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The role of heating and cooling in viscous sintering of pairs of spheres and pairs of cylinders

Nickolas D. Polychronopoulos (Polydynamics Inc., Dundas, Canada)
John Vlachopoulos (Department of Chemical Engineering, McMaster University, Hamilton, Canada)

Rapid Prototyping Journal

ISSN: 1355-2546

Article publication date: 3 February 2020

Issue publication date: 14 May 2020




This study aims to develop mathematical models for the determination of the effects of heating or cooling on neck growth in Selective Laser Sintering (SLS) and Fused Filament Fabrication (FFF). Two particle shapes are studied: spherical and cylindrical.


The time required for the coalescence (sintering) process is determined by balancing the work of surface tension forces and viscous dissipation. Heating and cooling effects are studied by incorporating temperature dependence of viscosity in an exponential form. Heating by a laser, convective and/or radiative heat transfer is assumed. It is also assumed that there are no temperature gradients within the coalescing molten polymers (lumped parameter heat transfer analysis).


The models predict faster sintering with heating and slower with cooling, as expected because of the effect of temperature on viscosity. For the isothermal case of pairs of cylinders, the present model predicts significantly longer time for completion of sintering than a previously developed and frequently cited model by Hopper.


An isothermal sintering model for two spheres was reworked for two long cylinders, and for the first time it has been compared to other models available in the literature. The mathematical models are capable of predicting neck growth under non-isothermal conditions for both spheres and cylinders. They are useful in assessment of bonding in selective laser sintering and fused deposition fabrication.



Polychronopoulos, N.D. and Vlachopoulos, J. (2020), "The role of heating and cooling in viscous sintering of pairs of spheres and pairs of cylinders", Rapid Prototyping Journal, Vol. 26 No. 4, pp. 719-726.



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