Page 200 - IJB-10-2

International Journal of Bioprinting Optimizing inkjet bioprinting

be that when the surface tension is insufficient to maintain reported. The cell was modeled as a viscoelastic fluid
85
the integrity of the droplet or lamella, elastic forces pull the inside a simple Newtonian droplet impacting a pool of
attached fingers and droplets back to the main body of the target simple Newtonian liquid. Droplet impact was
lamella, preventing droplet ejection and inhibiting prompt categorized into four stages. In the first stage, the droplet
splash phenomena. A study investigated the influence of dynamics are mainly controlled by inertia effects. In this
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inert PVP-based bio-inks for cell printing; the experimental stage, the droplet touches the target liquid and forms a
results indicated that an increase in the viscosity of the liquid neck at the interface, which spreads laterally due
bio-ink facilitated the deposition of droplets onto a wetted to surface tension forces. This slows down the droplet
substrate surface without causing splashing. This, in turn, considerably. The deceleration of the fluid at the former
greatly enhanced the precision of the primary droplet bottom of the droplet, combined with the capillary forces
80
deposition. Further analysis revealed that cell-laden bio- at the top of the droplet stretch the cell into an ellipsoid
inks with higher viscosity demonstrated higher measured shape, with the major axis parallel to the former target
average cell viability. This can be attributed to the presence fluid–gas interface. The characteristic time scale for
of polymer within the printed droplets, which provided this stage is d/2u. For the second stage, the stress and
cushioning effect during droplet impact on the substrate, deformation of the cell are governed by interfacial flow.
dissipating more energy. Consequently, this improvement in The droplet penetrates deeper into the target liquid and
energy dissipation enhanced the average cell viability, even decelerates further. The interfacial force at the upper
when subjected to higher droplet impact velocities, and portion of the droplet increases the pressure in the
maintained the proliferation potential of the printed cells. surrounding liquid, driving the liquid droplet downward
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to form a small crater similar to the simple (empty) droplet
5.2. Cell-laden droplet impact on media impact into a target fluid described above. During this
Typical bio-inks have low cell loading (φ < 0.01) and period, the von Mises stress in the cell increases the most,
therefore exhibit droplet impact behavior similar to that
of simple Newtonian fluids described above. At higher peaks, and then declines. The stress scales as / d c ,
c
cell loading (e.g., >10 cells/mL for 20 µm diameter cells, where µ is the cell’s shear modulus (in the order of 10
7
c
(φ > 0.04), the bio-ink exhibits shear-thinning properties, kPa for mammalian cells), and d is the diameter of the
c
and the drop impact behavior is still qualitatively similar cell. For a cell of 15 µm diameter, and a solution with a
to a Newtonian fluid with a corresponding equivalent surface tension of 50 mN/m, this gives a stress of order
viscosity. 75,81 The maximum spreading diameter of a 7 kPa. This stage lasts for order d / 8 . For a typical
3
shear-thinning fluid after impact was well predicted by inkjet aqueous droplet of 30 µm diameter, this stage lasts
the models for simple Newtonian fluids using a viscosity for order 8 µs. This condition is near the threshold for
given by the average of the infinite shear viscosity and survivability for mammalian cells, and therefore, most cell
the zero-shear viscosity. The transition between droplet damage likely occurs during this stage. Substituting this
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spreading and splashing for neutrally buoyant particles scaling into p = k(t - t ) t (Equation VII) and assuming
a b
s
on a hydrophilic surface is dependent on both Reynolds t >> t and k = 1, a = -1, b = - 0.5, the probability of cell
c
number and Weber number, and particle loading. survival at this stage scales as:
c
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Splashing is undesirable as it decreases cell placement
accuracy. For low particle loading, droplet spreading
12/
occurs for We Re < 350 and splashing occurs above d 8 14/
1/4
1/2
c
p  3 (VIII)
s
Vd Vd c d
2
this threshold. Here, Re = and We = ,
In the third stage, the interfacial forces cause the crater to
and ρ and η are the fluid density and viscosity, V is its close, and the cell undergoes damped spheroid oscillations.
characteristic velocity, d is the characteristic length scale,
3
typically the diameter of the jet, nozzle, or droplet, and γ is This stage lasts for order d / 8 , and the cell experiences
the surface tension. This threshold decreases to ~150, for a shear stress of less than order d / during this
2
particle loading between 0.1 and 0.5. For high cell loading time. The final stage is governed by the interaction between
c
c
(φ ~ 0.5), cells spread uniformly into a disk left behind on viscous dissipation and interfacial tension. Here, the cell
the droplet, on hydrophobic surfaces.
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further relaxes toward its resting shape, and the stress on
Droplet impact can have significant influence on cell the cell is significantly less than in the other stages. This
viability. A numerical model for single-cell dispensing stage lasts on the order of the viscocapillary timescale,
and associated stresses on the cell within a droplet was ud/σ. It is worth noting that a study has demonstrated that
Volume 10 Issue 2 (2024) 192 doi: 10.36922/ijb.2135