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