Table 5.
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 |