Page 268 - IJB-10-1

International Journal of Bioprinting Permeability of NiTi gyroid scaffolds

Electric, USA). A voxel size of 12.1 μm was achieved during R 2
0
2
r
the analysis indicating the high resolution of the method. The K 2ln r 1 P (IV)
f
f
reconstruction and segmentation of CT data were performed 4 0 P t
f
using VG Studio Max (Volume Graphics, USA). Geometry where u is the velocity of fluid [m/s], K is the permeability
integrity assessment and pore measurements were done with coefficient of fluid [mm ], P is pressure [Pa], ∇ is del
2
the built-in algorithms in VG software. operator, ε is the porosity of a specimen, μ is the dynamic
2.3. Experimental in-plane permeability viscosity of the working fluid [Pa.s], Δp = P - P is set
0
f
measurements pressure, r = R /R , R is an inlet radius, R is a front flow
f
0
f
f
0
To measure the permeability tensor, gyroid samples were position (matches with circle diameter, obtained from the
printed in the form of a disk with a diameter of 90 mm, a experiment for selected time), t is the time of observation.
height of 3 unit cells, and a hole for an inlet, as shown in Due to the quasi-isotropy of the porous structure, ellipse
Figure 1a. NiTi disks were placed into the transparent case recognition was conducted as circle recognition, with
to collect the oil from the outlet. For the manufacturing of the results fitted by Equation IV for isotropic flow front
the transparent case, digital light processing (DLP) using propagation.
Sonic Mini 8K (Phrozen, Taiwan) was employed. White 2.4. Flow characteristics analysis by CFD
transparent polymer (HARZ Labs, Russia) with 400 nm Fluid flow modeling was performed to analyze the mass-
working wavelength was used. Ultraviolet exposure time transport properties of the gyroid structures. The Navier–
and layer thickness were set to 1.8 s and 20 μm, respectively. Strokes equation (Equation V) and conservation of mass
The prepared sample for the experiment is shown in equation for incompressible fluid (I) were considered for
Figure 1b. An in-house-built setup for radial injection fluid flow simulation as:
was used for the in-plane permeability measurements,
as demonstrated in Figure 1c with main elements u u. u P u f (V)
2
designation. Silicone oil (Xiameter PMX-200) with t
specified viscosity of 114.6 mPa·s at room temperature of where ρ is the density of fluid [kg/m ], and f is body force
3
23°C was used as a working fluid. The pressure difference [N] (in our case, f=0).
was created by the pump under the control of a precise
electronic valve and a pressure gauge. The evolution of the Water was selected as a working fluid for the
fluid front during the impregnation of samples by the oil flow modeling. 17,18 The physical properties of water
3
-4
was recorded by the high-speed cameras. A representative (ρ = 997 kg/m ; μ = 8.899 × 10 Pa·s at the temperature
image from the video sequence is shown in Figure 1d. of 25°C) were assigned to the fluid domain for analysis.
The recorded propagation of the fluid front was processed Mass-transport is characterized in terms of pressure
with LabView software (Ver. 15.0.1, National Instruments, distribution, velocity distribution contour plots, and
2
USA). As a result, an ellipsoidal shape was recognized. permeability. Permeability is denoted by K [m ] and
All set-up elements were synchronized using Automated determined based on Darcy’s law in form (Equation VI).
Permeability Measurement System (Vitec, Russia) based mL
µ
on the NI cDAQ-9174 module (National Instruments, K =− ρ∆ (VI)
AP
USA). Three samples were manufactured and processed
by the described protocol for each combination of gyroid where m˙ is the mass flow rate [kg/s], L is length [m], A is
2
structure parameters (Table 1). cross-sectional area [m ], ), and ∆P is pressure difference [Pa].
According to the conservation of mass equation Each gyroid model for the fluid flow analysis consisted
for incompressible fluid (Equation I), Darcy’s equation of 27 RVEs with 3 RVEs in x, y, and z directions,
(Equation II), and continuity equation in the polar respectively. Each of the repeating 9 RVEs in a gyroid
coordinate system (Equation III), the permeability model was designed based on the chosen design parameters
coefficient can be expressed by Equation IV as follows: 39 of wall thickness and unit cell size; at the next step, the
fluid domain was obtained by the Boolean subtraction
incompressible

∇u 0 (I) operation of each variation. Next, the 3D models of gyroid
fluid domains were imported into MATLAB for mesh
Kp reconstruction. Afterward, 3D models were transferred
u (II)
into ICEM CFD (ANSYS) to add finite volume mesh with
isotropic 1 ∂  ∂  tetrahedral elements. The fluid flow was modeled on thus
p
p  r  (III) obtained finite volume mesh to provide the mass-transport
r
rr ∂  characterization and permeability calculation. Two
∂ 
∇
Volume 10 Issue 1 (2024) 260 https://doi.org/10.36922/ijb.0119