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International Journal of Bioprinting                                 Fluid mechanics of extrusion bioprinting




















                                                                                                Contraction
                                                                                                region


                              A                              B                                C
               Figure 8. Visualizations of some unusual behaviors of viscoelastic fluids. (A) Extrudate swell for
            Figure 8. Visualizations of some unusual behaviors of viscoelastic fluids. (A) Extrudate swell for viscoelastic fluid issuing from a die (nozzle).  Reprinted
                                                                                                     100
            with permission from ref.  Copyright © 2004, John Wiley and Sons. (B) Rod climbing of a viscoelastic fluid over the rotating rod. Adapted from ref.  (C)
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                            100
               viscoelastic fluid issuing from a die (nozzle).  Reprinted with permission from ref.  Copyright
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                                                           101
            Development of secondary flows at contraction flow with low Reynolds numbers (the geometry is similar to that in Figure 3). Reprinted with permission
            from ref.  Copyright 1994, The Society of Rheology.
                 102
               © 2004, John Wiley and Sons. (B) Rod climbing of a viscoelastic fluid over the rotating rod.
                                 102
               Adapted from ref.  (C) Development of secondary flows at contraction flow with low Reynolds
                                                               thinning and viscoelastic behavior. Additionally, the
                                                               biomaterials (listed in Table 4) are natural materials that
               numbers (the geometry is similar to that in Figure 3). Reprinted with permission from ref.
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                                                               can have different compositions depending on their source
               Copyright 1994, The Society of Rheology.        and processing, which affects their rheological behavior.
                                                               It is important to note that the absence of thixotropy as
                                                               a  listed  rheological  characteristic  for  a  biomaterial  in
                                                               Table 4 preclude the possibility of thixotropic behavior;
                                                               such behavior may emerge at certain concentrations or
                                                               compositions. Regarding thixotropy and viscoelastic
                                                               behavior, there is a lack of mathematical model fitted
                                                               to available test results in the literature, except for an
                                                               alginate-based bioink. 112
                                                               4. Extrusion multi-material bioprinting
                                                               Native tissues possess complex structures composed
                                                               of diverse types of materials and cells, with the ECM
                                                               organized delicately to fulfill the specific functions of
                                                               each tissue and organ.  To successfully replicate this
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                                                               complexity in bioprinting, it is necessary to combine
            Figure 9. Schematic diagram of the liquid bridge within a filament   multiple biomaterials and cell types in a single printing
            starching rheometer (FiSER).                       session. Extrusion-based multi-material bioprinting
                                                               methods can fall into two main categories: (i) multi-
                                                               material bioprinting without mixing and (ii) multi-
            studies include rheological test results, only a few have   material bioprinting with mixing. Over the past decade,
            fitted a flow behavior model to their data. Various   various techniques have been developed in both

               Figure 9. Schematic diagram of the liquid bridge within a filament starching rheometer (FiSER).
            models can be fitted to the flow behavior of biomaterials   categories to enhance the outcomes of bioprinting. Multi-
            depending on their concentrations and compositions. The   material  bioprinting  methods  without  mixing  enable

            table indicates that all listed biomaterials exhibit shear-  independent control of the flow of different biomaterials

            Volume 10 Issue 6 (2024)                       131                                doi: 10.36922/ijb.3973



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