Page 404 - IJB-9-4

International Journal of Bioprinting Impingement shear stress during microvalve-based bioprinting

maximum impingement shear stress was at H = 2.8 mm. To validate the results of numerical simulation and
Phares et al. also reported an analytical relation to our hypothesis that the impingement shear stress has
[32]
calculate the maximum wall shear stress in axisymmetric a detrimental effect on cell survival during microvalve
fully developed steady-state jet impingement as: bioprinting, we conducted a simple experiment: We printed
cell suspension of alginate solution at constant upstream
max. 44 .6 v Re 1 2 H 2 , H 8 (V-a) pressure but at different H. At low upstream pressure (0.6
2
D D bar), when the nozzle was very close to the platform (H <
1.2 mm and D = 300 µm), a significant number of cells
H
2
max. . 070 v Re 1 2 , 8 (V-b) were dead regardless of type (HaCaT and HUVECs). At
D higher upstream pressure (1.0 bar), a significant number of
The above formula shows that the maximum impingement dead cells was observed for H < 2.4 mm for both cell types.
shear stress occurs at H ⁄ D = 8, which matches our Since the nozzle wall shear stress is independent of H, the
results at high upstream pressure. However, it was not cell death at lower H can be attributed to impingement
confirmed at low upstream pressure when a droplet was shear stress. Therefore, depending on upstream pressure,
forming. In another study, Yonemoto and Kunugi used a minimum distance between the nozzle and platform is
[33]
an analytical approach based on an integral method and required to optimize the cell viability during microvalve
energy conservation to characterize the impingement of bioprinting. In a real three-dimensional (3D) bioprinting
a spherical droplet on solid surfaces. They defined two scenario, the biological structure is built layer-by-layer [34,35] .
regions: In capillary regions, the viscous dissipation is We believe that the results presented here are still valid for
negligible. Therefore, during impingement, the kinetic such cases because the viability assessments have been
energy of a droplet converts to adhesion and deformation performed for ten drops of hydrogel printed on top of each
energies. In the viscous region, the kinetic energy of a other.
droplet mainly dissipates through the viscous dissipation. The simulation predicted lower impingement shear
After some mathematical procedures and simplification, stress at a very short distance between nozzle and platform.
they showed that the total viscous dissipation energy However, the viability assessment did not confirm
during droplet impinging for a Newtonian fluid can be significant cell viability impediment at short distances (low
calculated as: H). This discrepancy might be due either to experimental
81 r deviation at short distances between nozzle and platform
E vis. m 2 uQ (VI)
d
64
h
m or to idealized hydrogel properties set in the simulation.
Where u , r , μ, and Q are droplet speed (m/s), droplet
d
m
maximum spreading radius (m), liquid viscosity (Pa·s), 5. Conclusion
and droplet volume (m ), respectively, and h is calculated In this work, we used a numerical simulation model of
3
m
as a function of dimensionless maximum spreading droplet ejection during microvalve-based bioprinting to
diameter during impinging. Since Equation VI is obtained calculate impingement and nozzle wall shear stress. For
based on an integral method, it offers an approximation of bioink, the physical properties of alginate 1.5% w/v were
average energy dissipation by shear and extensional stress used. The numerical results, validated by experimental
through the entire droplet spreading. A simple conclusion evaluations, revealed that the impingement-related
from the above equation is that the dissipation energy (and shear stress can exceed the wall shear stress in the nozzle
consequently the shear and extensional stress) increases in microvalve-based bioprinting. The amplitude of
by droplet velocity and volume. This is consistent with our impingement shear stress depended on nozzle-to-platform
numerical results as we captured higher impingement shear distance. Therefore, this critical issue should be addressed
stress by increasing either nozzle size or upstream pressure. by the adjustment of the distance between the nozzle and
Nevertheless, even if some agreement was observed the building platform to optimize the cell viability.
between our simulation results and the mentioned studies,
the fully developed and steady-state assumptions (in Acknowledgments
deriving Equation V), fully spherical droplet (in deriving
Equation VI), and Newtonian fluid assumption (in both The authors would like to thank Mr. Christoph Schmitz,
equations) are not valid during droplet ejection of cell- Department of Cardiovascular Engineering, RWTH
suspended alginate solution using a solenoid microvalve. Aachen University, for HSC, and Roswitha Davtalab
Additionally, a valuable future prospect would be to and Michael Weber, Department of Dental Materials
evaluate whether the bioink surface tension can be used to and Biomaterials Research, RWTH Aachen University
modulate the impingement shear stress. Hospital, for their technical support.

Volume 9 Issue 4 (2023) 396 https://doi.org/10.18063/ijb.743