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International Journal of Bioprinting                                   Cell viability in printing structured inks










































            Figure 11. Equivalent analysis of symmetric inks considering fluid forces. (A) Maximum shear stress in the walls corresponding to different material
            phases within the nozzles. (B) Corresponding equivalent homogeneous inks with different viscosity when the cell was in different fluid domains of the
            material phases. (C) Average shear stress in the walls corresponding to different fluid domains of the material phases, and average shear stress in the
            material phase interface within the nozzles. (D) Validation of equivalent shear stress within the nozzles using equivalent homogeneous inks.

            inks  were  prepared, with the analysis  results  shown in   For core–shell inks with different core layer radii,
            Figure 11B.                                        the core layer radius was referenced based on the
                                                               structured parameters of vascular-like inks.  Figure S19
               For the ink combination 3.23–3.394, the equivalent
            viscosity was 3.09 Pa·s when cells were in the flow domain   (Supplementary File) presents the qualitative results of
                                                               shear stress, with quantified data shown in Figure 12A and
            of phase 1, and 3.52 Pa·s when cells were in the flow domain   C. Figure 12A illustrates the maximum shear stress at the
            of phase 2.
                                                               wall and at the interface. Taking core–shell inks with a core
               Subsequently, the equivalent average shear stress   layer radius of 2.8 mm as an example, the maximum shear
            was validated. As depicted in  Figure 11C, for the ink   stress at the wall was 1.984e+02 Pa, and at the interface,
            combination 3.23–3.394, the average wall shear stress   it was 9.230e+01 Pa. As the core layer radius varied from
            corresponding  to  material  phase  1  and  material  phase   2.8  mm  to  3.3  mm,  the  shear  stress  at  the  wall  and  the
            2 was 6.630e+0 Pa and 6.867e+0 Pa, respectively. The   interface remained between 1.931e+2 Pa and 2.188e+2 Pa,
            average shear stress at the interface of material phases was   and between 8.124e+1 Pa and 1.088e+2 Pa, respectively.
            3.436e+0 Pa. The corresponding average wall shear stress   For different core layer radii, the maximum shear stress
            of the equivalent homogeneous inks for material phase   at the wall consistently exceeded that at the interface. This
            1 and material phase 2 was 6.096e+0 Pa and 6.941e+0   difference may be attributed to the small variation in the
            Pa, respectively (Figure 11D). This scenario was not   properties of the two-phase materials, which resulted in a
            unique; the average shear stress obtained for other ink   smaller velocity gradient at the interface compared to the
            combinations was also comparable to the corresponding   wall. Cells may be in the fluid domains of the core layer
            structured inks. Specifically, when cells were in the flow   and the shell layer. Given the different cell distributions
            domain corresponding to material phase 1, the average   in the two flow domains of the core layer and the shell
            shear stress obtained was consistently lower than that of   layer, corresponding equivalent homogeneous inks were
            the corresponding structured inks.                 prepared, with the analysis results shown in Figure 12B.

            Volume 10 Issue 4 (2024)                       254                                doi: 10.36922/ijb.2362
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