Investigation of thermoplastic melt flow and dimensionless groups in 3D bioplotting

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We investigate the key 3D bioplotting processing parameters, including needle diameter and dispensing pressure, on the shear rates, shear stresses, pressure drops, and swell ratios of extruded miscible polycaprolactone (PCL) blends having a range of viscosities. Assuming simple capillary flow, we construct flow curves and we estimate that the shear stresses inside the needle of the bioplotter range from 2500 to 20,000 Pa and the corresponding shear rates from 2 to 25 s−1, depending upon the viscosity of the blend. We further identify relevant dimensionless numbers that reflect the material rheological properties and processing conditions; these include the capillary number (Ca), Bond number (Bo), Weissenberg number (Wi), and elasticity number (El). At most processing conditions Ca > 1, whereas Bo < 1, suggesting that viscous forces dominated surface forces, except for needle diameters below 0.2 mm, where the flow approached micro-fluidic conditions. While Wi was below 1 at all conditions, El increased significantly with decreasing needle diameter. High El numbers at a needle internal diameter of 0.2 mm were associated with extrudate swell ratios above 2. Based on these results, we define ranges of operation in 3D bioplotting, which can serve as guidelines for process design. Even though this work is specific on the particular bioplotting equipment, the methodology described herein can be applied on any type of micro-extrusion equipment.

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  1. Bañobre-López M, Piñeiro-Redondo Y, De Santis R, Gloria A, Ambrosio L, Tampieri A, Dediu V, Rivas J (2011) Poly(caprolactone) based magnetic scaffolds for bone tissue engineering. J Appl Phys 109:07B313

  2. Bose S, Ke D, Sahasrabudhe H, Bandyopadhyay A (2018) Additive manufacturing of biomaterials. Prog Mater Sci 93:45–111

  3. Chien R-D, Jong W-R, Chen S-C (2005) Study on rheological behavior of polymer melt flowing through micro-channels considering the wall-slip effect. J Micromech Microeng 15:1389–1396

  4. Coogan TJ, Kazmer DO (2019) In-line rheological monitoring of fused deposition modeling. J Rheol 63:141–155

  5. Cox WP, Merz EH (1958) Correlation of dynamic and steady flow viscosities. J Polym Sci 28:619–622

  6. Dealy JM, Wissbrun KF (1999) Linear viscoelasticity. In: Melt rheology and its role in plastics processing. Springer Netherlands, Dordrecht, pp 42–102

  7. Falsafi A, Mangipudi S, Owen MJ (2007) Surface and interfacial properties. In: Physical properties of polymers handbook. Springer New York, New York, pp 1011–1020

  8. Fedorovich NE, Swennen I, Girones J, Moroni L, Van Blitterswijk CA, Schacht E, Alblas J, Dhert WJA (2009) Evaluation of photocrosslinked lutrol hydrogel for tissue printing applications. Biomacromolecules 10:1689–1696

  9. Findrik Balogová A, Hudák R, Tóth T, Schnitzer M, Feranc J, Bakoš D, Živčák J (2018) Determination of geometrical and viscoelastic properties of PLA/PHB samples made by additive manufacturing for urethral substitution. J Biotechnol 284:123–130

  10. Li JP, De Wijn JR, Van Blitterswijk CA, De Groot K (2006) Porous Ti6Al4V scaffold directly fabricating by rapid prototyping: preparation and in vitro experiment. Biomaterials 27:1223–1235

  11. Mackay ME (2018) The importance of rheological behavior in the additive manufacturing technique material extrusion. J Rheol 62:1549

  12. Mackay ME, Swain ZR, Banbury CR, Phan DD, Edwards DA (2017) The performance of the hot end in a plasticating 3D printer. J Rheol 61:229–236

  13. Maher PS, Keatch RP, Donnelly K, Mackay RE, Paxton JZ (2009) Construction of 3D biological matrices using rapid prototyping technology. Rapid Prototyp J 15:204–210

  14. McIlroy C, Olmsted PD (2017) Deformation of an amorphous polymer during the fused-filament-fabrication method for additive manufacturing. J Rheol 61:379–397

  15. Mehendale SV, Mellor LF, Taylor MA, Loboa EG, Shirwaiker RA (2017) Effects of 3D-bioplotted polycaprolactone scaffold geometry on human adipose-derived stem cell viability and proliferation. Rapid Prototyp J 23:534–542

  16. Mendes R, Fanzio P, Campo-Deaño L, Galindo-Rosales FJ (2019) Microfluidics as a platform for the analysis of 3D printing problems. Materials (Basel) 12(17):2839

  17. Murphy SV, Atala A (2014) 3D bioprinting of tissues and organs. Nat Biotechnol 32:773–785

  18. Noroozi N, Thomson JA, Noroozi N, Schafer LL, Hatzikiriakos SG (2012) Viscoelastic behaviour and flow instabilities of biodegradable poly (ε-caprolactone) polyesters. Rheol Acta 51:179–192

  19. Pastore Carbone MG, Di Maio E, Scherillo G, Mensitieri G, Iannace S (2012) Solubility, mutual diffusivity, specific volume and interfacial tension of molten PCL/CO2 solutions by a fully experimental procedure: effect of pressure and temperature. J Supercrit Fluids 67:131–138

  20. Phan DD, Swain ZR, Mackay ME (2018) Rheological and heat transfer effects in fused filament fabrication. J Rheol 62:1097–1107

  21. Pionteck J (2018) Determination of pressure dependence of polymer phase transitions by pVT analysis. Polymers 10:578

  22. Pipe CJ, McKinley GH (2008) Microfluidic rheometry. Mech Res Commun 36:110–120 3D bioplotter price list (2014): EnvisionTEC Gmbh. pp 5

  23. Ramkumar DHS, Bhattacharya M (1998) Steady shear and dynamic properties of biodegradable polyesters. Polym Eng Sci 38:1426–1435

  24. Rodd LE, Scott TP, Boger DV, Cooper-White JJ, McKinley GH (2005) The inertio-elastic planar entry flow of low-viscosity elastic fluids in micro-fabricated geometries. J Non-Newtonian Fluid Mech 129:1–22

  25. Saengow C, Giacomin AJ, Grizzuti N, Pasquino R (2019) Startup steady shear flow from the Oldroyd 8-constant framework. Phys Fluids 31:063101

  26. Sarker M, Chen XB (2017) Modeling the flow behavior and flow rate of medium viscosity alginate for scaffold fabrication with a three-dimensional bioplotter. J Manuf Sci Eng 139:081002

  27. Sheshadri P, Shirwaiker RA (2015) Characterization of material–process–structure interactions in the 3D bioplotting of polycaprolactone. 3D Print Addit Manuf 2:20–31

  28. Squires TM, Quake SR (2005) Microfluidics: fluid physics at the nanoliter scale. Rev Mod Phys 77:977–1026

  29. Wagner M, Kiapur N, Wiedmann-Al-Ahmad M, Hübner U, Al-Ahmad A, Schön R, Schmelzeisen R, Mülhaupt R, Gellrich NC (2007) Comparative in vitro study of the cell proliferation of ovine and human osteoblast-like cells on conventionally and rapid prototyping produced scaffolds tailored for application as potential bone replacement material. J Biomed Mater Res Part A 83:1154–1164

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Correspondence to Marianna Kontopoulou.

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Gopi, S., Kontopoulou, M. Investigation of thermoplastic melt flow and dimensionless groups in 3D bioplotting. Rheol Acta (2020).

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  • 3D bioplotter
  • Thermoplastics
  • Capillary flow
  • Dimensionless groups