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International Journal of Bioprinting Fluid mechanics of extrusion bioprinting

Interdigitation of streamlined precursor flows through multi-layer structure in the flow cross section is stabilized by
chaotic advection provides an efficient mixing mechanism crosslinking inside the printing head, preventing diffusion
for creeping flows at extremely low Reynolds numbers. 162,163 from completing the mixing process and achieving a
Therefore, helical mixers have been used by researchers for homogeneous mixture. This approach demonstrated the
mixing precursors inside multi-material heads. 141,164,165 ability to rapidly produce fine microstructures within
Helical mixers divide the streams of biomaterials into printed fibers in a controlled and predictable manner.
sub-streams, distribute them radially, and recombine Utilizing the laminar chaotic flow generated by the static
them to produce a multi-layer structure in the flow cross mixer, they achieved the stratification of different materials
section (interdigitation). A helical static mixing element in 3D printing. They successfully printed well-defined
divides each stream of biomaterial into two sub-streams. multi-layer fibers using 2, 3, 4, 5, and 6 helical mixer
The average layer thickness represents the mixing distance elements with resolution of approximately 500, 250, 125,
(d ) and depends on the number of mixing elements (m) 62.5, and 31.75 μm, respectively. Similarly, Samandari
mix
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and the number of biomaterials (α): et al. utilized a helical mixer-integrated coaxial
microfluidic device to divide alginate and GelMA solutions
d = d/s (XXXIII) streams into sub-streams with desired thicknesses. This
mix
approach allowed for the fabrication of millimeter-sized
where s is the number of layers 162,163 fibers with intricate microscale structures, comprising
successive microfilaments made of alginate and GelMA
s = α2 m–1 (XXXIV) hydrogels, stabilized by UV-crosslinking. The resulting
multiscale fibrous structure exhibited properties that
This demonstrates how helical mixers can shorten facilitated cell spreading and alignment. The studies of
the mixing distance of two biomaterial to d/2 . Puertas Chávez-Madero et al. and Samandari et al. highlight
m
163
168
et al. combined a single-nozzle dual-syringe system with the potential of continuous chaotic printing and static
141
a helical static mixer integrated into an extrusion bioprinter. mixer-based approaches for the precise fabrication of
This system enabled the printing of homogeneous strands complex structures with diverse material compositions
using a reactive hydrogel. The hydrogel precursors were and internal architectures.
extruded simultaneously from separate syringes, and the
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static mixer ensured homogeneous mixing and initiation of Ceballos-González et al. expanded on the multi-
the crosslinking reaction before extrusion. This approach material chaotic bioprinting heads designed by Chávez-
provided the bioprinter with a homogenous mixture of Madero et al. by incorporating additional inlets to
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biomaterials and crosslinker. produce radial and axial micropatterns inside the printed
fibers. Considering the relationship between the number
Static helical mixers have also been successful in the of layers and the number of mixing elements, as well as
bioprinting of constructs with gradient stiffness by mixing the number of axial inlets, they applied more control
stiff and soft cell-containing hydrogels in appropriate over the multi-layer structure of fibers by altering the
ratios. 164–167 Kuzucu et al. used a multi-material head number and position of inlets for different precursors.
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with a helical mixer to print 2D and 3D structures with Figure 13 illustrates their experimental observations and
controlled stiffness. They utilized carboxylated agarose computational simulation results for the multi-layer fiber
hydrogels with different stiffness as precursors. Figure 12
illustrates the 2D- and 3D-printed structures with structures produced with varying numbers of mixing
medium-soft and stiff-soft carboxylated agarose-native elements and inlet compositions. They also employed
agarose blend hydrogels, highlighting the variations in radial inlets in combination of axial ones to gain more
stiffness achieved by changing the flow rate of precursors control over the internal structure of the printed fibers.
during printing. Their results demonstrate the effectiveness By switching between different axial and radial inlets
of static helical mixers in achieving controlled mixing of during the printing process, they effectively controlled the
biomaterials for bioprinting purposes. internal structure of the printed fibers in both axial and
radial directions.
Helical mixers have also been utilized in a novel
technique, known as chaotic printing. The concept of 4.2.2. Multi-material heads with
chaotic printing was introduced by Chávez-Madero microfluidic micromixers
et al. as a method for creating intricate constructs at the Single-nozzle microfluidic multi-material printing heads
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micrometer or even submicrometer scale within printed are used in various bioprinting applications. While
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fibers. They utilized the chaotic flow generated by a helical they lack a dedicated mixing element, the co-flowing
mixer to print multi-material and multi-layer fibers. The streams of bioinks inside microchannels promote some

Volume 10 Issue 6 (2024) 136 doi: 10.36922/ijb.3973