Flow and hydrodynamic shear stress inside a printing needle during biofabrication
Open Access
- 24 July 2020
- journal article
- research article
- Published by Public Library of Science (PLoS) in PLOS ONE
- Vol. 15 (7), e0236371
- https://doi.org/10.1371/journal.pone.0236371
Abstract
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.Funding Information
- National Institutes of Health (HL120839)
- Deutsche Forschungsgemeinschaft (326998133)
This publication has 36 references indexed in Scilit:
- 25th Anniversary Article: Engineering Hydrogels for BiofabricationAdvanced Materials, 2013
- Lattice Boltzmann simulations on GPUs with ESPResSoThe European Physical Journal Special Topics, 2012
- A Simplified Method for Calculating Heat Transfer Coefficients and Friction Factors in Laminar Pipe Flow of Non-Newtonian FluidsJournal of Heat Transfer, 2012
- Lattice Boltzmann models for non-Newtonian flowsIMA Journal of Applied Mathematics, 2011
- Characterization of the flow behavior of alginate/hydroxyapatite mixtures for tissue scaffold fabricationBiofabrication, 2009
- Characterization of cell viability during bioprinting processesBiotechnology Journal, 2009
- ESPResSo—an extensible simulation package for research on soft matter systemsComputer Physics Communications, 2006
- Investigations of cell immobilization in alginate: rheological and electrostatic extrusion studiesJournal of Chemical Technology & Biotechnology, 2006
- On the reproducibility of the rheology of shear-thinning liquidsJournal of Non-Newtonian Fluid Mechanics, 2001
- Ueber die rechnerische Darstellung des Strukturgebietes der ViskositätColloid and Polymer Science, 1929