet diameter of 0.5 mm
of 0.0015 kgs and ink6040 was used as the extruded has greater MWSS than the corresponding conical and
−1
bioink. The substrate was set as a moving wall condition tapered conical nozzle for inlet pressure >0.15 MPa.
with the desired translational speed (1 mms , 5 mms , Besides this, the MWSS is lower in the cylindrical than
−1
−1
and 10 mms ) corresponding to the printing speed, the tapered conical and conical nozzles for all other
−1
whereas the nozzle position was stationary. As described combinations. This indicates that the cells would have
by Talluri , the movement of the nozzle is proportional higher survivability in the cylindrical nozzle. However,
[23]
to the movement of the substrate (bottom wall), and on examining the contours of MWSS for the three
acceleration is approximately 0. This means that the nozzles of outlet diameter 0.30 mm at 0.2 MPa presented
simulation with moving substrate is equivalent to the in Figure 3, the region where the most wall shear stress
simulation with moving nozzle. The pressure-implicit is experienced by the cell is confined closer to just the
with splitting of operators (PISO) method was used as outlet region of the tapered conical (Figure 3A) and
pressure-velocity coupling, and either the first- or second- conical nozzle (Figure 3B), which agrees with the
order upwind was used to discretize momentum. PISO findings of Liu et al. and Gómez-Blanco et al. . In
[24]
[8]
was chosen because solution convergence was obtained contrast, for the cylindrical nozzle, the entirety of the
within acceptable computational time without having cylindrical portion of the nozzle experiences a greater
to use even smaller timestep and lower iteration per wall shear stress (Figure 3C). While this particular
timestep. combination was chosen as a representative condition to
There are some inherent assumptions made while demonstrate where the region of MWSS occurred across
using computational simulations to reduce the complexity the three nozzles, similar characteristic contours were

A B

C

Figure 2. Variation of maximum wall shear stress with respect to different nozzle geometry at constant pressures. (A) 0.1 mm. (B) 0.3 mm.
(C) 0.5 mm.

48 International Journal of Bioprinting (2022)–Volume 8, Issue 2