Page 148 - IJB-10-6

International Journal of Bioprinting Fluid mechanics of extrusion bioprinting

approach explores the effect of nozzle geometry while Given the widespread use of helical mixers in
considering specific biomaterial properties, 176–178 and the industrial applications, numerous numerical simulations
other investigates the dynamics of biomaterials for a fixed are available in the literature that study the performance
nozzle geometry. 179–181 Most studies have neglected cell- of these mixers and the improvement of their geometry.
biomaterial interactions and model the bioink as a single- Numerical simulations of mixing two miscible biomaterials
phase non-Newtonian fluid due to the low volume fraction in an extrusion bioprinting head equipped with a helical
of cells in bioinks. 63,182,183 However, several researchers have mixer revealed an improvement in mixing efficiency as the
utilized simulations to study cell deformation during the power-law index of biomaterials increases. 192
bioprinting procedure. 177,184 Computational fluid dynamics (CFD) has been used
Computational fluid dynamics (CFD) simulations to simulate the process forces or pressure work required
have been used to predict the shear stress distribution in for cell-damage predictions based on various cell damage
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chamfered (straight) and tapered (conical) dispensing models. Ning et al. and Han et al. employed CFD to
nozzles, with results indicating a higher shear stress provide information on the pressure drop and stress
level inside chamfered nozzles compared to a tapered distribution in the flow of alginate-based bioinks as they
geometry. 185,186 The higher shear stress can lead to lower are extruded through chamfered dispensing nozzles. They
cell viability when using chamfered nozzles. Most CFD modeled bioinks, including alginate/RSC96 Schwann cells,
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63
studies have focused on the flow through the dispensing alginate/L8 myoblast cells, and alginate/human dermal
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nozzle and have explored the effects of printing pressure, fibroblasts cells, using the power-law non-Newtonian
model in their numerical simulations and analytical
nozzle geometry, and rheological properties of bioinks on calculations. Chirianni et al. used CFD to validate their
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the shear stress exerted on the cells in the bioink. 63,182,183
The distribution of wall shear stress for different nozzle cell-damage model with previous experimental test results.
They modeled bioinks based on alginate-based human
geometries suggests that optimizing nozzle geometry dermal fibroblasts as a Carreau-Yasuda non-Newtonian
involves balancing printing resolution and cell viability. fluid in their numerical simulations. Their numerical
The nozzles featuring a smaller convergence angle tend results for the distribution of shear and extensional stresses
to produce higher wall shear stress (Figure 14A–C), magnitude inside the nozzle are displayed in Figure 14D
potentially leading to adverse effects on cell viability. 187,188 and E. This figure illustrates how extensional stress peaks
Numerical simulations have also been employed in the contraction region of the nozzle.
to model the flow of bioinks inside coaxial dispensing Chávez-Madero et al. and Ceballos-González
162
systems. These simulations have been used to understand et al.169 used CFD simulation and massless particle
the parameters controlling the diameter, velocity, and mass tracking methods to predict the thickness and patterns
of the gel fiber near the nozzle outlet during the extrusion of the internal multi-layer structures generated by a
of hollow strands, 189,190 using biomaterials such as alginate helical mixer. The results were in good agreement with
with a crosslinker. experimental visualization and the theoretical average
In cases where extrusion involves mixing two or thickness of the internal layers (Figure 13B–D).
more biomaterials, and assuming the effect of cells in the Computational fluid dynamics (CFD) simulations play
flow of bioinks is negligible, the mixing of bioinks can a crucial role in microfluidic studies by providing data
be simulated by solving of the components’ transport about the distribution of velocity, pressure, concentrations,
equations (excluding considerations of chemical reactions and shear stress, which can be challenging to measure
and phase changes). 191 experimentally. Several computational simulations have
been conducted by researchers to investigate the effects of
D ρ ( Y )  shear stress on cell viability and explore the flow of various
i
Dt =− ∇⋅ J i (XXXIX) biomaterials inside customized nozzle geometries. 178,193
113
Zaeri et al. studied the flow in a coaxial microfluidic
where bioprinting chip numerically, where CFD was used to
 study the effect of printing parameters on the geometrical
J i =−ρ D im ∇ Y i (XL) outcome of the printed fiber. Their simulation did not
,
consider the deposition of fiber on the printing stage;
and Y is mass fraction of component i; and D is its instead, the structure of the fiber was investigated based on
i
i,m
diffusion coefficient. the flow structure at the nozzle outlet cross-section. They

Volume 10 Issue 6 (2024) 140 doi: 10.36922/ijb.3973