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Controlling Droplet Impact Velocity and Droplet Volume Improves Cell Viability in Droplet-Based Bioprinting
A

B

Figure 4. (A) Phase diagram of droplet splashing phenomenon computed using the splashing boundary conditions. (B) Representative high-
speed images of ejected droplet hitting the substrate surface at varying cell concentration (0 – 4 million cells/mL) at 5× zoom and the images
are taken at 144,000 fps. Increasing the cell concentration resulted in slower droplet velocity which helps to mitigate droplet splashing when
hitting the pre-wetted surface; scale bar = 250 µm.

ρVD + 12 γ = 3“ β 2 + γ 8 1 Thus, we obtain a scaling for the characteristic shear
2
stress as
i
LV
max
LV
0
β max
b 1  3 µV  β 2 (5)
i
+ 3 ρVD β max (4) τ ~   max
2
52 /
i
c 0 Re  2 bD 
0
where c = 2 is a geometric parameter, Γ= γ
LV
(1-cos θ) and θ is the dynamic contact angle at maximum Substituting this into equation (4), we obtain a
spreading. To estimate characteristic shear stress, we transcendental equation for shear stress,
approximate the shear stress τ based on the ratio of the bD 8  µV  12/
characteristic spreading velocity scale and characteristic ρVD + 12 γ LV = τ 2 0 “ +  3 i 
2
i
0
droplet height, h. We estimate the spreading velocity to µV i τ  2 bD 
0
scale as D /t , where t is the time from impact to  54 /
max max
max
maximum spread, expressed as t =bD max /V i [57] . Here, b γ + 3 b ρVD 0  τ b 2 DD   1 (6)
0
2
max
is the ratio of surface tension of drop liquid to that of LV c i  3µ V  Re
i
water . We estimate h from simple volume conservation, We plot shear stress as a function of impact velocity,
[57]
where we consider the spread droplet as a cylinder with initial droplet diameter, and droplet viscosity (Figure 5).
  3 2 This model predicts that shear stress increases strongly
2
height h and diameter D . We obtain h =   D / D max
.
max   0 with droplet velocity, predicting lower cell viability
3
32 International Journal of Bioprinting (2022)–Volume 8, Issue 1