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International Journal of Bioprinting Swelling–shrinking behavior of hydrogel

uL where c is the concentration of water vapor; D' denotes
R (III) the diffusion coefficient; and J is the diffusive flux vector,
e
which measures the amount of substance that flows
through a unit area during a unit time interval.
where ρ is the density of moist air;u is the flow speed;
μ is the dynamic viscosity of the fluid; and L is the According to the mass conservation equation
characteristic length, which can be estimated according to (Equation V), directly using RH as an input parameter
the proposed FEM model: in the calculation is impractical. Hence, to analyze
geometric variations under a variety of RH conditions,
the relationship between the vapor concentration and RH
L D D 2 (IV) must be clarified :
38
1
2
c
where D and D are the diameters of the printed RH = v (VII)
1
2
filament and the ambient air domain, respectively. Given c sat
the low speed of the moist airflow, the value of R e was
estimated to be lower than 2300. It implies that the flow where the c v and c sat are the concentration and saturation
condition of the ambient air should be defined as laminar concentration of water vapor, respectively. When defining
flow in the FEM model. Furthermore, as the density of RH in the FEM model, a conversion from RH to c v must
fluid exhibits little fluctuation with pressure in the model, be implemented in advance. By inputting the calculated c v
the laminar flow in the ambient air domain was regarded and corresponding c sat into the simulation, the geometric
as incompressible. variation of printed filaments under various ambient RH
conditions can be calculated. In the model, the c v was
2.2.3. Cold source of the plate set to the same value for both the ambient air and the
According to the configuration presented in Figure 1, outlet boundary.
hydrogel filaments are deposited onto a temperature- 2.3. Preparation of hydrogel filaments
controlled plate during the 3D printing of hydrogel for experimental validation
architectures. Hence, the top surface of the plate, To validate the reliability of the calculation results,
represented as a cold source in Figure 2, was defined as a printing trials were conducted using hydrogel filaments.
temperature boundary. Specifically, the initial temperatures F-127, selected for these trials, is a well-acclaimed
of the plate, the ambient air, and the printed filament were medical hydrogel material in regenerative medicine due
all set to room temperature in the FEM model. to its excellent biodegradation properties and outstanding
2.2.4. Water vapor transport at the biocompatibility.
fluid–fluid interface In this study, a 30% (w/v) F-127 solution was prepared
When hydrogel filaments are exposed to ambient air with for the 3D printing experiments. Specifically, the mixture
inappropriate RH levels, moisture exchange between the of 1.5 g F-127 powder (P2443-1KG, Sigma-Aldrich, USA)
hydrogel filaments and the surrounding environment often and 5 mL phosphate-buffered saline (Thermo Fisher
results in swelling or shrinking of the filaments. To account Scientific Inc., USA) was prepared and stored at 4°C for 24
for water vapor transport across the fluid–fluid interface, h. Before each 3D printing, the prepared 30% (w/v) F-127
the transport of diluted species model was utilized in the solution was transferred into syringes and centrifuged for
FEM simulation. To achieve the calculation of the diffusion 10 min at 4°C to remove air bubbles within the hydrogel
and the convection process of water vapor, a widely material. Hydrogel filaments with diameters of 0.2, 0.3,
adopted mass conservation equation, which is associated and 0.4 mm were then extruded using a self-designed
with Fick’s laws of diffusion, was employed: high-precision 3D printing device. A humidity-controlled
37
enclosure was used to maintain a constant ambient RH for
hydrogel filaments during and after the deposition process.
c To evaluate the geometric variation of the printed filaments
Ju
c
0 (V)
t under the RH of 50, 60, 70, 80, and 90%, an electronic
digital microscope (Inskam-316, Aomekie, China) was
employed to capture micrographs of the filament cross-
J D c (VI) sections. Representative geometric variations of hydrogel

Volume 11 Issue 4 (2025) 414 doi: 10.36922/IJB025220222