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Ng, et al.
across a nozzle-substrate distance of ~15 mm. The W =Oh Re 2 (2)
2
e
repeated droplet impacts quickly wet the substrate Oh Re 1.17 = 63 (3)
surface to form a layer of liquid film and transform It is to be noted that the above equation does not
the dynamics to droplet impacts on thin liquid films. provide insight on the magnitude of splashing, but
The outcome of the droplet impact can be classified as rather just qualitative information on whether splashing
(i) deposition, (ii) prompt splash, and (iii) corona splash. would occur. The calculated Oh Re 1.17 value for different
Droplet deposition is characterized by the absence of bio-inks in this study were 97.3 (0 million cells/mL),
splashing (without any break-up) on droplet impact [49,50] . 63.2 (1 million cells/ml), 52.3 (2 million cells/mL),
In contrast, prompt splash releases small droplets during 46.4 (3 million cells/mL), and 23.1 (4 million cells/mL),
the advancement of lamella immediately after impact [50,51] respectively (Figure 4A). The high-speed images
while the intact lamella forms a corona shape (bowl-like of droplet impact just above the substrate surface
structure) ejecting multiple small droplets during corona (0 – 4 million cells/mL) concurred with the above
splash [50,51] . equation; droplet splashing was observed for only
The droplet impact on a dry substrate surface 0 – 1 million cells/mL (Oh Re 1.17 > 63) and droplet
(0 – 4 million cells/mL) will always entrap a small air deposition was observed for 2 – 4 million cells/mL
bubble under its center under atmospheric conditions; (Oh Re 1.17 < 63) (Figure 4B). The increase in cell
our observation was corroborated by a previous study concentration resulted in significantly slower droplet
that highlighted the lubrication pressure in the thin air impact velocity (from 20.20 m/s for 0 million cells/mL
layer becomes strong enough to facilitate deposition to 5.77 m/s for 4 million cells/mL) which helped to
of sub-nanoliter droplets on non-wetted surface . mitigate droplet splashing and improve the printing
[51]
Subsequently, it was observed that the droplet impacts of accuracy.
all cell-laden bio-inks (1 – 4 million cells/mL) resulted in
droplet deposition for droplet impact on wetted substrate 3.4. Influence of droplet impact on printed cell
surface, whereas droplet splashing was observed for viability
0 million cells/mL. Besides being subjected to the shear stress within the
Repeated ejection of droplets on the pre-defined printing nozzle, the droplet impact during the printing
spot quickly wets the substrate surface to form a thin process led to cell deformation, and this droplet
and continuous liquid film and this transforms the deformation process has a significant effect on the
dynamics to droplet impacts on thin liquid films. Hence, viability of printed cells. The Live/Dead cell viability
high-speed images of the droplet impact on pre-wetted assay (green – viable cells, red – dead cells) was used to
substrate surface were captured. Droplet splashing obtain fluorescence images of printed cells on dry well
will occur when the ink properties and the process plates and analyze the influence of droplet impact velocity
parameters exceed a threshold value, which is known as on cell viability during DOD cell printing applications.
the splashing parameter, K [53] . The splashing parameter We estimate the shear stress on the cells during
is related with several dimensionless numbers, such as droplet impact via the droplet spreading model
the Reynolds number, R =ρV D /µ, the Weber number, (Table 3) . This scaling model is based on the balance
[57]
e
0
i
R =ρV D /γ , and the Ohnesorge number, Oh = We Re, between the initial kinetic energy of the droplet,
0.5
2
i
0
LV
e
where D is the initial droplet diameter before impact, V i E ~ ρ D V 2 capillary energy, E ~ γ D and viscous
2
0
3
is the droplet’s impact velocity, and ρ, μ, and γ are the k 0 i γ LV 0
LV
density, viscosity, and surface tension of the droplet’s dissipation, E ~ ∝ V D . Here, D is the initial droplet
2
∝
i
0
0
liquid. There are many variants to this splashing
parameter for different boundary conditions [56] , and the diameter prior to impact, V is the droplet’s impact
i
splashing parameter for this study can be expressed in velocity, and ρ, μ, and γ are the density, viscosity, and
LV
the form of surface tension of the droplet’s liquid. This model has
A∙Oh We = K c (1) been experimentally verified to correctly predict droplet
b
a
where A, a, and b is a constant which is dependent on spreading diameters as a function of impact velocity and
the boundary condition, and K is the splashing parameter, fluid properties for impact Reynolds numbers (Re=ρV i
c
2
which the droplet will splash when K is exceeded. In D /μ) between 40 and 6300 and Weber numbers (We=ρVi
0
c
these variants, the condition for droplet impact on thin D /γ ) between 1.1 and 414 for impacts on both hard and
LV
0
[57]
liquid film is similar to our printing condition, the a and soft, as well as smooth and rough surfaces . This model
b constants were obtained from the best fit-line using predicts that the maximum spreading ratio β = D /D
max
0
max
experimental data to obtain equation (3) : as transcendental equation:
[55]
International Journal of Bioprinting (2022)–Volume 8, Issue 1 31