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Ng, et al.
A Table 3. Summary of relevant splashing threshold.
Splashing Discussion Reference
threshold
K = Oh −0.37 Re This is the first existed [52]
c
splashing threshold model.
However, this model is only
appropriate for droplets on dry
surface. Therefore, it is not
suitable for our experiment.
K = Oh Re 1.25 , This splashing threshold [53]
c
K is 57.7 model is a variant for droplet
c
on wetted rough surface
(average roughness of 78
B μm) and smooth surface
(average roughness of 2.8
μm). However, this variant
does not correlate well with
our experiment as our glass
slide substrate with average
roughness in terms of nm.
K = Oh −0.4 We, This splashing threshold is [54]
c
K is 10396 valid for droplets on wetted
c
surface when the film
thickness is thick enough such
that the substrate roughness
is negligible. However, the
surface roughness of their
substrate is 1 μm.
Figure 5. Theoretical results for droplet spreading model using K = Oh Re 1.17 , This variant of splashing [55]
c
the properties of 4 million cells/mL cell-laden bio-ink. (A) Droplet K is 63 threshold is used for droplets
spreading shear stress as a function of impact velocity and droplet c on thin film. The substrate of
viscosity using 1× PBS solution with 4 million cells/mL with an their experiment has an average
initial droplet diameter of 80 µm. (B) Droplet spreading shear stress roughness of 10 nm. Besides,
as a function of impact velocity and initial droplet diameter for
droplet viscosity of 0.868 mPa.s. (B) For this plot ρ = 1010 kg/m , the author had experimented
3
γ = 63.48 mN/m, b = 0.868, c = 2, θ = 93°. with different liquids with a
Lv
wide range of viscosity and
at higher droplet velocities due to increased droplet surface tension, as opposed
spreading shear stress. to the previous splashing
This agrees with our observations that decreasing threshold variants which is
droplet impact velocity resulted in improved cell viability experimented on a single
(Figure 6A). It was also observed that the decrease in type of liquid. Therefore, this
average cell viability (%) increases exponentially with variant of splashing threshold
model is more suitable for our
increasing droplet impact velocity (Figure 6B). The application.
measured average cell viability (%) from the Live/
Dead cell viability assay showed a reduction of 0.44%
average cell viability for droplet impact velocity of impact velocity (< 5.77 m/s) of low-viscosity cell-laden
5.77 m/s to a reduction of 27.9 % average cell viability droplets is critical in achieving high cell viability of
for droplet impact velocity of 14.07 m/s (Table 4). more than 90 %.
The experimental data from this study showed that the Our model also predicts that shear stress decreases
droplet impact velocity has a significant effect on the with increasing droplet diameter, suggesting that it
average cell viability of the printed sub-nanoliter cell- is prudent to dispense cells using a small number of
laden droplets when the bio-ink viscosity is low (in larger drops rather than a large number of small drops
the order of 1 mPa.s). Hence, controlling the droplet to improve cell viability. Finally, shear stress increases

International Journal of Bioprinting (2022)–Volume 8, Issue 1 33