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International Journal of Bioprinting Nozzle geometry for enhanced cell viability

Figure 3. Schematic representation of the extrusion-based bioprinting process with 365 nm photocuring. During extrusion, the bioink undergoes
extensional and shear stresses, affecting cellular behavior.

where σ is Pr , representing the shear stress in the 2 C  c n d 3 n
s
2
2
capillary after the converging section at a radial position P n 3 tan 1 d 1 (III)
s

0 ≤ r ≤ d /2. Here, L is the capillary length, and ∆P is the
2
pressure drop in the capillary, which can be estimated
using Poiseuille’s law. The residence time of the cells in . d 3
the capillary (t ) is V/Q, where V is the volume of the P tan c 1 d 2 (IV)
e

s
c
c
cylindrical capillary, and Q is the volumetric flow rate. 1
3
In contrast, the damage to cells in the converging where γ˙ is calculated by 4Q/π(d /2) , which is the shear
2
c
section is due to both extensional and shear stresses. rate, and C and n are the consistency index and power-law
The total pressure drop in the converging section can be exponent of the fluid, respectively. A constant viscosity (η)
expressed as: of 0.15 Pa·s, was adopted for this analysis based on literature
values obtained under matching GelMA concentration
and temperature conditions. The flow was approximated
25
P P P c e, (II) as Newtonian, with a flow behavior index (n) of 1. This
c s,
c
assumption is supported by literature data indicating only
weak shear-thinning behavior for GelMA under similar
where P and P are the pressure drops associated with conditions; specifically, fitting of published rheological
c,e
c,s
shear and extensional flows, respectively. According to data yields a flow behavior index of approximately 0.92,
23
Cogswell relations, these components are given by: validating the use of the Newtonian approximation in
24
Volume 11 Issue 4 (2025) 320 doi: 10.36922/IJB025190182