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. Author manuscript; available in PMC: 2020 Apr 15.
Published in final edited form as: Trends Analyt Chem. 2018 Jul 5;106:37–52. doi: 10.1016/j.trac.2018.06.013

Table 5.

Few important Dimensionless Numbers in fluidics and effect of 3DP on them.

Dimensionless number Details Effect of 3D printing
Reynolds Number Inertial force/Viscous force convective momentum/viscous momentum
Forced Convection
Print finish and surface roughness affects the magnitude of Re drastically. Printing homogeneity must be characterized and accounted for.
Grashof Number (heat) Natural convection buoyancy force/Viscous force
Used to calculate Re for buoyant flow
Ditto as above
Grashof Number (mass) Controls the lengthscale to natural convection boundary layer thickness
Natural Convection
Richardson Number Buoyancy/Flow gradient Ditto as above
Prandtl Number (heat) Momentum/Species diffusivity Used to determine fluid or heat or mass transfer boundary layer thickness Structural print limit imposed by 3DP restricts the extent of diffusivity that can be achieved. 3DP tools with surface finish similar to conventional fluidic tools can only achieve the mixing or mixing-controlled reaction kinetics only by a fraction to that of conventional fluidics
Prandtl-Schmidt Number (mass)
Rayleigh Number (heat) Natural convection/Diffusive heat or mass transport Used to determine the transition to turbulence
Rayleigh Number (mass)
Capillary Number Viscous forces/Interfacial forces Raw material viscosity could impact the measurement of these quantities. Uncured resin trapped within the channels could affect fluid transport phenomenon
Elasticity Number Elastic effects/Inertial effects
Weissenberg Number Viscous forces/Elastic forces