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International Journal of Bioprinting Fluid mechanics of extrusion bioprinting

Figure 7. Optimal ranges of dynamic moduli and loss tangent for bioprinting of gelatine-alginate biomaterials. Adapted with permission from ref. 43
Copyright © 2018 IOP Publishing.

determined by integrating the stretching rate over time where η is the viscosity of the solvent in a viscoelastic
s
from the initiation of stretching : solution. The extensional viscosity of a bioink offers a clear
109
understanding of the extensional stress on cells, making it
t  R  a more accurate parameter for predicting cell viability than
i
γ = γ dt’= −2 ln  0  (XXVI) using Equation IV. Extensional rheology of bioink can
e ∫ 0 e   Rt ()   affect the dynamics of gobbling drop and extrudability, as
discussed in Section 2.2.
where R is the initial radius of the liquid bridge.
0
Given the significant role of extensional rheology in the
F behavior of a viscoelastic fluids, especially in extensional
By defining the extensional stress as τ = π R E 2 , the flows, some researchers define the relaxation time of the
109
e
mid
viscoelastic fluid based on the time constant (λ ) for the
e
exponential decay of the liquid bridge midpoint radius.
transient extensional viscosity (η ) can be calculated as 109
E
As aforementioned, bioinks may exhibit all three sub-
τ classes of non-Newtonian rheology. Table 4 presents the
η = 3 η + e (XXVII) rheological characteristics and flow behavior models for
E
s
γ i e some common biomaterials. While most bioprinting
Volume 10 Issue 6 (2024) 130 doi: 10.36922/ijb.3973