Michael
Kessler
^{a},
Hervé
Elettro
^{b},
Isabelle
Heimgartner
^{a},
Soujanya
Madasu
^{a},
Kenneth A.
Brakke
^{c},
François
Gallaire
^{b} and
Esther
Amstad
*^{a}
^{a}Soft Materials Laboratory, Institute of Materials, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland. E-mail: esther.amstad@epfl.ch
^{b}Laboratory of Fluid Mechanics and Instabilities, Institute of Mechanical Engineering, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
^{c}Mathematics Department, Susquehanna University, Selinsgrove, PA 17870, USA

Received
7th July 2020
, Accepted 27th October 2020

First published on 28th October 2020

Many natural materials display locally varying compositions that impart unique mechanical properties to them which are still unmatched by manmade counterparts. Synthetic materials often possess structures that are well-defined on the molecular level, but poorly defined on the microscale. A fundamental difference that leads to this dissimilarity between natural and synthetic materials is their processing. Many natural materials are assembled from compartmentalized reagents that are released in well-defined and spatially confined regions, resulting in locally varying compositions. By contrast, synthetic materials are typically processed in bulk. Inspired by nature, we introduce a drop-based technique that enables the design of microstructured hydrogel sheets possessing tuneable locally varying compositions. This control in the spatial composition and microstructure is achieved with a microfluidic Hele-Shaw cell that possesses traps with varying trapping strengths to selectively immobilize different types of drops. This modular platform is not limited to the fabrication of hydrogels but can be employed for any material that can be processed into drops and solidified within them. It likely opens up new possibilities for the design of structured, load-bearing hydrogels, as well as for the next generation of soft actuators and sensors.

A possibility to gain true control over the local composition of soft materials is the immobilization and solidification of reagent-loaded drops in obstacle-free microfluidic devices. Drops can be immobilized in obstacle-free Hele-Shaw cells for example using acoustic waves^{14} or electrostatic potentials.^{15,16} However, such active methods rely on complicated microfabrication methods and require external energy sources, such that up-scaling becomes tedious. An elegant, passive method to immobilize drops in an obstacle-free Hele-Shaw cells is the use of microfluidic traps. This method relies on the minimization of the surface energy of drops: when drops with a diameter larger than the channel height are squeezed into the cell, they deform into pancakes, thereby increasing their surface area and hence total energy, E = γA; here γ is the interfacial tension and A the drop surface area. Squeezed drops can relax if they encounter a trap which is a restricted area where the channel height is locally increased. In this case, the surface energy of drops decreases. The gradient in surface energy between the squeezed and partially relaxed state of drops leads to a trapping force that opposes the drag force and hence, enables immobilization of drops. Studies conducted in Hele-Shaw cells demonstrated that larger traps produce larger trapping forces while larger drops experience larger drag forces.^{17} Devices that immobilize drops in microfluidic traps have been employed to monitor the evolution of cells,^{18,19} chemical reactions,^{18} or to investigate cross-talks between emulsion drops.^{20,21} However, this strategy has never been used to design macroscopic materials with well-defined locally varying compositions.

In this paper we introduce a microfluidic trapping device that enables the design of hydrogel sheets with locally varying compositions. To achieve this goal, we study the influence of the geometry of traps on their trapping strengths. We demonstrate that the trapping strength depends on the depth, area, and in-plane geometry of the trap. Based on these experimental results we introduce a mathematical model and perform simulations to predict the trapping strength. These tools facilitate the design of Hele-Shaw cells containing traps with different trapping strengths that enable the immobilization of different types of drops at well-defined locations. To demonstrate the potential of this device, we fabricate different microstructured hydrogel sheets with locally varying compositions.

Our simulations reveal three different trapping regimes that depend on the ratio of W to the radius of curvature r: if r > W/2, the part of the drop that relaxes into the trap forms a spherical cap, as shown in Fig. 2c to the left; we color-coded this regime orange. In this case, the deformation of the drop into the trap is limited by r, as has been described earlier.^{23} By contrast, if r < W/2, the trap is wide enough for the drop to fully enter such that it touches the trap ceiling and flattens against it. The part of the drop contained in this type of traps attains a shape what we call a dome, shown in Fig. 2c in the middle; we color-coded this regime blue. In this regime, the deformation of the drop into the trap is limited by the trap depth p. If R < W/2, the projected area of the drop fully lies inside the trap and the drop attains the shape of a pancake that is much more relaxed compared to that in the channel, as shown in Fig. 2c to the right; we color-coded this regime green.

Our and others^{23} results suggest that the trapping force is influenced by the decrease of the surface energy of a drop upon its relaxation into a trap. An interesting physical proxy to quantify the drop deformation into the trap is to determine the volume fraction of the drop contained in the trap. Although this parameter has a priori no direct physical meaning and its relation to Q_{C} cannot be generalized, it allows to determine to what extent a drop relaxes into a trap of a given depth. This information is acquired by imaging a drop when it is squeezed in the Hele-Shaw cell and while it is trapped. We calculate the volume of the pancake contained in the Hele-Shaw cell with our model by measuring its radius R from optical microscopy images and taking the known value of the channel height h, as detailed in the ESI.† The volume of the drop contained in the trap is calculated from the volume difference of the pancakes located in the channel between the trapped and untrapped states. For 2r > W, the drop volume contained in traps is independent of p, as shown by the orange solid symbols in Fig. 3b. By contrast, if 2r < W, the drop volume contained in traps increases with p, as shown by the blue solid symbols in Fig. 3b. To test our findings, we evaluate the volume fraction of drops contained in traps with varying p using Surface Evolver simulations and a mathematical model, as detailed in the ESI.† These results are in excellent agreement with our experimental ones, as shown in Fig. 3b by the empty symbols for simulations and crosses for the modelling. They confirm that the extent of relaxation of drops in traps is independent of p if 2r > W, but increases with increasing p if 2r < W. Further, for a fixed trap in-plane geometry, the volume fraction of the drop in the trap scales with the change of its surface area. As a result, for a fixed in-plane trap geometry, the critical flow rate and the volume fraction of the drop in the trap show similar slopes, as exemplified in blue for large, circular traps in Fig. 3a and b. From this finding, we deduce that the range over which the trapping strength can be varied is much wider if the trap diameter exceeds 2r. Note that this condition is not valid for very shallow traps, as discussed in the ESI.†

(1) |

(2) |

Fig. 4 Surface area model for drops squeezed in a Hele-Shaw cell. a) Surface area as a function of the channel height for the model proposed by Lv^{27} using elliptic integrals (green), the model proposed by Nie et al.^{28} using a truncated sphere (blue), the model proposed in this work using a disk with surrounding half-torus (black), and Surface Evolver simulation data (red, empty symbols). Inset: Schematic illustration of a drop squeezed in a channel of height h with indicated radius of the resulting pancake R, the length of contact between the drop and the channel x_{a}, and the radius of curvature r. b) A comparison of our model (black, solid symbols) with simulation data obtained from Surface Evolver (red, empty symbols) shows excellent agreement of the two data sets with errors below 0.3% over a wide range of channel heights. |

To describe the total surface area of trapped drops, that includes the surface area of the pancake and the cap that resides in the traps, we extend our model using geometric arguments, as detailed in the ESI† and Fig. S1. The calculated values are in excellent agreement with values obtained from Surface Evolver simulations, as shown in Fig. S1.† These estimations greatly facilitate the design of optimized traps. The agreement between our model and simulations further indicates that the approximation for r is justified to describe the relaxation of drops into traps, even for cases where R ∼ h.

To investigate the reason for the increase in Q_{C} with increasing number of corners of the traps, we simulate the relaxation of drops into traps with different in-plane geometries in steady state using Surface Evolver. Drops that are immobilized in triangular traps strongly retract from the corners to maximize the radius of curvature and hence, to minimize the Laplace pressure within the drops, as shown in Fig. 5d. The interface position can be understood as an equilibrium location in a geometrical singularity, in this case the corners, where the Laplace pressure within the drop is minimized. As a result of this retraction, the decrease in surface area is much smaller for drops immobilized in triangular traps than that of drops immobilized in circular traps, as shown in Fig. 5e. The difference in surface area between trapped and untrapped drops increases with increasing N and is most likely a contributing factor for the observed increase in Q_{C}.

We hypothesize that another contributing reason for the observed decrease in Q_{C} with decreasing N could arise from increased drag forces. The size of gutters that form when drops retract from the trap corners increases with decreasing number of sides. As the size of gutters increases, more continuous phase can flow into them. We expect this effect to impart higher drag forces on the drop, thereby decreasing Q_{C}. To test this hypothesis, we add gutters to the polygonal traps with N = 4, 6, ∞ by increasing their length threefold, as exemplified in the inset of Fig. 5f for the circular trap. For these trap geometries, we use N* to refer to the number of corners of the polygons and modified, elongated geometries. We orient the elongated traps to minimize the modification of the drop relaxation compared to the regular polygonal case. Additional gutters do not measurably influence Q_{C} of square traps. By contrast, they significantly decrease Q_{C} of hexagonal and circular traps, as shown in Fig. 5f. Triangular and square traps possess relatively large gutters and hence increased drag forces compared to circular traps, such that the addition of even larger gutters does not measurably alter Q_{C}. By contrast, hexagonal and circular traps possess gutters that are too small to significantly increase the drag force exerted on drops. If large gutters are added to these geometries, the drag force increases and hence, Q_{C} decreases. These results indicate that the lower values of Q_{C} for triangular and square traps can at least partially be assigned to the drag force exerted on drops by the continuous phase flowing into the gutters. Note that the orientation of triangular and square traps relative to the flow of the continuous phase does not measurably influence Q_{C}, as shown in Fig. S2.† These results demonstrate that Q_{C} can also be tuned over a considerable range with the in-plane geometry of traps.

To demonstrate the power and versatility of our platform to fabricate functional hydrogel sheets possessing well-defined microstructures, we design hydrogel sheets encompassing polyelectrolyte microgels. To achieve this goal, we produce aqueous drops loaded with the monomer AMPS (2-acrylamido-2-methylpropane sulfonic acid), a crosslinker and a photoinitiator, and immobilize them in large hexagonal traps. Untrapped drops are removed before the immobilized drops are converted into PAMPS particles by illuminating them with UV light to initiate the polymerization reaction within them, as shown in Fig. 8a. The oil is subsequently replaced with an aqueous matrix solution containing PEGDA and a photoinitiator. During this solution exchange, the polyelectrolyte particles swell by at least a factor three in in-plane diameter, as indicated with the red circles in Fig. 8a and b. After the matrix precursor is polymerized, the integral hydrogel sheet is removed from the microfluidic chip. To demonstrate its functionality, we immerse the microstructured sheet in a solution containing cresyl violet perchlorate, a positively charged dye. The dye is selectively adsorbed within the polyelectrolyte particles, as indicated by their change in color. This example demonstrates the versatility of this device in terms of materials that can be used to introduce micropatterns and functionality into hydrogel sheets.

Our results demonstrate that our device is well-suited to fabricate micropatterned hydrogel sheets. Importantly, this technology is not limited to trapping water-in-oil emulsions but can also be used to trap oil-in-water emulsions. To demonstrate this feature, we form drops composed of a fluorinated oil that encompass surfactants. These drops are dispersed in an aqueous solution containing PEGDA and a photoinitiator. After the oil drops are trapped and untrapped drops are removed, we polymerize the PEGDA to obtain a hydrogel sheet possessing well-defined highly regular micropores, as shown in Fig. 9.

For the sheets with selective absorption we use an aqueous solution containing 20% (w/w) AMPS (2-acrylamido-2-methylpropane sulfonic acid, Sigma-Aldrich, USA) as a monomer, 3% (w/w) N,N′-methylenebisacrylamide (Sigma-Aldrich, USA) as a crosslinker, and 11 μl ml^{−1} 2-hydroxy-2-methylpropiophenone (Sigma-Aldrich, USA) as a photoinitiator. The sheets are stained using an aqueous solution containing 0.8 mg ml^{−1} cresyl violet perchlorate (Sigma-Aldrich, USA).

For the fabrication of porous hydrogel sheets we render all surfaces hydrophilic. We employ the fluorinated oil phase described above as the dispersed phase and an aqueous phase containing 50% (w/w) PEGDA700, 2% (w/w) 2-hydroxy-2-methylpropiophenone, and 1% (w/w) Pluronic F127 Krill, a surfactant, as the continuous phase. The surface profile of the pore is recorded using a VK-X360K 3D Laser Scanning Confocal Microscope (Keyence, Belgium).

- M. J. Harrington, A. Masic and N. Holten-Andersen, Science, 2010, 328, 216–220 CrossRef CAS.
- L. V. Zuccarello, Tissue Cell, 1981, 13, 701–713 CrossRef.
- N. Holten-Andersen, T. E. Mates, M. S. Toprak, G. D. Stucky, F. W. Zok and J. H. Waite, Langmuir, 2009, 25, 3323–3326 CrossRef CAS.
- N. Holten-Andersen, G. E. Fantner, S. Hohlbauch, J. H. Waite and F. W. Zok, Nat. Mater., 2007, 6, 669–672 CrossRef CAS.
- T. Priemel, E. Degtyar, M. N. Dean and M. J. Harrington, Nat. Commun., 2017, 8, 14539 CrossRef.
- Y. Hu, Z. Wang, D. Jin, C. Zhang, R. Sun, Z. Li, K. Hu, J. Ni, Z. Cai, D. Pan, X. Wang, W. Zhu, J. Li, D. Wu, L. Zhang and J. Chu, Adv. Funct. Mater., 2020, 30, 1907377 CrossRef CAS.
- B. Özkale, R. Parreira, A. Bekdemir, L. Pancaldi, E. Özelçi, C. Amadio, M. Kaynak, F. Stellacci, D. J. Mooney and M. S. Sakar, Lab Chip, 2019, 19, 778–788 RSC.
- P. Kunwar, A. V. S. Jannini, Z. Xiong, M. J. Ransbottom, J. S. Perkins, J. H. Henderson, J. M. Hasenwinkel and P. Soman, ACS Appl. Mater. Interfaces, 2020, 12, 1640–1649 CrossRef CAS.
- W. Liu, Y. S. Zhang, M. A. Heinrich, F. De Ferrari, H. L. Jang, S. M. Bakht, M. M. Alvarez, J. Yang, Y. C. Li, G. Trujillo-de Santiago, A. K. Miri, K. Zhu, P. Khoshakhlagh, G. Prakash, H. Cheng, X. Guan, Z. Zhong, J. Ju, G. H. Zhu, X. Jin, S. R. Shin, M. R. Dokmeci and A. Khademhosseini, Adv. Mater., 2017, 29, 1–8 Search PubMed.
- T. J. Hinton, Q. Jallerat, R. N. Palchesko, J. H. Park, M. S. Grodzicki, H. J. Shue, M. H. Ramadan, A. R. Hudson and A. W. Feinberg, Sci. Adv., 2015, 1, e1500758 CrossRef.
- T. Bhattacharjee, S. M. Zehnder, K. G. Rowe, S. Jain, R. M. Nixon, W. G. Sawyer and T. E. Angelini, Sci. Adv., 2015, 1, 4–10 Search PubMed.
- C. B. Highley, C. B. Rodell and J. A. Burdick, Adv. Mater., 2015, 27, 5075–5079 CrossRef CAS.
- L. Ouyang, C. B. Highley, W. Sun and J. A. Burdick, Adv. Mater., 2017, 29, 1604983 CrossRef.
- A. Fornell, C. Johannesson, S. S. Searle, A. Happstadius, J. Nilsson and M. Tenje, Biomicrofluidics, 2019, 13, 044101 CrossRef.
- R. De Ruiter, A. M. Pit, V. M. De Oliveira, M. H. G. Duits, D. Van Den Ende and F. Mugele, Lab Chip, 2014, 14, 883–891 RSC.
- A. M. Pit, M. H. G. Duits and F. Mugele, Micromachines, 2015, 6, 1768–1793 CrossRef.
- P. Abbyad, R. Dangla, A. Alexandrou and C. N. Baroud, Lab Chip, 2011, 11, 813–821 RSC.
- E. Fradet, C. McDougall, P. Abbyad, R. Dangla, D. McGloin and C. N. Baroud, Lab Chip, 2011, 11, 4228 RSC.
- S. Sart, R. F. X. Tomasi, G. Amselem and C. N. Baroud, Nat. Commun., 2017, 8, 469 CrossRef.
- G. Etienne, A. Vian, M. Biočanin, B. Deplancke and E. Amstad, Lab Chip, 2018, 18, 3903–3912 RSC.
- P. Gruner, B. Riechers, B. Semin, J. Lim, A. Johnston, K. Short and J. C. Baret, Nat. Commun., 2016, 7, 10392 CrossRef CAS.
- K. A. Brakke, Exp. Math., 1992, 1, 141–165 CrossRef.
- R. Dangla, S. Lee and C. N. Baroud, Phys. Rev. Lett., 2011, 107, 1–4 CrossRef.
- C. W. Park and G. M. Homsy, J. Fluid Mech., 1984, 139, 291–308 CrossRef.
- R. Dangla, S. C. Kayi and C. N. Baroud, Proc. Natl. Acad. Sci. U. S. A., 2013, 110, 853–858 CrossRef CAS.
- M. Nagel, P. T. Brun and F. Gallaire, Phys. Fluids, 2014, 26, 032002 CrossRef.
- C. Lv, 2017, arXiv:1704.05830 [cond-mat.soft].
- Z. Nie, M. S. Seo, S. Xu, P. C. Lewis, M. Mok, E. Kumacheva, G. M. Whitesides, P. Garstecki and H. A. Stone, Microfluid. Nanofluid., 2008, 5, 585–594 CrossRef CAS.
- Y. Xia and G. Whitesides, Annu. Rev. Mater. Sci., 1998, 28, 153–184 CrossRef CAS.
- S. L. Anna, N. Bontoux and H. A. Stone, Appl. Phys. Lett., 2003, 82, 364–366 CrossRef CAS.
- G. Etienne, M. Kessler and E. Amstad, Macromol. Chem. Phys., 2016, 1–10 Search PubMed.

## Footnote |

† Electronic supplementary information (ESI) available. See DOI: 10.1039/d0lc00691b |

This journal is © The Royal Society of Chemistry 2020 |