Open AccessFlow and hydrodynamic shear stress inside a printing needle during biofabrication
Author(s) -
Sebastian J. Müller,
Elham Mirzahossein,
Emil N. Iftekhar,
Christian Bächer,
Stefan Schrüfer,
Dirk W. Schubert,
Ben Fabry,
Stephan Gekle
Publication year - 2020
Publication title -
plos one
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.99
H-Index - 332
ISSN - 1932-6203
DOI - 10.1371/journal.pone.0236371
Subject(s) - biofabrication , shear thinning , shear rate , nozzle , shear stress , mechanics , materials science , microfluidics , rheology , shear (geology) , rheometer , viscosity , newtonian fluid , composite material , mechanical engineering , physics , nanotechnology , engineering , biomedical engineering , tissue engineering
We present a simple but accurate algorithm to calculate the flow and shear rate profile of shear thinning fluids, as typically used in biofabrication applications, with an arbitrary viscosity-shear rate relationship in a cylindrical nozzle. By interpolating the viscosity with a set of power-law functions, we obtain a mathematically exact piecewise solution to the incompressible Navier-Stokes equation. The algorithm is validated with known solutions for a simplified Carreau-Yasuda fluid, full numerical simulations for a realistic chitosan hydrogel as well as experimental velocity profiles of alginate and chitosan solutions in a microfluidic channel. We implement the algorithm in an easy-to-use Python tool, included as Supplementary Material, to calculate the velocity and shear rate profile during the printing process, depending on the shear thinning behavior of the bioink and printing parameters such as pressure and nozzle size. We confirm that the shear stress varies in an exactly linear fashion, starting from zero at the nozzle center to the maximum shear stress at the wall, independent of the shear thinning properties of the bioink. Finally, we demonstrate how our method can be inverted to obtain rheological bioink parameters in-situ directly before or even during printing from experimentally measured flow rate versus pressure data.