High-resolution stereolithography: Negative spaces enabled by control of fluid mechanics

Significance Additive manufacturing has the potential to revolutionize conventional microfluidic fabrication processes by enabling three-dimensional (3D) design and production of complex geometries with enhanced functional components in a single manufacturing step. However, current tradeoffs between exposure energy and optical penetration depth of the print material limit resolution in stereolithography-based processes. We have developed, injection continuous liquid interface production (iCLIP) enabling the fabrication of high-resolution 3D microstructures not before possible through the control of fluid mechanics. iCLIP technology empowers the creation of freeform microfluidic devices, offering unparalleled 3D design freedom for design applications ranging from biomedical device engineering, microelectronic fabrication, and advanced separation sciences.


Measuring UV Penetration Depth of Resins
To ascertain the depth to which UV light penetrates a series of resins, a working curve calibration was performed.To identify the penetration depth and critical exposure energy the Beer-Lambert relationship, referenced in Main Text Equation 1, is used: Equation S1:  !=   "  $%&/( !Where n is the number of layers from the dead zone, I0 is the intensity of the UV irradiation at the dead zone, t is the UV exposure time, s is the layer slice thickness of each exposure, and Dp is the penetration depth (1)(2)(3)(4).
The Beer-Lambert relationship can be rearranged to establish the Jacobs' working curve equation (5): Where Cd is the cure depth, E0 is the UV dose energy delivered, and Ec is the critical UV dose energy to cause polymerization at a corresponding cure depth, Cd.Using Jacob's working curve equation, a set of resin dots was subjected to different levels of UV dose energy.Specifically, a thin glass slide was placed on the printer build window.The resin of interest was then placed on the glass slide.After which each resin dot was exposed to a varying UV dose energy.The cured thickness of each resin dot was measured using a Mitutoyo 547-500S Height Gauge (Mitutoyo, IL) (Fig. S2).To determine the corresponding UV penetration depth (Dp) and critical dose energy (Ec), the cured thickness of each resin dot and the respective logarithm of UV dose were plotted and fitted using a linear least-squares solver.From the fit parameters the Dp and Ec of each tested resin were determined (Fig. S2).

UV Light Accumulation Model
The accumulated dosage in an arbitrary part geometry was determined by calculating the total UV dose each individual voxel receives after each exposure and all subsequent exposures.Given any geometry designed in a computer-aided design tool, we sliced the part into png files along the Z-axis using Autodesk Netfabb 2023 with a layer height of 5 µm and an XY resolution of 4.8 µm pixels.Each slice was represented with black and white pixels to represent exposed and unexposed voxels, respectively.The slices were then sequentially imported into a Python script which calculated the accumulated dosage at each voxel based on the Beer-Lambert relation as referenced in Main Text Equation 1 (4, 6, 7): where n is the number of layers from the dead zone, I0 is the intensity of the UV irradiation at the dead zone, t is the UV exposure time, s is the layer slice thickness of each exposure, and Dp is the penetration depth determined by the resin's material properties at the UV wavelength 385 nm.
By using open-source libraries such as OpenCV 2 and NumPy, we created a binary 3D array, A, with a shape of (X, Y, Z) to represent each voxel where the integer 1 represented an exposed voxel, and 0 represented an unexposed voxel.To simplify the calculation without having to iterate over every layer with every subsequent layer, we can create a lower left triangular matrix XD with a shape of (Z, Z): where En is the dose energy n layers away from the dead zone: We then further indexed 2D arrays Axz or Ayz with a shape of (X, Z) and (Y, Z), respectively, to get the accumulated dosage matrix Δn of every voxel in the XZ or YZ planes at a specific build layer n: After calculation of the final dose at each pixel in the X, Y, and Z directions all voxels in designed negative space which exceeded the critical polymerization energy, En > Ec for a specified layer height, were colored blue to represent overcuring and voxels which remained uncured, or a voxel which En < Ec for a specified layer height, remained white.

3D Prints
Main Text Figure 1: The prints identified in Figure 1C were printed using PR-48 resin, KeySplint Hard resin, and Whip Mix Surgical Guide resin.The evaluation of these channels can be found in Figure S4A and S4C, Figure 3B and 3D, and Figure S4B and S4D, respectively.The prints in Figure 1D were printed utilizing KeySplint Hard resin.Main Text Figure 2: The sinuous microstructure was printed using KeySplint Hard resin.Under CLIP conditions (Figure 2A), the injection rate was set to 0 μL/min.In contrast, under iCLIP conditions (Figure 2B), the injection rate of KeySplint Hard resin was set to 5 μL/min.Main Text Figure 3: All microfluidic channels were printed using KeySplint Hard.For CLIP conditions, the injection rate remained at 0 μL/min.Conversely, under iCLIP conditions, the injection rate was set at 1.1 times the minimum turnover number.Main Text Figure 4: All microfluidic channels were printed using Whip Mix Surgical Guide resin.Main Text Figure 5

Derivation of Turnover Number
The iCLIP process requires displacing trapped resin in negative spaces with fresh resin to prevent overcuring.Here we present a derivation to relate the required resin turnover with UV penetration depth of a print resin (5).
In this case, the turnover number can be defined as the volume of negative space within a certain number of layers which must be displaced before a subsequent exposure can occur.Specifically, the turnover number (Tu) can be represented by the following: where z is the vertical layer height required to be flushed and s is the print layer height.Using this relationship, we hypothesize that we need to reach a resin turnover number high enough to flush all resin out of a negative space that has accumulated a dose, E, larger than the critical flush dose, E * .Adapting Beer-Lambert's Law, we are given the expression: where E0 is the exposure energy dose at z=0 and Dp is the UV penetration depth of a resin.Ultimately using this relationship, we define Tu as a function of the UV penetration depth of a resin, layer height, and exposure dose.
: Main Text Figure 5A -5E were printed with KeySplint Hard.The injection rate of Figure 5A was set to 4 μL/min.The injection rate for Figure 5B-5E was set to 2.5 μL/min.Figure 5F was printed with PR-48 resin.The injection rate was set to 2 μL/min.

Fig. S2 .
Fig. S2.Measuring penetration depth.(A) Measuring penetration depth schematic.(B) Working Curve Calibration of resin with Dp 237 µm.(B) Working Curve Calibration of resin with Dp 237µm.(C) Working Curve Calibration of resin with Dp 237 µm.(D) Working Curve Calibration of resin with Dp 210 µm.(E) Working Curve Calibration of resin with Dp 160 µm.(F) Working Curve Calibration of resin with Dp 138 µm.(G)Working Curve Calibration of resin with Dp 101 µm.(H) Working Curve Calibration of resin with Dp 87 µm.(I) Working Curve Calibration of resin with Dp 65 µm.

Fig. S3 .
Fig. S3.UV accumulation energy in microchannel designs.(A) UV accumulation energy model in resin with Dp 101 µm in varying channel geometries.(B) UV accumulation energy model in resin with Dp 101 µm in varying channel diameters.(C) UV accumulation energy model in resin with Dp 65 µm in varying channel diameters.(D) UV accumulation energy model in resin with Dp 237 µm in varying channel diameters.

Fig. S4 .
Fig. S4.Mitigating overcuring in varying microfluidic channel sizes with varying resins.(A) Resulting CLIP and iCLIP prints of varying channel diameters in resin with Dp 65 µm.(B) Resulting CLIP and iCLIP prints of varying channel diameters in resin with Dp 237 µm.(C) Evaluating resolution of varying channel diameters printed with resin Dp 65 µm using the CLIP and iCLIP systems.(D) Evaluating resolution of varying channel diameter printed with resin Dp 237 µm using the CLIP and iCLIP systems.

Figure S5 .
Figure S5.Mitigating overcuring in varying microfluidic channel geometries and sizes.(A) Resulting CLIP and iCLIP prints of varying channel diameters from 50 µm to 200 µm.All scale bars 500 µm.

Fig. S6 .
Fig. S6.Resolution of microfluidic channels printing with resins of varying penetration depths as a function of turnover number.