(108d) Dimensional Analysis in Vat Photopolymerization of Embedded Negative Micron-Scale Features and Strategies for the Fabrication of Microfluidics

Vat photopolymerization (VPP), like most additive manufacturing (AM) technologies, primarily excels at the fabrication of positive features. The creation of embedded negative features is far less developed, albeit necessary for printing microfluidics. For VPP to compete with subtractive manufacturing, the critical question is how small an enclosed negative feature can be produced in the vat process. Only the resin viscosity has been manipulated (reduced) to obtain smaller negative features. However, a phenomenological description of channel clogging by resin dragging and a predictive tool for the VPP of embedded hollow features remain absent. We report an equation to predict the Lowest Printable Characteristic Length (LPCL) of encased channels derived from classical dimensional analysis of the viscous, interfacial, gravitational, capillary, and inertial forces at play as the hollow spaces form in the vat. While dimensionless groups for metal AM are reported, this is the first dimensionless group for VPP. We obtained two dimensionless groups (Π₁ and Π₂), from which an equation was established as a function of resin viscosity (µ), surface tension (g), gravitational field (g), resin-polymer contact angle (cos q), and density (r). The model is built on the properties of six commercial resins and validated against an additional resin to cover a range of LPCL between 300 and 800 nm. The LPCL scales with the density, viscosity, and surface tension (contact angle) with powers following that order. Co-flow droplet generators were printed using these insights to demonstrate the utility of the Π terms in guiding resin formulation for the VPP of negative micron-scale features.

The production of embedded microchannels is still challenging with laser-based vat-photopolymerization (LB-VPP) and liquid-crystal (LC) display vat-photopolymerization (LCD-VPP). Hence, we utilized our insights to determine the lowest printable channel diameter (LPCD) that can be attained with an LCD-VPP printer. We optimized the printing orientation, channel length, and exposure time based on the LPCD for embedded microchannels within a centrifugal disc (CD) microfluidic device. A printing orientation of 90° was confirmed to yield the LPCD overall combined with an exposure time of 22 seconds for a commercial clear resin. After evaluating two additional resins, it was concluded that the effect of printing orientation and channel length is independent of the resin. On the other hand, optimal exposure time changes in response to the resin’s viscosity and polymerization kinetics. We report the first 3D printing of a microfluidic in assembly modules that can be printed at the ideal printing orientation to achieve the true LPCD of the machine in the entire device. A functional CD microfluidic device can be fabricated with cylindrical channels as small as 300-400 µm with LCD-VPP, and this LPCD is closely related to the resin viscosity. Moreover, a complex design consisting of concentrical channels of 2000 µm and 800 µm was successfully printed in the three resins. We anticipate that these observations can be extrapolated to other PAM technologies, for which the LPCD is even smaller.