TPMS (Triply-Periodic Minimal Surface) lattices are unique in that they can be modeled by a single equation in 3D space, with surfaces defined as every location within the design boundary where the implicit function equals some isovalue (typically equal to 0). An interesting property of these is that in fluidic applications, TPMS lattices have a very high surface area to pressure drop ratio - meaning, as the flow passes through the lattice, it experiences minimal resistance yet is highly likely to encounter a surface boundary. This is incredibly useful for both particle filtration and heat exchange, and particularly for heat exchangers, these structures can be modified to include multiple interwoven bifurcating fluid domains.
Equations for the three main types of TPMS lattices I work with
Heat Exchangers
Example of a counter-flow heat exchanger modeled in COMSOL. TPMS type: Schwarz, with a 001-111 vector rotation
Z-component velocity field slices in COMSOL for the two counter-flow fluid domains
Unit Cell Geometries
A key focus was generating these structures so that the flow bifurcates, rather than passing directly through the heat exchanger or filter. While there are many more types of TPMS and countless modifications that can be made, these images below represent the ones that both bifurcate and are most likely to be 3D-printable. Rotating the structure’s principal axis (denoted by 001, representing a (0,0,1) normal vector to the XY plane) to other vectors such as (1,1,0) or (1,1,1) allowed for the fluid flow to be passed through the optimal direction for bifurcation.
Here, blue represents a solid feature, and shades of pink represent the fluid domains. The flow is oriented so it passes from top to bottom, and any number of these unit cells can be connected periodically.
Left: Diamond (standard 001 orientation); Right: Gyroid (001-110 rotation)
Left: Diamond (001-111 rotation); Right: Schwarz (001-111 rotation)
Alternate custom TPMS design with two solid and two fluid domains, for very high surface areas at the expense of being more difficult to manufacture
Filter Cartridges
Face masks for COVID often have shortcomings in either their availability, fit to the user’s face, or effectiveness of filtration. A group at Cornell was looking to create 3D-printable custom face masks to improve some of these issues, and they wanted to take inspiration from the bifurcating structures in animal noses to design novel printable filters. Having worked with similar structures in the past, I joined their team and developed a lattice-based filter which can be easily printable using a variety of printing technologies (FDM, SLA, DLS…), which redirects flow through various copper-infused cleaning elements at 50% less pressure drop (the amount of force it takes to breathe through) compared with their other designs.
Below are some images of the cartridge prototypes we printed and tested, using various types of TPMS lattices:
Left: Diamond (standard 001 orientation); Right: Gyroid (001-110 rotation)
Left: Diamond (001-111 rotation); Right: Schwarz (001-111 rotation)
Additional Info
Please contact me if you would like to know more about these and how they were modeled. Or, check out my “TPMS Modeler” repository on GitHub