Structures that are periodic on a microscale in three dimensions are abundant in nature, for example, in the cellular arrays that make up living tissue. Such structures can also be engineered, appearing in smart materials1,2,3,4, photonic crystals5, chemical reactors6, and medical7 and biomimetic8 technologies. Here we report that fluid–fluid interfacial energy drives three-dimensional (3D) structure emergence in a micropillar scaffold. This finding offers a rapid and scalable way of transforming a simple pillar scaffold into an intricate 3D structure that is periodic on a microscale, comprising a solid microscaffold, a dispersed fluid and a continuous fluid. Structures generated with this technique exhibit a set of unique features, including a stationary internal liquid–liquid interface. Using this approach, we create structures with an internal liquid surface in a regime of interest for liquid–liquid catalysis. We also synthesize soft composites in solid, liquid and gas combinations that have previously not been shown, including actuator materials with temperature-tunable microscale pores. We further demonstrate the potential of this method for constructing 3D materials that mimic tissue with an unprecedented level of control, and for microencapsulating human cells at densities that address an unresolved challenge in cell therapy.
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The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request. Source data are provided with this paper.
The code for the simulation study is available from the corresponding author upon reasonable request.
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E.I. was funded through the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 675412. H.Y. was funded through the Grant in Aid for JSPS Research Fellows (grant no. JP16J06211), the Keio University Research Grant for Young Researcher’s Program, Keio University Doctorate Student Grant-in-Aid Program and Grant for Basic Science Research Projects from The Sumitomo Foundation. X.W. was funded through the Swedish Childhood Cancer Foundation (grant no. MT2017-0024). A.H. and P.N. were funded through the Wallenberg Academy Fellows Program (grant no. KAW 2015.0178). J.S. and S. Bagheri were funded through the Knut and Alice Wallenberg Foundation (grant no. KAW 2016.0255). We thank Mercene Labs for their donation of the OSTE precursor. We thank K. Okumura, Ochanomizu University for providing a place for experiments. We thank Y. Hirata, The University of Tokyo, K. Kasahara and H. Onoe, Keio University for supporting confocal microscopy.
The authors declare no competing interests
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Extended Data Fig. 1 Schematic illustration of scaffolds S, S’ and S’’ and the polygon necks in their unit lattice cells.
Schematic perspective views of 3×3×3 unit lattice cells of scaffold geometries S (A), S’ (B), S’’ (C). (D) Close-up of a square cuboid unit lattice cell of scaffold S, indicated with dashed lines, containing micropillars that form polygons RP and RS, indicated with red lines. One Schwartz P minimal surface, bounded by a skewed rhomb RS, is illustrated by red shading. The white dashed lines indicate the geodesics on the Schwartz surface, and s is the saddle point at their intersection. (E) Close-up of a square cuboid unit lattice cell of scaffold S’’, indicated with dashed lines, containing micropillars that form polygons RP, SQ and T, indicated with red lines. One triangular surface, bounded by T, is illustrated by red shading.
Blue surface is the interface between two liquids. (A) Diamond particle emerged. (Parameters: μ2 /μ1 = 1.2, cos(θ) = −0.37, Ca = 0.0068). (B) Spherical particle emerged. (Parameters: μ2 /μ1 = 1.2, cos(θ) = −0.62, Ca = 0.0068). (C) Only secondary fluid retained. (Parameters: μ2 /μ1 = 1.2, cos(θ) = −0.69, Ca = 0.0023).
Extended Data Fig. 3 Triple-phase ordered composites of gas, liquid, and solid microparticles in a gas, liquid, or solid continuous matrix inside a micropillar scaffold.
Scale bars are 1 mm.
Photographs of released blue-dyed water with an average radius of 204 ± 20 μm (sd, n=33) (A) and alginate particles with the length and the width of the gel particles as 755 ± 55 μm and 565 ± 65 μm (sd, n=50), respectively (B) and (C,D) their respective size distribution. The scale bars of (A) and (B) are 1500 µm and 500 µm, respectively.
(A) Design of photomask. (B) A device for electrical measurement. (C) Procedure for DIB measurement. i) Stacking of particle arrays and arrangement of Ag/AgCl electrodes. ii) Stacked arrays of particles. iii) A photograph showing inserted electrodes. iv) Focused-on three particles in contact. v) Expected droplet interface bilayers. (D) Procedure for measurement of DIBs in series. i) Stacking of particle arrays and arrangement of Ag/AgCl electrodes. ii) Stacked arrays of particles. iii) A photograph showing 5 connected particles. iv) Focused-on three particles in contact. (E) & (F) Measured time course of current and histogram of calculated conductance for a network in (C) and (D). t0 is time when the first step and largest step was observed, respectively.
(A) Printing red and blue dye solution pattern into particles in an array by directly getting them into contact with a pillar array. (B) Three layers of particle arrays with differently injected samples. (C) Schematic images showing stacked two layers of a particle array and morphology of 5 contacting particles.
Supplementary Materials, methods and experimental details, Text, Figs. 1–8, Tables 1–8 and captions for Supplementary Videos 1–5.
Top-view video of the fluid–fluid interfacial energy driven 3D structure emergence in a microscaffold (FLUID3EAMS), forming a droplet array with 1 mm periodicity of alginate-gel precursor solution of glycerol (blue dyed) in mineral oil with 1 mg ml−1 Span 80 (transparent).
Side-view video of the fluid–fluid interfacial energy driven 3D structure emergence in a microscaffold (FLUID3EAMS), forming a 3D droplet array with 1 mm lateral periodicity of 50% aqueous solution of glycerol (blue dyed) in mineral oil with 1 mg ml−1 Span 80 (transparent).
Animation videos for the fluid–fluid interfacial energy driven 3D structure emergence in a microscaffold (FLUID3EAMS) under three different fluidic conditions: 1, diamond-shaped particle is created (parameters: μ2/μ1 = 1.2, cos(θ) = −0.37, Ca = 0.0068); 2, spherical particle (parameters: μ2/μ1 = 1.2, cos(θ) = −0.62, Ca = 0.0068); 3, only secondary fluid retained (parameters: μ2/μ1 = 1.2, cos(θ) = −0.69, Ca = 0.0023). Blue surface in the video is the interface between primary and secondary liquid.
Perspective-view video of droplets release by lateral flow diagonal to the lattice of the scaffold.
Top-view video of printing pattern of colored dye solutions into a droplet array by directly getting droplets into contact with a pillar in which a tiny amount of dye solution is adhered.
Numerical data of experiments and simulations in 3D plot.
Numerical data obtained from electrical measurements for Fig. 3b, top.
Numerical data obtained from dimension measurements for Extended Data Figs. 4c,d.
Numerical data obtained from electrical measurements for Extended Data Fig. 5e.
Numerical data obtained from electrical measurements for Extended Data Fig. 5f.
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Yasuga, H., Iseri, E., Wei, X. et al. Fluid interfacial energy drives the emergence of three-dimensional periodic structures in micropillar scaffolds. Nat. Phys. 17, 794–800 (2021). https://doi.org/10.1038/s41567-021-01204-4
Nature Physics (2021)