The technique, called continuous chaotic printing, relies on static mixers: passive elements with no moving parts that are inserted into extrusion printheads. As two or more inks flow through these elements under laminar conditions, the flow is repeatedly split, stretched, and reoriented. Each mixing element duplicates existing material interfaces, so the number of internal layers grows exponentially along the length of the mixer. Unlike approaches that demand microstructured nozzles, optical patterning systems, or external electric, magnetic, or acoustic fields, chaotic printing is inexpensive, scalable, and mathematically predictable—and it is gentle enough to handle fragile mammalian cells.

In the new study, the researchers pushed the platform beyond the traditional Kenics static mixer, testing three additional geometries borrowed from industrial chemical engineering: the Ross mixer, the Mini-SMX, and the full SMX. Each geometry stamps a distinctive microarchitectural fingerprint onto the printed filament. Kenics elements produce the familiar aligned, multilayered lamellae, reaching feature sizes of about 60 micrometers with four elements yielding 16 layers within roughly a millimeter. Ross-based constructs display asymmetric, wave- or flame-like architectures, while the Mini-SMX generates symmetric motifs reminiscent of flowers or radiant forms. The SMX mixer, evaluated with one and two elements, produces flame-like structures with pronounced segregation of the two ink phases toward opposite sides of the cross-section.

Critically, these patterns are not accidents. Computational fluid dynamics simulations of the flow at each mixer outlet closely mirrored the experimentally observed cross-sections of printed hydrogel fibers, confirming that chaotic advection under laminar flow is deterministic rather than stochastic. Complex spatial patterns emerge from repeated stretching and folding of fluid streams despite the absence of turbulence or any moving mechanical components. Under the printing conditions used—fluid viscosities close to that of water—the resulting microarchitectures are dictated primarily by mixer geometry and topology, not by random perturbations. That predictability means researchers can design an internal structure on a computer and expect to see it materialize in the printed filament.

The team also demonstrated the flexibility of the approach across three distinct deposition modes. In continuous wet-printing, filaments are extruded directly into a calcium chloride bath that crosslinks alginate. In dripping, discrete spherical constructs form by droplet detachment, yet the internal architecture survives the formation process intact. In direct ink writing, viscoelastic materials are patterned by pressure-driven extrusion into grid-like constructs, each filament retaining discernible internal microstructure. Reproducing such interleaved architectures by conventional extrusion printing would require ultra-fine nozzles and sequential layer-by-layer deposition of distinct domains, which is impractical for continuous filament fabrication. Chaotic printing achieves the same result in a single, high-throughput step.

Because the goal of chaotic printing differs fundamentally from classical mixing, the researchers reframed how mixer performance should be judged. In conventional applications, a static mixer is judged by how completely it homogenizes fluids, and mixers with higher Lyapunov exponents—measures of how rapidly neighboring fluid elements separate—such as the SMX are considered superior. In chaotic printing, the objective is not homogenization but the rapid generation of controlled interfacial area over short residence lengths. Quantifying the intermaterial perimeter separating red and green domains in printed cross-sections, the team found that interface growth is often approximately linear over the few mixing elements relevant to biofabrication, rather than exponential. The Kenics mixer was a notable exception, showing clear exponential growth consistent with its deterministic 2-to-the-n lamellar multiplication mechanism.

The fluid dynamics analysis revealed a fundamental trade-off. SMX-type mixers, with their intersecting baffle structures, generate the highest instantaneous rates of interface proliferation and the finest features, but they impose significantly larger pressure drops due to repeated obstruction and redirection of flow. The Ross mixer produces the sharpest velocity transitions and localized zones of accelerated flow near blade edges, which promote strong interface stretching but also create aggressive shear peaks. The Kenics geometry achieves effective flow reorientation with comparatively moderate pressure penalties and smoother shear distributions, making it particularly attractive for shear-sensitive living cells. The Mini-SMX emerged as a compelling middle ground, capable of high interface densities with a lower pressure cost than the full SMX design. The choice of mixer, the authors argue, should follow the architectural objective—feature size, structural regularity, energetic efficiency—rather than classical mixing metrics alone.

To prove the concept has biological teeth, the team turned to living systems. Caco-2 intestinal epithelial cells were printed within a blend of alginate and GelMA using a hollow tube, a three-element Kenics mixer, and a one-element SMX mixer. Cell viability remained high across all conditions at day one and day twenty after printing. More strikingly, constructs printed with the single-element SMX spontaneously developed organized multicellular clusters over three weeks, and immunofluorescence staining revealed expression of tissue-relevant markers including Villin and Vimentin, along with F-actin and nuclei. The chaotic microenvironment was permissive enough to support long-term culture, self-organization, and functional marker expression—from a minimal setup with no external fields or complex optics.

Bacteria provided an even more vivid demonstration of spatial control. Using a Mini-SMX printhead with two inlets and a single mixing element, the researchers printed Escherichia coli, a facultative anaerobe expressing green fluorescent protein, in the outer regions of fibers while confining Bifidobacterium bifidum, a strict anaerobe, to the core. The peripheral E. coli shielded the oxygen-sensitive B. bifidum from ambient oxygen, and after 48 hours the anaerobe reached approximately ten to the ninth colony-forming units per gram in structured constructs—significantly higher than in pre-mixed controls, where populations homogenized completely. This rational compartmentalization of a synthetic microbial consortium points toward gut-mimetic systems, controlled cross-feeding platforms, and engineered biofilms in which gradients of nutrients, metabolites, or mechanical properties can be designed into the material itself.

The third proof of concept moved from biology to chemistry. Phosphate-rich and calcium-rich gelatin inks were co-extruded through a printhead containing three Ross mixing elements, generating interdigitated domains with distinct ionic compositions embedded in a single continuous gelatin matrix. Calcium phosphate precipitated precisely at the internal interfaces between the domains, visualized by tetracycline-based fluorescence staining. Because both inks share the same polymeric matrix and are crosslinked throughout by transglutaminase, the construct remains mechanically integrated despite its chemically distinct microregions. This capacity to spatially program chemical transformations within soft materials opens routes to biomineralization, catalysis, and bioinspired composites with functional gradients or hybrid living-nonliving features.

Taken together, the work establishes static mixer geometry as a genuine design parameter—one that simultaneously controls microarchitecture, interface generation, shear exposure, and pressure loss. By expanding the chaotic printing toolbox beyond Kenics elements to Ross, Mini-SMX, and SMX geometries, and by validating the platform across wet-spinning, dripping, and direct writing, the researchers have broadened the design space available to bioprinting, soft matter, catalysis, and synthetic biology. The broader promise is seductive in its simplicity: complex, nature-like internal organization encoded passively within a printhead, in a single continuous fabrication step, using equipment that many laboratories already own. As the authors suggest, future directions may include interfacial reactivity for sensing, directed nutrient diffusion, and even the synthesis of inorganic phases within hydrogel scaffolds—turning chaos itself into a tool for structuring complexity.

Subject of Research: Chaotic bioprinting of microarchitected soft materials using different static mixer geometries

Article Title: From Flow to Function: Using Different Static Mixers to Fabricate Microarchitected Materials Via Chaotic Printing

Article References: Bolívar‐Monsalve, E. J., Ceballos‐González, C. F., Quevedo‐Moreno, D. A., Rendón‐Moreno, I. I., Cantoral‐Sánchez, A., Ambriz‐González, H., Alvarez, M. M., & Trujillo‐de Santiago, G. (2026). From Flow to Function: Using Different Static Mixers to Fabricate Microarchitected Materials Via Chaotic Printing. Advanced Science, 13(55), Article e76626. https://doi.org/10.1002/advs.76626

Image Credits: AI Generated

DOI: 10.1002/advs.76626

Keywords: chaotic printing, static mixers, bioprinting, microarchitecture, hydrogels, chaotic advection, computational fluid dynamics, synthetic microbial consortia, biomineralization, direct ink writing, soft materials, Caco-2 cells

The physics of microscale flow is what makes mixing on a chip so difficult. In channels whose widths are measured in micrometers, fluids with constant viscosity, known as Newtonian fluids, flow in a laminar regime, meaning viscous forces overwhelm inertial ones. The Reynolds number, the dimensionless ratio of inertial to viscous forces, typically falls well below one in such devices, far under the threshold of roughly 2000 where turbulence begins. Without turbulence, there is no chaotic churning to scramble two streams together; species move between streams mainly by diffusion. The Péclet number, which compares advective to diffusive transport, is likewise low in microchannels, so diffusion dominates. For large biomolecules, whose diffusion coefficients can be as small as ten to the minus fourteen square meters per second, this makes mixing painfully slow unless the channel geometry is cleverly engineered to stretch and fold the fluids into each other.

Engineers tackle this problem with two broad families of micromixers. Active micromixers inject energy from outside, using electric or magnetic fields, acoustic waves or thermal gradients to stir the fluids, but the extra transducers add cost and complexity, and the applied fields can damage delicate biological samples. Passive micromixers, by contrast, rely entirely on channel geometry and flow conditions to maximize contact between the streams, inducing mixing through splitting and recombination of flow, vortices and fluid collisions. Because they are cheap to fabricate and easy to integrate, passive designs have become the workhorses of lab-on-a-chip systems. What has been missing, the Portuguese team argues, is a passive device that simultaneously achieves efficient mixing under unequal inlet flow rates and guarantees that the mixed fluid arrives at multiple detection sites in equal amounts, a combination essential for running several biomarker tests on a single chip at the same time.

The new platform consists of a passive mixing region followed by a compensation chamber that stabilizes the flow and three millimetric reaction chambers sized to accommodate future integration of miniaturized optical detectors such as LEDs and photodiodes. The researchers built four two-dimensional designs by pairing two micromixer geometries with two reaction chamber diameters, 3500 and 5000 micrometers. The first geometry, dubbed Tesla-shaped, adapts a structure originally conceived by Nikola Tesla, in which the flow is partially split at a constriction, accelerating through the narrow passage while the remainder curls into a vortex and emerges in the opposite direction, dramatically increasing interaction between the species. The team set the constriction widths to 50 and 90 micrometers and repeated the mixing unit eight times along the channel. The second geometry, half-moon-shaped, borrowed from a topology-optimized design, places two semicircular structures symmetrically on opposite walls with a central obstacle that divides the flow; the two streams then form vortices and collide. Here the researchers doubled the original dimensions to a maximum channel width of 400 micrometers and replicated the unit four times along a five-segment serpentine.

Before fabricating anything, the team ran transient finite element simulations in COMSOL Multiphysics, solving the Navier-Stokes equations for laminar flow coupled with the transport of diluted species. Water was the working fluid, and the inlets were driven at three flow rate ratios: 1:1, 1:3 and 1:6, with the reference inlet fixed at 5 microliters per minute while the second ranged from 5 to 30 microliters per minute. A preliminary three-dimensional study confirmed that a cheaper two-dimensional model captured the physics faithfully, and a mesh independence study settled on a coarse refinement of roughly ten thousand to twenty thousand elements per geometry. The simulations showed that in the Tesla-shaped device mixing was nearly complete by the second mixing structure, while in the half-moon design it was almost finished by the end of the first serpentine segment. Quantitatively, both geometries reached simulated mixing indices of almost 100 percent within 20 seconds, indicating essentially homogeneous concentration across the channel width.

The experimental devices were made in polydimethylsiloxane, the transparent, biocompatible elastomer beloved of microfluidics researchers, using a low-cost replica molding process with SU-8 epoxy molds fabricated by ultraviolet soft lithography, notably without cleanroom facilities. The testing rig combined a two-syringe pump for precise flow control, bubble extractors at the inlets, an inverted optical microscope with a high-speed camera, and a spectrophotometer to analyze the collected fluids. Blue and yellow dyes served as the test fluids, and each device ran continuously for 20 minutes under the three flow ratios, with all experiments repeated three times. Mixing efficiency was quantified from microscopy images by measuring the standard deviation of pixel intensities across the channel: a well-mixed stream shows a uniform grayscale, while an unmixed one shows dark blue flanks and a bright yellow center.

The results confirmed the simulations with some instructive nuances. The Tesla-shaped micromixer consistently outperformed the half-moon version, showing a more uniform color distribution at the channel end and slightly higher mixing indices, with both geometries exceeding the 80 percent target. The half-moon device retained a slight color variation at the outlet, a shortfall the authors attribute partly to air bubbles accumulating near the vertices of its semicircular structures. Interestingly, mixing improved at higher flow rates, because stronger inertial effects promote chaotic advection and increase the interfacial contact between the streams, a reminder that even in the laminar world inertia can be harnessed rather than merely tolerated. Spectrophotometric analysis of the outlet fluids, tracking absorbance at 400 and 640 nanometers and the ratio between them, showed similar spectral profiles across all three outlets, further evidence of effective mixing and distribution.

On the distribution side, the size of the reaction chambers turned out to matter enormously. In the Tesla-shaped device with 3500 micrometer chambers, the coefficient of variation of collected volumes hovered around or below 25 percent, but enlarging the chambers to 5000 micrometers pushed that figure down to around or below 10 percent, meeting the uniformity target, and the differences were not statistically significant. The same trend appeared in the half-moon family, where the smaller-chamber version showed statistically significant volume disparities between the central and lateral outlets while the larger-chamber version did not. The team also noted a recurring cosmetic quirk: the central outlets tended to look slightly greener than the lateral ones, because the laminar flow profile mixes more thoroughly in the fast-moving center of the stream, an effect that could be mitigated by widening the channel feeding the central chamber.

The best all-around performer was the Tesla-shaped multiplexer with 5000 micrometer chambers, which balanced strong mixing with the most even fluid delivery, although its 3500 micrometer sibling achieved marginally better mixing uniformity at high flow ratios. The authors are candid about limitations: the study used Newtonian test fluids within a restricted flow range, the dyes can leave residues in the channels over time, and occasional bubble entrapment perturbed the half-moon geometry. Real biological samples, functionalized reaction chambers and surface-interaction studies will be needed before the platform can compete with validated multiplexed diagnostics. Still, the achievement is significant: a fully passive, low-cost chip that mixes fluids at flow rate ratios as steep as 1:6 and splits the result three ways with volumes uniform to within about 10 percent. With future work on geometry optimization and biofunctionalization, the researchers envision these multiplexers forming the fluidic backbone of lab-on-a-chip systems that screen multiple biomarkers simultaneously, bringing faster, cheaper and more portable diagnostics closer to the clinic.

Subject of Research: Passive microfluidic mixing and multiplexed fluid distribution for point-of-care diagnostics

Article Title: Multiplexer microfluidic platform for mixing and driving Newtonian fluids under high flow rate ratios

Article References: Ferreira, F., Sousa, P. J., Minas, G., Lima, R. A., Pinto, V. C., & Catarino, S. O. (2026). Multiplexer microfluidic platform for mixing and driving Newtonian fluids under high flow rate ratios. Results in Engineering, 32, Article 113345. https://doi.org/10.1016/j.rineng.2026.113345

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.113345

Keywords: microfluidics, micromixer, point-of-care diagnostics, lab-on-a-chip, passive mixing, Tesla valve, PDMS, laminar flow, multiplexing, biosensing, chaotic advection, fluid dynamics