Up-and-down transformable embedded ink writing strategy for soft 3D architectures

Domain: physics
Published: 2025-12-12
Editorial outcome: minor_revision

Abstract
The fabrication of 3D soft material architectures is essential for advancing fields such as soft robotics, wearable technologies, and biological engineering. However, conventional embedded 3D printing is constrained by rheological complexity and nozzle-dependent structural limitations. Here, we introduce transformable embedded ink writing (TEIW), a 3D printing strategy that bypasses these issues by triggering rapid, autonomous self-assembly of 2D-printed patterns into predefined 3D structures. TEIW employs yield-stress inks within a Newtonian-like fluid bath, where net gravitational-buoyancy forces drive the filaments to go upward or downward. Through tailored density contrasts, controlled viscosity, and mechanical coupling between structural elements, complex shape transformation is directed with physical intelligence embedded in the printed structure itself, requiring no external intervention. This strategy demonstrates broad compatibility with materials including silicone elastomers, acrylate-based resins, and hydrogels, enabling applications spanning customizable microelectronics, perfusable networks, and cryptographically encoded devices. Furthermore, TEIW’s ability to integrate various components in a single print establishes a platform for next-generation systems requiring spatiotemporal multi-material control.

Introduction
The fundamental principle of “form follows function” underscores the importance of 3D structures, where the material’s architecture directly dictates its performance and unlocks untapped possibilities for functional applications across scales. This design philosophy is particularly significant in the realm of soft materials, which underpin innovations in emerging fields such as soft robotics1,2, smart wearables3, and advanced medical devices4. In recent years, extrusion-based 3D printing, particularly direct ink writing (DIW), has emerged as a powerful tool for rapid prototyping of customizable soft systems5–9. In a typical DIW process, viscoelastic ink is extruded through a nozzle onto a substrate in ambient air to build the designed structure10. Although conventional DIW is cost-effective and highly scalable, its layer-by-layer printing manner often requires auxiliary structures to support overhang or complex geometries, complicating the fabrication process. Moreover, structural integrity relies on the ink’s ability to solidify rapidly, which limits material choices, especially for silicone elastomers that typically exhibit low curing kinetics11,12. To overcome these challenges, embedded ink writing (EIW) has been developed, wherein inks are extruded into a liquid bath instead of directly into air13–16. The supporting bath is typically a yield-stress liquid, which can locally fluidize under shear from the moving nozzle and rapidly transition back to a solid state once the shear is released17,18. In this way, it provides omnidirectional support and enables freeform fabrication. As a result, EIW has demonstrated versatility across diverse applications, including strain sensors19, pneumatic actuators8, vascular networks20, and cell-laden scaffolds fabrication21.

Nevertheless, the EIW method introduces its own challenges. Firstly, the process demands careful rheological compatibility between the ink and the bath material. Mismatches in yield stress or viscosity could cause filament irregularities22–24. Moreover, the use of a yield-stress bath in turn requires the ink to possess even higher yield stress to maintain structural fidelity25. The incorporation of rheological modifiers (e.g., nanoparticles) further complicates ink formulation and may impair the material’s properties. Secondly, the EIW process remains heavily dependent on the extrusion nozzle26,27. The printable height is constrained by the nozzle length. Longer nozzles are prone to deflection due to resistance from the support fluid, compromising printing accuracy. In addition, when printing near or across previously deposited ink filaments, the nozzle can induce mechanical disturbances in the bath, making it difficult to achieve high geometric fidelity.

Aiming to address these challenges, this work presents a printing strategy termed transformable embedded ink writing (TEIW), which enables the fabrication of 3D structures through the self-assembly of 2D-printed patterns via a net gravitational-buoyant force. This density-driven mechanism enables printed filaments to ascend in regions of higher buoyancy or sink under greater gravity, thereby autonomously transforming planar precursor patterns into preprogrammed 3D architectures within seconds to minutes. TEIW operates within a Newtonian-like fluid support bath, which reduces the strictness of rheological compatibility requirements in conventional ink-bath systems. Once the ink is released from the nozzle, TEIW circumvents the structural height limitations imposed by nozzle length and avoids the need for complex 3D trajectory control. Moreover, the self-assembly nature of the process inherently avoids distortions caused by nozzle interference. In contrast to externally stimulated 4D printing28 or magnet-assisted morphing strategy29, our approach requires no specialized responsive materials and accommodates a broader spectrum of soft materials, including elastomers, hydrogels, photocurable resins, and polymer composites. Building on this material generality, we demonstrate applications spanning customizable microelectronics, perfusable vascular networks, and cryptographically encoded functional devices. This strategy thus offers a simple and versatile route to fabricating delicate multifunctional 3D structures, opening avenues in soft material manufacturing.

Results
Principle of TEIW
The TEIW process is predicated on direct writing of 2D planar patterns within a Newtonian-like fluid medium, followed by autonomous 3D shape transformation governed by buoyancy-gravity interactions (Fig. 1a). This contrasts fundamentally with conventional embedded ink writing (CEIW), which relies on viscoelastic yield-stress fluids to stabilize deposited filaments (Fig. 1b). In CEIW, the support bath exhibits shear-thinning behavior, which flows under nozzle-induced shear stress and behaves as a solid once the stress is removed. Its pairing with higher yield-stress inks enables the maintenance of filament geometry and position, wherein the bath’s yield stress defines the maximum force exerted on the ink filaments17,18,23,25,30. In TEIW, the support medium is a Newtonian-like fluid with constant viscosity and density within the operating range. When an ink is extruded into the bath, each filament segment experiences the gravity Fg = ρink gπr2L and buoyancy Fb = ρbath gπr2L, where ρink and ρbath are the density of the ink and bath, g is the acceleration of gravity, r and L are the radius and length of the ink filament, respectively. The net driving force Fdrive = Fg − Fb determines vertical motion of the ink filament: positive Fdrive causes sinking, while negative values result in flotation. By systematically adjusting printing parameters (extrusion pressure P and nozzle velocity v), discrete filament segments with tailored Fdrive can be printed. For example, continuously extruding ink into a Newtonian-like bath with varying volumetric flow rates (Q1 < Q2 < Q3 < Q4) produces four distinct segments with differential axial weight distribution (Fig. 1c). Over time scales of seconds to minutes, these segments migrate to their target depths, guided by their respective Fdrive, to self-assemble into the desired 3D architectures. This transformation is then rapidly stabilized (typically within a minute) by initiating solidification via IR-induced thermal curing or photoinitiation, effectively locking the structure in place. The TEIW platform supports four fabrication modalities (Fig. 1d). (i) Freestanding structures: After shape transformation, the support medium is removed, leaving intact 3D constructs. (ii) Integral structures: Ink and bath components are co-cured to form a monolithic 3D structure. (iii) Hollow architectures: Sacrificial inks are selectively dissolved to create microfluidic channels. (iv) Hybrid printing: This modality relies on the coexistence of different stabilization mechanisms within a single bath. A fine-scale ink (e.g., hydrogel) is first deposited and stabilized in situ, analogous to CEIW processing, owing to its minimal buoyancy-gravity forces and intrinsic rheology. Subsequently, a second ink (e.g., conductive elastomer) with tailored properties to undergo programmed TEIW is deposited, which autonomously assembles around or within the pre-formed structure. This approach enables the seamless integration of different materials and printing mechanisms without requiring bath exchange or complex sequential processing.

Transformation dynamics governed by material physics
In embedded 3D printing systems, the intricate interplay of the rheology of the extruded ink and its surrounding bath governs the filament morphology and structural supporting capability. A comprehensive investigation involving a diverse set of ink-bath combinations was systematically conducted. The detailed formulations, material properties, and designations of all inks and baths used throughout this study are documented in Table 1 and Supplementary Fig. 1. To ensure structural integrity, all inks formulated for this study were yield-stress fluids. The position change of ink filaments in the z-axis is investigated using 700 µm-diameter Ink-1 filaments printed at ~3 mm below the liquid surface (Supplementary Fig. 2). In a conventional EIW process, the yield stress of the bath (Bath-0) stabilizes the deposited filament at its printed position (Fig. 2a). The density differentials exhibit negligible effects compared to dominant rheological parameters. In the TEIW process, Newtonian-like fluids serve as the support bath. The Newtonian nature of these baths is confirmed by their linear shear stress-shear rate relationships, and their storage modulus (G’) is consistently lower than their loss modulus (G’’). To elucidate the impact of density differentials (Δρ = ρink − ρbath) on filament behavior, ink-bath pairs were selected with varying density contrasts. For Ink-2 (0.990 g/cm³) and Bath-1 (0.998 g/cm³), the ink filament exhibited upward migration behavior (Fig. 2b). It ascended 2.3 mm in 4 min due to positive buoyancy (Δρ = −0.008 g/cm³), with no lateral displacement. Conversely, when ρInk-1 (1.016 g/cm³) exceeds ρBath-2 (0.998 g/cm³), a gravity-driven descent transformation occurred. Under this moderate density contrast (Δρ = +0.018 g/cm³), a 1 mm displacement was observed over 9 min (Fig. 2c). Images illustrating this sinking behavior, along with the results from other ink-bath combinations, are provided in Supplementary Figs. 3 and 4. A direct correlation was revealed between the magnitude of the density difference and the extent of vertical displacement within a given time frame. For instance, with a larger density mismatch of Δρ = +0.050 g/cm³ (ρInk-1 = 1.016 g/cm³, ρBath-3 = 0.966 g/cm³), a 4.6 mm vertical translation was achieved within 5 min (Fig. 2d).

To quantitatively understand the correlation between density contrast and displacement dynamics, the driving force for filament motion (Fdrive) is given by:
Fdrive = (ρink − ρbath) gπ d2/4 L (1)
where d and L are the filament diameter and length, respectively. Under low Reynolds number conditions prevalent in this system (Re ≈ 3.33 × 10−6 ≪ 1), this motion is resisted by a viscous drag force Fdrag. Given the finite aspect ratio characteristic of the printed filament (L/d ~ 50), the drag force must be described by a modified form of Stokes’ law that accounts for its non-spherical geometry and end effects31. Such filaments can be approximated as slender cylinders. For transversely moving (axis perpendicular to motion) finite-length cylinders in viscous fluids, the hydrodynamic drag force Fdrag is described by:
Fdrag = [4π ηL / ln(L/d) + Cconst] vt (2)
where η is the dynamic viscosity of the bath, and vt is the terminal velocity. The logarithmic term ln(L/d) accounts for length-to-diameter ratio effects on drag resistance, while the constant term Cconst is derived from experimental corrections for end effects. At terminal velocity (vt), the filament reaches dynamic equilibrium, where the driving force is balanced by the viscous drag force (Fdrive = Fdrag). Substituting the expressions for both forces yields the terminal velocity:
vt = (ρink − ρbath) g d2 / [6 ηbath ln(L/d) + Cconst] (3)
It reveals that while density contrast dictates the direction of motion, both the density contrast and the bath viscosity conjointly govern the motion kinetics. Figure 2c, d show that the settling time for a 1 mm displacement can be drastically reduced by 89%, from 9 min to 1 min, achieved through the synergistic effect of decreasing bath viscosity from 9.20 Pa·s to 4.18 Pa·s while increasing the density contrast. The inverse dependence of velocity on bath viscosity is further supported by the additional systems provided in Supplementary Figs. 5 and 6. This rate amplification is crucial for time-sensitive materials, as it significantly accelerates the overall printing process, enabling rapid stabilization before material solidification. Experimental observations confirm that the terminal velocity is attained within 150 ms. Therefore, vt can be regarded as the characteristic deposition speed. The above analysis confirms that the modified Stokesian framework can offer quantitative guidelines for selecting bath viscosity (ηbath) and density contrast (Δρ) to match deposition kinetics with material-specific solidification constraints.

Optical micrographs show that the cross-sections of ink filaments preserved a circular morphology after transformation and solidification (inset of Fig. 2). This well-defined shape is primarily maintained by the ink’s own yield-stress and viscoelastic properties immediately upon deposition, with the Newtonian-like bath providing negligible resistance to flow and thus minimal mechanical stress on the filament. Furthermore, by employing silicone-based ink-bath pairs with a near-zero interfacial tension (γ ≈ 0 mN/m), filament shrinkage and deformation did not occur. In contrast, systems with higher interfacial tension (e.g., γ ≈ 20 mN/m epoxy-silicone systems) induced Plateau-Rayleigh instability, causing ink filaments to break up into droplets within seconds (Supplementary Figs. 7 and 8)32,33. Notably, these droplets also underwent gravity-driven descent (Supplementary Fig. 9), suggesting potential for droplet-embedded patterning and an alternative deposition modality for functional composites34,35.

Printing parameters regulation
With density and viscosity fixed in the system, the filament diameter (d) is a key determinant of deposition velocity, as described by Eq. (3). This diameter is governed by the volumetric flow rate (Q), which can be controlled through extrusion pressure (P) and nozzle velocity (v), according to the Hagen-Poiseuille law (Q = πr4ΔP/8ηL) and fluid continuity principle (Q = π d2/4 v)36. It leads to the predictive relation d = 2 sqrt(Q/πv). Experiments using a 610 µm nozzle and Ink-1/Bath-1 as a model system showed that the filament diameter increased from 360 µm to 600 µm as P was raised from 40 to 80 psi at a constant v of 5 mm/s (Fig. 3a, b and Supplementary Fig. 10a, b). Conversely, at a fixed P of 60 psi, decreasing v from 13 to 3 mm/s resulted in a diameter increase from 400 to 620 µm. These results are consistent with the theoretical framework. Since the terminal velocity vt ∝ d2, this ability to precisely control diameter via P and v provides direct regulation over the kinematic behavior of filaments (Supplementary Fig. 10c, d), enabling programmable 3D transformation without the need for mechanical nozzle changes.

In the current model system, filament curling occurred under low extrusion pressure (P ≤ 55 psi) or high nozzle speed (v ≥ 7 mm/s) when using a 610 µm nozzle (Fig. 3a, b). This instability arose from the ink’s inability to fully recover its microstructure after rapid shear thinning37. The Newtonian-like bath, lacking a yield stress, did not provide any stabilizing confinement, thereby allowing this inherent ink instability to appear as free-form curling. Notably, switching to a finer nozzle within the same ink-bath system produced thinner filaments that exhibited reduced disturbance and improved stability (Supplementary Fig. 11)38. More importantly, it enabled access to a distinct low-velocity deposition regime. When the filament diameter falls below 270 µm, the corresponding settling velocity drops below 0.1 mm/min (Fig. 3c). Within this low-velocity regime, defined here as the “static zone”, the filament can be stabilized rapidly via curing (~1 min) before significant displacement occurs (Supplementary Fig. 12), enabling precise shape retention analogous to conventional EIW.

Based on the above framework, the temporal evolution of the filament’s z-position can be quantitatively predicted. Given that the ink filament sinks at an essentially uniform velocity, the deposition distance D is effectively approximated by D = vt × t, where t is the duration. This predictive capability was validated by the close agreement between the experimental data and the theoretical prediction for a 660 µm diameter filament, as shown in Fig. 3d. Furthermore, this model enables synchronization control. By deliberately delaying printing by a time Δt of a thinner filament to compensate for its slower sinking rate, two filaments with a 40 µm diameter difference were synchronized to reach the same depth simultaneously (Fig. 3e). Conversely, printing 680 µm and 640 µm filaments simultaneously resulted in a pronounced vertical offset of 1.5 mm (Fig. 3f). These results show that the filament diameter variations, encoded via printing parameters, can be translated into time-dependent deposition differences.

Experiments with non-uniform and curved filaments reveal that the sinking velocity is dictated by fluid-structure interactions arising from their geometry (Supplementary text and Fig. 13). A heterogeneous filament sinks more slowly than a uniform filament of the same maximum diameter, as the mechanical coupling between segments of different diameters restrains the overall motion. Similarly, greater filament curvature leads to a slower descent. These findings form the basis for a rational workflow proposed to guide the optimization of the TEIW printing process by addressing key factors such as the ink-bath system and printing parameters (Supplementary Fig. 14).

3D structural construction
Through a combination of printing parameters (P, v) and path geometry, predictable transformation of 2D patterns into complex 3D architectures can be achieved. Demonstrations include curvilinear structure, double helix, tetrahedron, and bifurcation structure, with experimental details provided in Supplementary Fig. 15 and Supplementary Table 1. With reference to computer-aided design (CAD) blueprints, a 3D helix was fabricated via printing a planar spiral pattern with graded printing pressures (P4 > P3 > P2 > P1), which induces diameter variations along the continuous filament (Fig. 4a). Thicker, high-pressure segments sank faster than thinner, low-pressure regions, establishing a continuous curvature gradient along the spiral. The deformation arose from the relative motion between adjacent turns. The faster-sinking outer segments dragged the slower inner segments downwards, while the slower-sinking inner sections restrained the outer ones, resulting in smooth, continuous helical geometries. Similarly, by alternating the nozzle velocity, a segmented linear filament transformed into a waveform pattern (Fig. 4b). The faster-sinking segments descended ahead of the slower-sinking ones, forcing the straight filament to buckle periodically in the vertical plane, transforming it into a stable, undulating 3D structure.

Dual helical structures were realized by printing a continuous filament in a serpentine pattern with programmed flow rate variations (Fig. 4c). Each section of the pattern exhibited a high-flow side (blue) and a low-flow side (gray), and adjacent sections had this orientation reversed. During transformation, the high-flow side descended faster, thereby generating a localized torque at the junctions and lifting the low-flow side upward. The systematic reversal of the force gradient along the path caused these torques to alternate in direction, prompting the entire structure to twist and coil into a stable, double-helical morphology. The rapid self-assembly (≤ 10 s) demonstrates programmable kinetic control through filament-level force modulation.

The tetrahedral structure, a closed three-dimensional architecture, was achieved via velocity-graded triangular motifs (Fig. 4d). The central high-flow-rate region (v3 = 3 mm/s) exhibited a larger diameter and higher driving force compared to the peripheral low-flow-rate segments (v1, v2, v4 = 7, 5, 10 mm/s). This systematic heterogeneity established an asymmetric force distribution across the triangular pattern. During sinking, the high-drive central region experienced preferential descent, but its motion was constrained by mechanical connectivity to the slower peripheral arms. This constraint converted the vertical force imbalance into a distributed bending moment, triggering simultaneous upward folding along three pre-defined edges. The entire structure underwent coordinated large deformation, evolving into a stable tetrahedron within 5 min. Structural integrity was maintained through dynamic force equilibrium during the transformation, without nozzle-induced disturbances affecting the structure.

To explore bioprinting potential, CAD-designed 2D bifurcation patterns were printed using colored Ink-1 (Fig. 4e). By assigning different printing velocities, differential deposition between slow trunk segments and fast terminal branches introduced a controlled force imbalance. This programmed kinematic imbalance drives spontaneous 3D vascularization, inducing out-of-plane bending to yield vessel-like structures that mimic natural arteriovenous branching networks. This mechanism overcomes filament interference challenges inherent in conventional 3D branched printing. The z-axis fidelity of the above structures was quantified by comparing the as-printed heights with the theoretical depths predicted by Eq. (3) for straight filaments, yielding values from 86.48% to 98.16% (Supplementary Fig. 16a). The observed variance stems from geometric and interfacial factors beyond this simplified model. For a direct comparison, 3D structures were also printed using the conventional EIW method in a reported yield-stress support bath25 (Supplementary Fig. 16), whereas TEIW demonstrated higher geometric accuracy while maintaining a comparable preparation time (Supplementary Fig. 17).

Material versatility and functionality
The versatility of the TEIW strategy is demonstrated through its application to three material systems, each representing a different printing mode, including bulk curing of silicone elastomers to form monolithic structures, printing of discrete, self-supporting structures with photocurable resins, and direct writing of perfusable microchannels using sacrificial hydrogels. All three systems utilized Bath-3 and were based on yield-stress inks. The printing of a CAD-designed flower structure, employing velocity gradients (vmax = 10 mm/s, vmin = 5 mm/s), was performed in the three systems to induce differential deposition between petal tips and the central region (Fig. 5a). The silicone elastomer bulk structure was fabricated using the Ink-2/Bath-3 system with a positive density contrast of 0.024 g/cm³ (Fig. 5b). Programmed velocity gradients between petal segments drove controlled trajectory divergence through differential Stokesian settling, enabling autonomous 3D shaping. The process comprised three steps, including 60 s for 2D printing, 250 s for post-printing transformation, and 60 s for complete solidification under infrared light. The curing kinetics of the silicone elastomer in this work were tailored using additives. An inhibitor secured a minimum 24-h printing window at room temperature, while an added platinum catalyst facilitated the infrared-induced curing within 1 min to ensure printing accuracy.

A high-density photocurable ink, composed of acrylic resin and silicone elastomer precursor, was printed within Bath-3 (Fig. 5c). The significant density mismatch enabled ultrafast deposition, completing 2D-to-3D transformation within 20 s. The resulting structure was then stabilized by UV curing for 10 s. The cured flower structure was directly picked up from the bath, preserving the bath’s reusability.

The 3D channels in Fig. 5d were fabricated using Pluronic F-127 hydrogel as a sacrificial ink. The printed filaments, with diameters ranging from 710 µm to 1010 µm, were printed at room temperature within 40 s. With a density of 1.020 g/cm³, the ink sank and formed the 3D structure within 120 s. The bath was then cured via infrared irradiation, and sacrificial ink was removed via cold deionized water flushing. Perfusion with dyed water verified the channels’ interconnectivity and structural integrity. These demonstrations highlight the TEIW strategy’s robust adaptability, enabling precise spatiotemporal control over 3D structure formation across elastomeric, photocurable, and hydrogel systems while maintaining process scalability and mechanical fidelity.

Carbon-based conductive inks (1.450 g/cm³) were directly printed into a silicone support bath, with the ink ultimately embedded within the cured elastomeric matrix (Fig. 6a). The bath’s optical transparency enables visual confirmation of 3D circuit geometries, while its inherent mechanical robustness protects embedded structures from external forces, such as compressive loads. Results show that 3D circuits embedded in the support bath maintained continuous conductivity when subjected to a compressive load ranging from 0 to 500 g, with a resistance variation of less than 0.5%. This performance arises from the bath’s elastomeric encapsulation, which uniformly distributes mechanical stress and prevents structural failure of the conductive pathways.

A key advantage of the TEIW strategy is its capability for hybrid multi-material printing by synergistically combining distinct deposition mechanisms within a single process. This is demonstrated by sequentially printing two functional materials into the same support bath (Fig. 6b). First, a Pluronic F-127 sacrificial hydrogel filament was deposited. Due to its small diameter (480 µm) and small density contrast with the bath (Δρ = +0.054 g/cm³), the filament experienced negligible buoyancy-driven motion, remaining stabilized in its predesigned position, a behavior analogous to conventional EIW and effectively creating a static reference structure. Subsequently, a conductive ink filament (220 µm diameter) with a significant positive density contrast (Δρ = +0.484 g/cm³) was printed adjacent to the hydrogel structure. This second ink actively underwent TEIW, with programmed velocity gradients driving its autonomous 2D-to-3D transformation into a helical architecture within 1 min. This hybrid approach achieved seamless dual-material integration without cross-interference. After thermal curing of the bath and removal of the sacrificial hydrogel, the resulting structure contained perfusable microchannels alongside fully functional helical conductive circuits, as confirmed by dyed fluid perfusion (Fig. 6c) and powering an LED (Fig. 6d). The helical circuits also function as thermal sensors, with fluid circulation in the adjacent channels inducing real-time resistance changes (Supplementary Fig. 18). The parallel use of static and dynamic mechanisms within the same bath significantly expand the utility of the technique for creating integrated, multi-functional devices. Furthermore, this strategy supports conventional layer-by-layer stacking on the bath substrate, enabling the fabrication of dense, volumetric objects (Supplementary Fig. 19).

TEIW enabled the direct embedment of a 3D fluorescent “grass” pattern within a bulk thermochromic pigment (TC-P)-doped support bath, creating a monolithic, dual-functional optical system. This one-step integration ensures fine interfacial contact between the hidden pattern and the responsive matrix. Upon gradient heating (28.4 °C–74.1 °C), the TC-P layer decolorizes from the top down, while UV light penetrates to reveal the progressively unmasked fluorescence from the embedded grass pattern (Fig. 6e, f). This spatially and thermally regulated transition demonstrated reversible encryption over 50 cycles (Supplementary Fig. 20), showing promise for high-grade anti-counterfeiting and confidential data display.

Methods
Materials
SE1700 and Sylgard184 were purchased from Dow Corning. Ecoflex 00-10, Ecoflex 00-30, Ecoflex 00-50, THIVEX, Silicone Thinner, and pigment were purchased from Smooth-on. Fumed silicone dioxide (15 nm), 1-ethynyl-1-cyclohexane (99%,) and tertiary butanol (GR, ≥99.5%) were obtained from Shanghai Macklin. Pluronic-F127 (Mw: ~12,600 g/mol) was purchased from Sigma-Aldrich, and UV-curing acrylic resin U10 was acquired from AILIKE. A platinum catalyst (Karstedt’s catalyst, Platinum(0)-1,3-diethenyl-1,1,3,3-tetramethyldisiloxane complex, Pt ~2000 ppm) was bought from Zhenjiang Jusheng New Energy Co., Ltd. Graphite conductive ink (DT-7837) was purchased from Taizhou Tongjie Technology Co., Ltd. A commercial microencapsulated thermochromic powder (leucodye-based) was obtained from Shenzhen Dongfang Jubao Industrial Co., Ltd. Fluorescent powder (SrAl₂O₄:Eu, Dy) was purchased from Tai’an Jinzhi New Materials Co., Ltd. All the chemicals were used as received.

Ink preparation
For silicone inks, an inhibitor composed of 1-ethynyl-1-cyclohexane and tertiary butanol in a weight ratio of 1:38.75 was used to extend the printing window to 48 h. For Ink-1, the SE1700 base was mixed with its curing agent at a weight ratio of 10:1, using a planetary mixer (SpeedMixer DAC 150.1 FVZ-K) at 2500 rpm for 3 min, then 1 wt% of inhibitor was added to the total mixture and mixed at 2500 rpm for 3 min. For Ink-2, 2 g of Ecoflex 00-30 Part B and 0.02 g of the inhibitor were mixed at 2500 rpm for 2 min. Then 0.2553 g of silica was added and mixed at 3000 rpm for 4 min. The mixed components were cooled in a refrigerator at -18 °C for 5 min. The same cooling process was repeated after each mixing step. Subsequently, 2 g of Ecoflex 00-30 Part A was added and mixed at 3000 rpm for 4 min. The mixture was blended three times, with cooling after each cycle.
For the sacrificial hydrogel ink, 3.33 g of PF-127 powder was dissolved in 10 ml of deionized water at 4 °C to prepare a 25 wt% solution, and restored to room temperature to achieve the corresponding hydrogel. The photocurable ink was prepared by mixing U10 and SE1700 (the base and curing agent pre-mixed at a 10:1 ratio as described above) in a weight ratio of 7:3 at 1600 rpm for 30 s. To enhance the visibility of print filament, 1 wt% of pigment was added to the total ink mixture after blending, and the mixture was then mixed at 2500 rpm for 3 min. For the conductive ink, no further treatment was performed. It was directly loaded into a black light-proof syringe. For the fluorescent ink, Sylgard 184 and its curing agent were first blended at a 10:1 weight ratio, and after adding 1 wt% of inhibitor to the total mixture, it was homogenized at 2500 rpm for 3 min. Subsequently, 6 wt% of silica was incorporated into the silicone mixture and mixed at 3000 rpm for 3 min three times, with the mixture being cooled in the refrigerator for 5 min after each mixing. Then, 1 wt% fluorescent powder was added, followed by three sequential mixing cycles at 2000 rpm for 30 s each. All the mixed inks were transferred to a 10 cc syringe and degassed at 2800 rpm for 3 min to remove air bubbles.

Bath preparation
For Bath-0, 10 g of Ecoflex 00-30 Part B and 0.1 g of inhibitor were mixed at 2500 rpm for 2 min. Then, 10 g of Part A and 0.2 g of THIVEX were mixed at 2500 rpm for 2 min. After carefully scraping the mixture remaining at the bottom of the mixing tank and on the walls with a spatula, the mixture was blended again at 2500 rpm for 3 min. Finally, the two mixtures were mixed at 3000 rpm for 3 min, with three cycles of mixing and cooling. For Bath-1, 10 g of Ecoflex 00-30 Part B and 0.1 g of inhibitor were mixed at 2500 rpm for 2 min, then 10 g of Part A was added and mixed at 3000 rpm for 3 min and cooled, then repeated twice. Bath-2 was prepared in the same procedure as Bath-1 using Ecoflex 00-10. For Bath-3, the base and curing agent of Sylgard 184 were mixed at a weight ratio of 10:1, then 1 wt% of inhibitor was added to the total mixture. The mixture was mixed at 3000 rpm for 3 min and cooled, then repeated twice. For the thermochromic support bath, Sylgard 184 base and curing agent were first mixed at a weight ratio of 10:1. Then, 0.5 wt% of THIVEX, 0.1 wt% of thermochromic powder, and 1 wt% of the catalyst were sequentially added and blended at 2500 rpm for 3 min. After all the support bath mixtures were completed, they were transferred to a customized acrylic container and vacuum degassed for 30 min.

Rheology
Rheological tests were performed using an Anton Paar MCR 302 rheometer at room temperature, equipped with a 25 mm diameter parallel plate geometry measurement system with a 1.0 mm gap between the parallel plates. The apparent shear viscosity was obtained by performing logarithmic scan steady state flow tests using angular frequency ranging from 0.1 to 100 rad/s. In the frequency scan tests, the storage and loss modulus of the materials were measured in the linear viscoelastic range, through an angular frequency range with a strain amplitude of 0.5%, from 0.1 to 10,000 rad/s. To characterize the yield stress of the support matrix, stress sweeps were performed from 0.1 to 100 Pa at an oscillatory frequency of 1 Hz.

3D printing
Direct ink writing was performed on a dispensing system (F4200N.1 Compact Benchtop Robot). The extrusion pressure was controlled by a DC 200 digital dispenser (Fisnar) with a vacuum compression pump, and the pressure was set at 10 psi-80 psi. Stainless-steel nozzles with inner diameters of 160, 210, 420, 520, and 610 µm was used. The printing speed was set at 1–20 mm/s, depending on the properties of the material and the requirements of the print pattern. During the printing process, the nozzle was immersed in a support bath at a depth of ~3 mm. After printing, the nozzle was removed from the support bath at a speed of 1 mm/s. The whole process was carried out at room temperature.
After 3D printing and transformation of the architecture, the system underwent solidification. For silicone elastomer systems, immediate thermal curing was conducted using a 250 W infrared lamp positioned 10 cm vertically above the support bath. Complete crosslinking of both ink and bath was achieved within 10 min.
The channeled system was printed using a needle with an inner diameter of 420 µm, at a printing pressure of 40 psi and a printing speed of 1 mm/s, to extrude the PF-127 hydrogel into the Sylgard 184 support bath. The curing protocol was then applied in the same manner as for silicone elastomer systems. Then, samples were immersed in an ice-water bath for 5 min to liquefy the sacrificial hydrogel. The liquefied ink was then removed via aspiration, followed by three rinsing cycles with ice-cold water.
For the UV photocurable systems, the photocurable ink, prepared by mixing U10 and SE1700 (the base and curing agent pre-mixed at a 10:1 ratio as described above) in a 7:3 weight ratio, was extruded into the Sylgard 184 support bath. Using a needle with an inner diameter of 520 µm, the ink was printed at a pressure of 20 psi and a printing speed of 5 mm/s to print the designed 2D pattern. For solidification, the bath system was placed in a UV curing chamber (3535KXD, UVGO) and exposed to 365 nm, 240 W ultraviolet light for 15 s. The cured 3D architectures were then extracted from the support bath, wiped with a lint-free wipe to remove residual bath material, and cleansed with an anionic surfactant-based detergent solution.
The conductive system used graphite conductive ink printed into the Sylgard 184 support bath that additionally contains 1 wt% platinum catalyst. A needle with an inner diameter of 210 µm was used to print a planar spiral with a minimum radius of 18 mm, a maximum radius of 2.5 mm, and consisting of 3 turns. The printing process was conducted at a printing speed of 4 mm/s and a pressure of 10–40 psi. After 3D printing and shape transformation, the structure was immediately thermally cured using a 250 W infrared lamp positioned 10 cm vertically above the support bath. The crosslinking of the support bath was completed within 1 min, and the conductive ink solidified through solvent evaporation.
For dual-material printing, PF-127 sacrificial ink was first extruded through a 210 µm inner diameter nozzle under 40 psi to construct 3D helical scaffolds with a uniform radius of 10 mm, a height of 6 mm, and four turns within the support bath. Subsequently, graphite conductive ink was extruded through a 160 µm nozzle with a dispensing pressure of 20 psi−50 psi, forming a planar spiral with an outer radius of 7 mm, an inner radius of 1.5 mm, and three turns, at a depth of 2 mm in the support bath. After 1 min, the planar spiral configuration spontaneously transformed into a 3D architecture driven by the density contrast. The solidification and removal of the sacrificed ink followed the protocol mentioned above.
For the encrypted system, a 3D biomimetic “grass” structure comprising five radially arranged blades was printed, using the fluorescent ink within a Sylgard 184 support bath containing thermochromic pigments. Each blade was 6 mm long and presented a 72° outward inclination angle from the central axis. The printing used a 210 µm inner diameter nozzle and 4 mm/s speed, with varying pressures of 20 psi, 20 psi, 20 psi, 30 psi, and 40 psi for each blade. After printing, the support bath was infrared cured following the same curing steps as for Sylgard 184.
The detailed 3D printing settings are provided in Supplementary Data 1.

Imaging
The position variations of the filaments and the structure transform process were recorded by an industrial camera (Basler ace acA800-510uc) installed on the side of the printer. Imaging was performed with an optical magnification of 20× using a macro lens configuration. To minimize the inaccuracy caused by the disturbance generated by the nozzle entering and leaving the support bath process, each filament was printed 3 times, and the middle section of the print filament was recorded. Images were captured at 1 min intervals. The ImageJ software was used to measure the diameter of print filaments and the deviation. Data are presented as mean ± SD. Due to the high reproducibility, error bars may be smaller than the symbols. Full statistical data are available in the Supplementary Information. Printed filament cross-sections were obtained by slicing with a blade, imaged, and analyzed by optical microscopy (Eclipse Ni-U, Nikon).

Physical properties measurement
The density of all inks and support baths was measured using a densitometer (SJ-300GY, Shuju), with three measurements conducted for each sample (5 g per measurement).
The electrical resistance was measured by using a digital source meter (Keithley 2450) with a four-probe configuration. Copper wires (diameter: 100 µm) were inserted into the two terminals of the conductive structure, forming a closed circuit with an LED bulb powered by a programmable DC power supply (Zhaoxin RXN-305D). For the encrypted visualization, the sample was heated on a hot stage from 28.4 °C to 74.1 °C to realize a visible chromatic transition. Then the illuminated patterns were observed under UV light (365 nm) in complete darkness. Surface temperature was recorded by an infrared thermal imager (E6390, FLIR).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "(1) Figure 1 summarizes the proposed mechanism of the TEIW strategy, but several technical inconsistencies require clarification. In Figure 1b, the authors state that in conventional embedded printing, the ink typically exhibits a higher storage modulus (G′) than loss modulus (G″), and that the ink has a higher shear modulus than the support bath. This generalization lacks supporting rheological data or references and should be substantiated. More critically, in Figure 1c, the differentiation among segments Q1–Q4 is attributed to variations in net force, yet the schematic does not clarify whether these differences stem from ink density, filament radius, or segment length. Given the apparent geometric similarity and assuming constant density, Q1 should also undergo downward motion, contradicting what is shown in the illustration. Furthermore, in Figure 1d(iv), the light blue helical filament appears identical to that in (iii), but its interpretation is ambiguous. Does it represent a newly printed ink deposited after sacrificial material removal? If so, the figure should be redesigned to clearly indicate the sequential steps and materials involved. Without explicit clarification, such illustrations may mislead readers.\n(2) The figures in the manuscript require several adjustments to improve clarity. For example, in Figure 2, the font size of axis tick values and in-figure annotations (e.g., G′ink) is too small to be clearly legible, and no error bands are shown in the line plots.\n(3) It is suggested that Figures 3c–e be moved to the Supporting Information, as they do not appear central to the main conclusions.\n(4) The formation of the DNA-like double-helix structure in Figure 4b is unclear. Based on the 2D pattern shown in Figure 4b(i), it is not evident how the two sugar-phosphate-like backbones—analogous to those in DNA—are generated.\n(5) The Introduction highlights geometric fidelity and nozzle-induced disturbances as major challenges in embedded printing, but the current study does not appear to address these issues directly. Please clarify the relevance of these points to the presented approach.\n(6) The term \"equilibrium depths\" mentioned in line 66 is unclear. Does it refer to the point at which the filament reaches mechanical force balance? Will the filament remain stationary afterward? Please clarify what causes this equilibrium state and what subsequent behavior the filament exhibits.\n(7) In line 169, the mention of shear-thinning fluids appears to refer to the SE 1700 ink, as the Ecoflex 00-30 bath behaves as a Newtonian fluid based on the presented rheological data. Moreover, filament distortion in embedded printing is typically attributed to localized liquefaction and backflow of the supporting bath induced by nozzle movement. Please provide theoretical justification for the statement that “this instability mechanism stems from incomplete stress dissipation.”\n(8) The manuscript does not report the density of Pluronic F127 in Figure 6, making it unclear whether the filament rises or sinks within the PDMS bath. Additionally, what is the crosslinking time of the PDMS bath, and does the F127 filament continue to move during this period? Please add these key parameters near the relevant results section to improve readability.\n(9) In line 282, the term \"silicone support bath\" is mentioned—does this refer to PDMS? Is it the same support material used for the multi-material printing shown later? If so, why does the Pluronic F127 filament deform in Figure 5 but not in the 3D channel shown in Figure 6? Additionally, the rationale for adding spiral channels around the conductive circuits is not explained. What functional role do these surrounding channels play, and what is the intended application of this structure? Overall, the manuscript is loosely organized, requiring readers to frequently cross-reference earlier sections to identify materials and parameters. Reorganizing the text could substantially improve clarity and readability.\n(10) All printed examples are based on 2D filament layouts followed by shape transformation. Please clarify whether this method is capable of producing fully volumetric multilayer 3D structures, such as cubes or spheres.\n(11) Would it be more appropriate to retitle the section in lines 330–339 as “Conclusion”?", "reviewer_2": "1. The authors claimed that conventional EIW struggles with printing intricate 3D geometries, particularly intersecting and overlapping paths. However, the existing path-design strategy (DOI: 10.1126/science.adj6152) has already addressed these issues. How does the proposed method demonstrate advantages over these existing strategies, and what evidence supports these advantages?\n2. While the authors have elucidated rheological differences between conventional EIW and the proposed TEIW method, comparative demonstrations of efficiency and fidelity are missing. It is recommended to print identical structures using both techniques and measure differences in fabrication time and structural accuracy.\n3. The paper employs distributions of pressure and path speed to control the settling positions of printed structures, resulting in variable filament diameters as illustrated in Fig. 3. If specific channel diameters are required to realize functions, such as actuator chambers in robotics or biomimetic vascular systems, how would the proposed method reliably achieve these precise dimensions?\n4. Regarding the printing of spherical structures, how can this geometry be fabricated effectively using the proposed approach?\n5. The paper emphasizes gravity and buoyancy imbalance as key factors for accurate deposition of 2D patterns. However, additional phenomena, such as bubble formation during nozzle movement, dynamic flow behaviors induced by velocity fields (DOI: 10.1021/acsami.7b19818), and viscous stresses (DOI: 10.1126/sciadv.1500655), should also be examined to comprehensively understand the deposition mechanism.\n6. Given that deposition distance depends not only on velocity but also on duration, printing complex 2D patterns requiring extended fabrication times might lead to mismatches in final settling positions. It is recommended that authors explore the operational window of their method and provide strategies for effective time management to ensure accurate deposition for arbitrary geometries.\n7. To strengthen the current demonstrations provided in Fig. 4, a fidelity analysis comparing the printed structures against the intended design models along the z-axis would significantly enhance the manuscript.\n8. To ensure reproducibility, the authors should clarify the statistical methods used in rheological characterization and parameter control sections, specifying how reliability and repeatability were assessed.", "reviewer_3": "1) The introduction provides a brief overview of the method, the limitations and the research gaps. It is recommended that the authors revise the introduction to better highlight the state-of-art of the work. More details could be given on the extrusion-based techniques and their limitations and how the EIW technique overcomes the limitations. Also, discuss the important parameters in the EIW technique that affect the process (e.g., ink rheology, the ink-bath interactions) and how the proposed TEIW resolves these issues. Citing more references will create a more comprehensive literature review.\n2) It is suggested to include the microscopic images of the ink filaments (Figure 2, supplementary file) in the main text. I would suggest grouping with Figure 7 as they represent the outcome of the observed rheological behavior.\n3) In Figure 3, please revise the figure caption and add a few annotations to the panels (c), (f), (g) and (h) for better understanding of the reader. For example, in panels (g) and (h), the concept of blue and green plots is unclear to the reader.\n4) As there are various inks used in this study, it would be better to consistently label all the graphs with the specific ink system. This would make it easier for the reader to follow the results without needing to cross-reference the text.\n5) In section “3D structural construction” the results are pretty descriptive, please describe the more complex mechanical transformation happening in different structures (e.g., such as in tetrahedron) in more detail. I would suggest summarizing the key points from “Deformation-Dependent Deposition Behavior of Heterogeneous Filaments” section of the supplementary material to provide a detailed explanation on the mechanisms. Also, it is recommended that the authors incorporate a summary of the key findings from Supplementary Figure 11 into the main results section.\n6) It is suggested to include Supplementary figure 1 regarding the ink and bath rheology in the main text to better support the discussion and the findings related to the material behavior.\n7) Please provide a clearer explanation on how the Time-dependent vertical displacement profiles, z-positions and other experiments were used to design the printing process parameters. Please explain the importance of these experiments for designing the process.\n8) Please add a short description of the rheology results and their importance in the conclusions sections."}, "author_response": "We thank the reviewers for your valuable comments and suggestions. In response, we have\nreorganized the structure and refined the language of the manuscript to better highlight the novelty of our\nwork. Specifically, the Introduction has been rewritten to more clearly articulate our contributions.\nThere are several improvements we want to mention in addition to the point-by-point response.\n The term F has been replaced with F to unambiguously denote the driving force for filament\nnet drive\nmotion, avoiding potential confusion with the total net force in the system.\n The description \"Newtonian fluid\" has been updated to \"Newtonian-like fluid\" to more accurately\nreflect the rheological behavior that the support bath exhibits under our operating conditions.\n We have added a perspective to the Conclusion on extending this work by incorporating multi-\nphysics simulations, predictive computational algorithms and a multi-inlet system for real-time\ndensity control in the future.\nThe point-by-point response is as follows.\nComments from Reviewer #1\nThis manuscript presents a transformable embedded ink writing (TEIW) strategy that enables the rapid\nself-assembly of 2D-printed patterns into predefined 3D architectures. The core innovation lies in\nreplacing the conventional yield-stress supporting bath with a Newtonian fluid, addressing a previously\nunderexplored niche in embedded printing. By leveraging programmable ink–bath density mismatch, the\nauthors demonstrate control over filament motion in the supporting medium. Although the study is\nreasonably complete, several aspects require clarification and revision. I recommend major revision.\nSpecific comments are provided below.\n(1) Figure 1 summarizes the proposed mechanism of the TEIW strategy, but several technical\ninconsistencies require clarification. In Figure 1b, the authors state that in conventional embedded\nprinting, the ink typically exhibits a higher storage modulus (G′) than loss modulus (G″) and that the\nink has a higher shear modulus than the support bath. This generalization lacks supporting rheological\ndata or references and should be substantiated. More critically, in Figure 1c, the differentiation among\nsegments Q1–Q4 is attributed to variations in net force, yet the schematic does not clarify whether these\ndifferences stem from ink density, filament radius, or segment length. Given the apparent geometric\nsimilarity and assuming constant density, Q1 should also undergo downward motion, contradicting what\nis shown in the illustration. Furthermore, in Figure 1d(iv), the light blue helical filament appears\nidentical to that in (iii), but its interpretation is ambiguous. Does it represent a newly printed ink\ndeposited after sacrificial material removal? If so, the figure should be redesigned to clearly indicate the\nsequential steps and materials involved. Without explicit clarification, such illustrations may mislead\nreaders.\nResponse:\nThank you for your comments. We acknowledge the need for clarity and have revised the figure and text\naccordingly. Here, we address each concern:\n(ⅰ) Regarding the rheological supporting references\nWe have now revised the text to more precisely reflect the well-established rheological\nrequirements for conventional EIW. The assertion that, in conventional EIW, the ink typically possesses\na higher storage modulus (G′) than loss modulus (G″) and a higher shear modulus than the support bath\nspecifically pertains to systems employing yield-stress fluid baths. This principle was first rigorously\nestablished in the seminal work by Lewis and colleagues (ACS Appl. Mater. Interfaces 2018, 10, 23353-\n23361), which states: “First, the ink must be a shear-thinning yield stress fluid that controllably flows\nout of the print nozzle when a specified pressure is applied. Qualitatively, inks possess a shear elastic\nmodulus, G ′, and yield stress, τ , that are approximately an order of magnitude larger than those of\nink y,ink\nthe matrix, G ′ and τ , respectively, as reported previously.” And “The matrix materials must also\nmatrix y,matrix\nconsist of shear-thinning, yield stress fluids, which possess a sufficiently high G ′ to support the\nmatrix\nprinted structures and a τ that is low enough to allow the translating nozzle to move freely\ny,matrix\nthroughout the matrix.”\nThis foundational requirement has been consistently validated and summarized in subsequent\nreviews. For instance (ACS Biomater. Sci. Eng. 2021, 7, 4736-4756): “Structured fluids usually have\ntwo states: (1) a solidlike state when shear stress applied is lower than the material’s yield stress; (2) a\nliquid state when the fluids experience a high shear stress…. As a result, structured fluids have become\nthe mainstream bath materials for both e-3DP and support bath-enabled 3D printing.”\nFurthermore, a very recent review by Thareja et al. (Curr. Opin. Colloid Interface Sci. 2025,77,\n101918) re-emphasizes that for bio-inks to be printable into a yield-stress bath, they must satisfy G′ >\nink\nG′ to locally fluidize the bath while maintaining structural integrity. It is further supported by other\nbath\nkey references in the field (Biomed. Eng. Lett. 2020, 10, 453–479; Matter 2024, 7, 668–684).\nWe have amended the manuscript to clarify this context and have added these key references.\nRevised Texts in Page 3:\n“In CEIW, the support bath exhibits shear-thinning behavior, which flows under nozzle-induced shear\nstress and behaves as a solid once the stress is removed. Its pairing with higher yield-stress inks enables\nthe maintenance of filament geometry and position, wherein the bath’s yield stress defines the maximum\nforce exerted on the ink filaments17,18,23,25,30.”\n(ⅱ) Regarding Fig. 1c\nIt is correct that with a constant ink density, all segments (Q -Q ) should experience a downward\n1 4\nnet force. The key differentiating factor is indeed the filament radius. The variation in flow rate (Q < Q\n1 2\n< Q < Q ) is achieved by adjusting the printing speed, which directly results in filaments with different\n3 4\ndiameters. The segment with the smallest flow rate (Q ) has the smallest filament radius and thus the\n1\nsmallest driving force for descent. To address this directly, we have revised Fig. 1c. The icons for\nsegments Q -Q are now drawn with visibly different diameters to accurately represent their physical\n1 4\ndistinction. Arrowed trajectories have been added to the top-view schematic to clearly indicate the\ndirection of printing. In the distance-time plot, we have added contour lines to show that all segments,\nincluding Q , migrate downward over time.\nThe main text has been amended to state: “For example, continuously extruding a high-density ink (ρ >\nink\nρ ) horizontally into a Newtonian-like bath with varying volumetric flow rates (Q < Q < Q < Q )\nbath 1 2 3 4\nproduces four distinct segments with differential axial weight distribution (Fig. 1c).”\n(ⅲ) Regarding Fig. 1d(iv)\nWe change the expression from “multi-printing” to “hybrid printing”, which refers to the\nintegration of distinct stabilization and deposition mechanisms within a unified process, rather than the\nuse of multiple materials or separate support baths. In the revised Fig.1d(iv) and accompanying text, we\ndemonstrate that the first ink is designed and printed such that it is stabilized in situ. This is achieved\nthrough a combination of its fine diameter (resulting in a negligible net buoyancy-gravity force, F ≈\ndrive\n0), its intrinsic rheology, and the viscous drag of the bath. This embodies the principle of direct writing\nand stabilization, akin to conventional EIW. The second ink is deposited with different parameters (e.g.,\nlarger diameter, higher density) so that it experiences a significant non-zero F . It then undergoes\ndrive\nautonomous shape transformation via the TEIW mechanism, navigating around or through the pre-\ndeposited, stabilized structure of the first ink. Both mechanisms, direct stabilization and autonomous\ntransformation, are realized within the same support bath. This simultaneous use of two physical\nprinciples for patterning different materials in 3D space is one of the highlights of our work. It allows for\nthe creation of complex, multi-functional architectures in a monolithic process.\nTo eliminate ambiguity, we revised the schematic coloration to distinguish individual ink\ncompositions, and revised the text to show the essence of the \"hybrid printing\" methodology. Fig. 1d(iv)\nnow clearly features two distinct filament colors, representing two different inks. Numbered steps (Step\n1, Step 2) have been added to explicitly indicate a two-step sequential process. In Step 1, the ink (e.g.\nstructural hydrogel) is deposited analogous to conventional EIW processing. Step 2: A functional ink\n(e.g., conductive elastomer) is deposited via the TEIW method, where it undergoes autonomous 3D\ntransformation around the scaffold created in Step 1.\nWe have revised the manuscript to make this explanation clearer and appreciate the opportunity to\nhighlight this aspect of our work. The detailed experiments are illustrated in Fig. 6b and corresponding\ntext in Page 16, Para 2.\nRevised Texts in Page 4:\n“(ⅳ) Hybrid printing: This modality relies on the coexistence of different stabilization mechanisms within\na single bath. A fine-scale ink (e.g., hydrogel) is first deposited and stabilized in situ, analogous to CEIW\nprocessing, owing to its minimal buoyancy-gravity forces and intrinsic rheology. Subsequently, a second\nink (e.g., conductive elastomer) with tailored properties to undergo programmed TEIW is deposited,\nwhich autonomously assembles around or within the pre-formed structure. This approach enables the\nseamless integration of different materials and printing mechanisms without requiring bath exchange or\ncomplex sequential processing.”\nThe revised Fig.1 is as follows.\nFig. 1 Conceptual illustration of the TEIW. a Schematic illustration of the TEIW platform. b\nRheological comparison between (i) CEIW and (ii) TEIW, with their relative position evolvement. c\nDynamic 2D-to-3D self-assembly driven by buoyancy-gravity interplay, where the moving distance is\ncontrolled by the volumetric flow rates. d Printing modalities enabled by TEIW: (i) freestanding\nstructures via bath removal, (ii) integral structures through co-curing, (iii) hollow architectures using\nsacrificial inks, (ⅳ) hybrid printing of multi-materials via sequential steps.\n(2) The figures in the manuscript require several adjustments to improve clarity. For example, in Figure\n2, the font size of axis tick values and in-figure annotations (e.g., G′ink) is too small to be clearly legible,\nand no error bands are shown in the line plots.\nResponse: Thank you for your comments. We have revised Figure 2 accordingly.\nThe font sizes of all axis labels, tick values, and in-figure annotations have been increased to ensure\nclear legibility.\nFig. 2 Vertical displacement of ink filaments as a function of material properties. Each row, from\nleft to right, sequentially presents time-dependent vertical movement of the ink filament, shear stress-\nshear rate curve of the bath with inset SEM images of the filament cross-sections (scale bar: 100 μm),\nmodulus curves for ink and bath, and density of the materials. The ink-bath pairs are a Ink-1, Bath-0,\nb Ink-2, Bath-1, c Ink-1, Bath-2, and d Ink-1, Bath-3.\nError bars were represented in all relevant line plots, however, due to the low variability (SD = 0.6–\n5% of means), the error bars are often smaller than the plot symbols and may not be fully visually\napparent in the figure at its current scale. The complete statistical dataset, including all exact mean and\nstandard deviation values, is provided in the Source data File.\nTo clarify this to readers, we added the following demonstration in Methods, Section Imaging.\n“Data are presented as mean ± SD. Due to the high reproducibility, error bars may be smaller than the\nsymbols. Full statistical data are available in Supplementary Information.”\n(3) It is suggested that Figures 3c–e be moved to the Supporting Information, as they do not appear\ncentral to the main conclusions.\nOur Response: As suggestion, Figs. 3c-e along with Fig.3b are relocated to the Supporting Information\n(now Supplementary Fig. 10), retaining a concise reference in the main text to ensure data continuity.\nRevised Texts in Page 9:\n“Experiments using a 610 µm nozzle and Ink-1/Bath-1 as a model system showed that the filament\ndiameter increased from 360 µm to 600 µm as P was raised from 40 to 80 psi at a constant v of 5 mm/s\n(Fig. 3a,b and Supplementary Fig. 10a,b). Conversely, at a fixed P of 60 psi, decreasing v from 13 to 3\nmm/s resulted in a diameter increase from 400 to 620 µm. These results are consistent with the theoretical\nframework. Since the terminal velocity v∝d2, this ability to precisely control diameter via P and v\nt\nprovides direct regulation over the kinematic behavior of filaments (Supplementary Fig. 10c,d), enabling\nprogrammable 3D transformation without the need for mechanical nozzle changes.”\nSupplementary Fig. 10 a Relationship of filament diameters with extrusion pressure and printing speed\n(nozzle diameter 610 μm). b Filament diameter versus volumetric flow rate. c Experimental and\ntheoretical terminal velocity (v) of Ink-1 filament as a function of volumetric flow rate (Q) in Bath-1.\nt\nSolid lines represent model predictions from Eq. (3). As C was set to 0.84, a correlation coefficient\nconst\nof 0.97 was obtained, with a p-value of <0.001, confirming a strong linear relationship. d v vs. Q for\nt\nInk-1 in a lower viscosity bath (Ecoflex 00-30+5 wt% Thinner). With C maintained at 0.84, the\nconst\nresulting correlation coefficient was 0.88, with a p-value of <0.001. The increased slope demonstrates\nthat reducing bath viscosity accelerates the shape transformation kinetics, as predicted by the inverse\ndependence of v on bath viscosity (η).\nt\n(4) The formation of the DNA-like double-helix structure in Figure 4b is unclear. Based on the 2D pattern\nshown in Figure 4b(i), it is not evident how the two sugar-phosphate-like backbones—analogous to those\nin DNA—are generated.\nResponse:\nWe have revised the schematic in Figure 4b (now moved to Fig.4c) and the manuscript to explain this\nmechanism more clearly. The double-helix is not pre-deposited as two separate backbones. Instead, it is\nformed from a single, continuous filament printed in a serpentine 2D pattern. The transformation is driven\nby programmed, alternating differences in the local filament diameter along its length. During printing,\nthe moving speed (v) and extrusion flow rate (Q) are modulated with the serpentine path. This creates\nsegments with a larger diameter ( ~600 µm) adjacent to segments with a smaller diameter (~350 µm) on\nthe opposite side. As established by Eq. 1, the driving force (F ) is proportional to the square of the\ndrive\nfilament radius (F ∝ d²). Therefore, the thicker segments (blue) experience a significantly larger\ndrive\ndownward force than the thinner segments (gray). This differential in F creates a bending moment\ndrive\n(torque) at each junction between a thick and thin segment. The high-force segment sinks, while the low-\nforce segment provides resistance, causing the entire structure to twist at these junctions to relieve the\nmechanical stress. Since the diameter modulation is alternated systematically, the direction of the\ntwisting torque also alternates. This sequential, counter-rotational twisting along the continuous filament\nleads to the emergent, spontaneous self-assembly of the global double-helical structure.\nWe have expanded the explanation in the main text and have revised the schematic panel to visually\nillustrate this step-by-step transformation process from the 2D pattern to the 3D helix more clearly. The\nrevised figure is as follows.\nRevised Texts in Page 12:\n“Dual helical structures were realized by printing a continuous filament in a serpentine pattern with\nprogrammed flow rate variations (Fig. 4c). Each section of the pattern exhibited a high-flow side (blue)\nand a low-flow side (gray), and adjacent sections had this orientation reversed. During transformation,\nthe high-flow side descended faster, thereby generating a localized torque at the junctions and lifting the\nlow-flow side upward. The systematic reversal of the force gradient along the path caused these torques\nto alternate in direction, prompting the entire structure to twist and coil into a stable, double-helical\nmorphology. The rapid self-assembly (≤10 s) demonstrates programmable kinetic control through\nfilament-level force modulation.”\n(5) The Introduction highlights geometric fidelity and nozzle-induced disturbances as major challenges\nin embedded printing, but the current study does not appear to address these issues directly. Please\nclarify the relevance of these points to the presented approach.\nResponse:\nTo address these issues, we have rewritten the Introduction to clarify how the TEIW approach addresses\nthe challenges of geometric fidelity and nozzle-induced disturbances.\nThe core of our strategy is that it decouples the act of printing from the act of 3D structure formation.\nIn conventional embedded ink writing, the nozzle must physically trace out the entire 3D path, making\nfidelity and nozzle interference intrinsic problems. In contrast, TEIW uses the nozzle only to deposit a\n2D precursor pattern. The final 3D geometry is achieved through a subsequent, nozzle-free, self-\nassembly process driven by gravitational-buoyancy forces in a low-viscosity bath. Therefore, the\nmechanical disturbances caused by a nozzle moving through a yield-stress bath near previously printed\nfilaments are entirely avoided in TEIW because the nozzle is retracted and inactive before the\ntransformation begins.\nAs for enhancement of geometric fidelity, TEIW enables precise control over final 3D positions, as\nquantitatively demonstrated by the high z-axis fidelity (86.48%–98.16%) achieved across various\nstructures (Supplementary Fig. 16a). A direct comparison between the TEIW and CEIW fidelity is now\nadded in Supplementary Fig. 16b-d, showing that the TEIW printed 3D structures exhibit superior fidelity.\nThe experimental results throughout the manuscript serve as direct evidence that our approach\nsuccessfully mitigates these issues.\nSupplementary Fig. 16 Printing fidelity. a Z-axis fidelity of the 3D structures. b-d Comparisons\nbetween conventional CEIW and TEIW method for b the tetrahedral frame, c the branched vascular\nnetwork, and d the flower pattern. For each structure, (i) and (ii) show the top and side views of the print\nfabricated by CEIW, respectively. (iii) Comparison of the XY and Z directional fidelity between TEIW\n(blue) and CEIW (gray). The CEIW process was conducted in a yield-stress bath (Sylgard 184:1700, 7:3\nweight ratio) using the same printing parameters as TEIW. The as-printed structures via CEIW show\nsignificant fidelity loss, particularly at path crossings, under high printing speeds, and in regions\nrequiring repeated nozzle passes.\nRevised text in Page 3, Introduction section:\n“TEIW operates within a Newtonian-like fluid support bath, which reduces the strictness of rheological\ncompatibility requirements in conventional ink-bath systems. Once the ink is released from the nozzle,\nTEIW circumvents the structural height limitations imposed by nozzle length and avoids the need for\ncomplex 3D trajectory control. Moreover, the self-assembly nature of the process inherently avoids\ndistortions caused by nozzle interference.”\nRevised text in Page 12:\n“The z-axis fidelity of the above structures was quantified by comparing the as-printed heights with\nthe theoretical depths predicted by Eq. (3) for straight filaments, yielding values from 86.48% to 98.16%\n(Supplementary Fig. 16a). The observed variance stems from geometric and interfacial factors beyond\nthis simplified model. For a direct comparison, 3D structures were also printed using the conventional\nEIW method in a reported yield-stress support bath25 (Supplementary Fig. 16b), whereas TEIW\ndemonstrated higher geometric accuracy while maintaining a comparable preparation time\n(Supplementary Fig. 17).”\n(6) The term \"equilibrium depths\" mentioned in line 66 is unclear. Does it refer to the point at which the\nfilament reaches mechanical force balance? Will the filament remain stationary afterward? Please\nclarify what causes this equilibrium state and what subsequent behavior the filament exhibits.\nResponse:\nWe apologize for the confusion caused by our use of the term \"equilibrium depths\" as this term implies\na mechanical force balance which is not the primary stopping mechanism in our process. However. the\nintended meaning is the pre-programmed target depth for each filament segment. The filament does not\nstop sinking due to the balance of gravity, buoyancy, and drag alone. It would continue to move at its\nterminal velocity indefinitely in a liquid bath. The process is instead actively halted by a rapid, user-\ninitiated solidification trigger (e.g., IR-induced thermal curing, or photoinitiation) which is applied once\nthe filament is estimated to have reached its predetermined target position. The solidification process is\nsufficiently fast to immobilize the structure effectively and preserve the designed 3D architecture.\nWe have revised the manuscript to remove the term \"equilibrium depths\" and to provide a more\naccurate description of this controlled solidification process. Thank you for prompting this critical\nclarification.\nRevised Texts in Page 4:\n“Over time scales of seconds to minutes, these segments migrate to their target depths, guided by their\nrespective F , to self-assemble into the desired 3D architectures. This transformation is then rapidly\ndrive\nstabilized (typically within a minute) by initiating solidification via IR-induced thermal curing or\nphotoinitiation, effectively locking the structure in place.”\n(7) In line 169, the mention of shear-thinning fluids appears to refer to the SE 1700 ink, as the Ecoflex\n00-30 bath behaves as a Newtonian fluid based on the presented rheological data. Moreover, filament\ndistortion in embedded printing is typically attributed to localized liquefaction and backflow of the\nsupporting bath induced by nozzle movement. Please provide theoretical justification for the statement\nthat “this instability mechanism stems from incomplete stress dissipation.”\nResponse: The mention of shear-thinning in line 169 indeed refers specifically to SE 1700 ink, while the\nEcoflex 00-30 bath is Newtonian fluid as noted. We also agree that in conventional embedded printing\nin yield-stress fluids, filament distortion is often attributed to bath liquefaction and backflow.\nHowever, the curling instability we describe here originates from the intrinsic rheological response\nof the shear-thinning ink itself under non-optimal printing conditions. Shear-thinning inks like SE 1700\npossess a polymer network that breaks down under applied shear stress (inside the nozzle) and\nsubsequently recovers when the stress is removed. This recovery is not instantaneous. It is governed by\na characteristic stress relaxation time.\nWhen the extrusion pressure is too low, the shear stress applied may be insufficient to fully fluidize\nthe ink or to maintain a stable, continuous extrusion. As the imperfectly relaxed ink exits the nozzle,\nelastic recovery and non-uniform structural reformation can cause the filament to buckle or curl\nimmediately upon deposition, rather than forming a straight segment.\nWhen the nozzle speed is too high, the time available for the ink to experience shear within the\nnozzle is reduced. The ink exits the nozzle in a highly sheared, fluidized state but is deposited so rapidly\nthat it does not have sufficient time to recover its network and regain yield stress before the moving\nnozzle ceases to provide confinement. This leads to a lack of shape retention in the freshly deposited\nfilament, causing it to deform under its own weight or residual stresses, manifesting as curling.\nIn both scenarios, the core issue is a mismatch between the timescales of the printing process and\nthe ink's intrinsic rheological timescales (for relaxation and recovery). This is distinct from the bath-\ninduced instabilities common in yield-stress supports. We have revised the manuscript to clarify this\npoint and better emphasize the role of the ink's rheology and included additional references.\nRevised Texts in Page 9:\n“This instability arose from the ink’s inability to fully recover its microstructure after rapid shear\nthinning37. The Newtonian-like bath, lacking a yield stress, did not provide any stabilizing confinement,\nthereby allowing this inherent ink instability to appear as free-form curling. Notably, switching to a finer\nnozzle within the same ink-bath system produced thinner filaments that exhibited reduced disturbance\nand improved stability (Supplementary Fig. 11) 38.”\n(8) The manuscript does not report the density of Pluronic F127 in Figure 6, making it unclear whether\nthe filament rises or sinks within the PDMS bath. Additionally, what is the crosslinking time of the PDMS\nbath, and does the F127 filament continue to move during this period? Please add these key parameters\nnear the relevant results section to improve readability.\nResponse:\nWe thank the reviewer for these critical questions, which have helped us improve the clarity of our\nmanuscript. The density of the Pluronic F127 ink is 1.020 g/cm³. The density difference with the PDMS\nsupport bath (0.966 g/cm³) is Δρ = +0.054 g/cm³. This positive value confirms that the filament sinks\nwithin the bath. We have now added this key parameter in the relevant results section (Page 14) with the\nstatement “With a density of 1.020 g/cm³, the ink sank and formed the 3D structure within 120 s.” This\ninformation is now also included in Table 1. The density contrast between the sinking PF-127 filament\nand the support bath is further illustrated in Fig. 5d(ii) as follows.\nTo address the question on crosslinking time and filament motion, we have performed additional\ncrosslinking kinetics experiments, now provided as Supplementary Fig. 12. This figure clearly shows the\ntemporal evolution of the PF-127 filament displacement until solidification is complete. The results\nindicate that the pure PDMS support bath fully crosslinks under infrared (IR) light heating within 3\nminutes, while the addition of 1 wt% platinum catalyst reduces the IR-induced crosslinking time to 1\nminute. In both cases, the printed filament exhibited continuous sinking motion throughout the entire\nperiod prior to solidification. Importantly, in the system with the catalyst, the total displacement is limited\nto approximately 130 μm. This predictable and small deviation can be effectively compensated for by\nstarting the irradiation slightly ahead of the target deposition point, thus ensuring high printing precision.\nSupplementary Fig. 12 Filament sinking behavior and crosslinking kinetics under different\nsupport bath conditions. a Silicone bath with 1 wt% catalyst cured in 1 min, b pure support bath cured\nin 3 mins after infrared irradiation. For each condition: (i) sinking distance of the PF-127 filament over\ntime, (ii) optical images captured during the sinking process, and (iii) state evolution of the support bath\nat different time points. The printed filament underwent continuous motion throughout the entire duration\nprior to solidification of the bath. To compensate for such displacement, initiating solidification by a time\ninterval corresponding to the sinking velocity would be an effective approach.\n(9) In line 282, the term \"silicone support bath\" is mentioned—does this refer to PDMS? Is it the same\nsupport material used for the multi-material printing shown later? If so, why does the Pluronic F127\nfilament deform in Figure 5 but not in the 3D channel shown in Figure 6? Additionally, the rationale for\nadding spiral channels around the conductive circuits is not explained. What functional role do these\nsurrounding channels play, and what is the intended application of this structure? Overall, the\nmanuscript is loosely organized, requiring readers to frequently cross-reference earlier sections to\nidentify materials and parameters. Reorganizing the text could substantially improve clarity and\nreadability.\nResponse:\nWe have extensively reorganized the manuscript to improve its clarity, as detailed in the points below.\n(ⅰ) Yes, the \"silicone support bath\" consistently refers to the polydimethylsiloxane (PDMS)-based bath\nthroughout the manuscript. It serves as the universal support material for all experiments, including the\nmulti-material printing.\n(ⅱ) The apparent difference in filament deformation is primarily governed by the filament diameter,\nwhich dictates the sinking kinetics. The PF-127 hydrogel filament in Fig. 5, printed with a 420 μm nozzle,\n(diameter range: 710–1010 μm), sinks rapidly and deforms visibly. In contrast, the structure in Fig. 6 was\nprinted with a 210 μm nozzle, yielding a thinner filament (~480 μm) with extremely low sinking kinetics.\nTo explain this phenomenon, we established a model relating deposition velocity to filament diameter\n(new Fig. 3c). While the specific critical diameter depends on the ink-bath system, the model universally\nreveals a \"static zone\" regime: when the filament diameter falls below a critical value, the sinking\nvelocity becomes negligible (<0.1 mm/min). The Fig. 6 filament, being smaller and closer to this regime\nin its own system, sinks much more slowly. This, combined with the accelerated curing in the catalyst-\nadded bath, effectively preserves its shape.\nFig. 3c Terminal sinking velocity as a function of filament diameter. Experiments were conducted using\nInk-1/Bath-1 and 610 μm nozzle.\nDiscussions added in Page 10:\n“More importantly, it enabled access to a distinct low-velocity deposition regime. When the filament\ndiameter falls below 270 µm, the corresponding settling velocity drops below 0.1 mm/min (Fig. 3c).\nWithin this low-velocity regime, defined here as the “static zone”, the filament can be stabilized rapidly\nvia curing (~1 min) before significant displacement occurs, enabling precise shape retention analogous\nto conventional EIW (Supplementary Fig. 12).”\nRevised text in Page14:\n“The printed filaments, with diameters ranging from 710 μm to 1010 μm, were printed at room\ntemperature within 40 s.”\nRevised text in Page 16:\n“First, a Pluronic F-127 sacrificial hydrogel filament was deposited. Due to its small diameter (480 μm)\nand small density contrast with the bath (Δρ=+0.054 g/cm³), the filament experienced negligible\nbuoyancy-driven motion, remaining stabilized in its predesigned position, a behavior analogous to\nconventional EIW and effectively creating a static reference structure.”\n(ⅲ) The integration of spiral microfluidic channels around the conductive circuit exemplifies our\nplatform's capacity for creating monolithic, multi-functional systems. In this specific design, the channels\nenable active thermal management. As shown in new Supplementary Fig. 18, circulating temperature-\ncontrolled fluid (water) allows us to use the adjacent circuit as a highly sensitive thermal sensor, as its\nresistance reliably shifts with fluid temperature.\nSupplementary Fig. 18 Real-time thermal sensing with a microfluidic-conductive hybrid device.\nThe integrated device functions as a thermal sensor by monitoring the resistance change of an embedded\nconductive channel in response to temperature variations induced by fluid flow in an adjacent\nmicrofluidic spiral. a Initial resistance. Resistance changes upon flowing b 50 °C hot water and c 0 °C\nice water through the microfluidic channel.\nMore broadly, this structure is a prototype showcasing the potential of our manufacturing strategy.\nIt proves that we can seamlessly integrate diverse physical components (electronic and fluidic) into a\nsingle device. The choice of materials for each component opens a vast design space. For instance, by\nchoosing different functional inks for the circuit or different fluids for the channels, the same integrated\narchitecture could be repurposed for applications ranging from real-time reaction monitoring in\nmicroreactors to drug delivery in lab-on-a-chip devices or even dynamic shape-morphing in soft robots.\n(ⅳ) To improve readability, we have reorganized the manuscript and introduced a new Table 1 at the\nbeginning of the Results section. This table compiles all key materials and parameters, drastically\nreducing the need for cross-referencing and providing readers with a clear and concise overview.\nTable 1 Ink and bath information\nMaterials Density Viscosity Note\n(g/cm3) (Pa.s)\nInk-1 SE 1700 1.016 3.60×104 Yield-stress ink\nInk-2 6 wt% SiO /Ecoflex 00-30 0.990 2.36×103 Yield-stress ink\n(weight ratio 7:3）\nHydrogel ink PF-127 hydrogel 1.020 1.88×104 Yield-stress ink\nConductive ink graphite/inorganic 1.450 1.35×106 Yield-stress ink\naluminosilicate\nFluorescent ink 6 wt% SiO / 1.010 3.22×103 Yield-stress ink\n2\n1 wt% fluorescent powder/\nSylgard 184\nBath-0 2 wt% Thivex/Ecoflex 00-30 0.977 1.70×102 Yield-stress bath\nBath-1 Ecoflex 00-30 0.998 2.90 Newtonian-like\nbath\nBath-2 Ecoflex 00-10 0.998 9.20 Newtonian-like\nbath\nBath-3 Sylgard 184 0.966 4.18 Newtonian-like\nbath\nThermochromic 0.5 wt% Thivex/0.1wt% 0.982 1.27×102 Newtonian-like\nsupport bath thermochromic bath\npowder/Sylgard 184\n(10) All printed examples are based on 2D filament layouts followed by shape transformation. Please\nclarify whether this method is capable of producing fully volumetric multilayer 3D structures, such as\ncubes or spheres.\nResponse:\nThe self-assembly-driven TEIW mode itself is indeed suboptimal for fabricating solid, dense objects like\nspheres. This is because the Newtonian fluid prevents the complete coalescence of adjacent filaments\ninto a continuous solid mass.\nHowever, as we now demonstrate, our overall platform is fully capable of producing such\nvolumetric structures. By simply switching to a direct-write, layer-by-layer printing modality within the\nsame support bath, we can fabricate dense 3D objects. This approach uses the container's base as a\nsubstrate and is analogous to conventional embedded 3D printing, but within our Newtonian bath\nenvironment.\nAs shown in the new Supplementary Fig. 19, we printed a densely packed solid cube, confirming\nthe feasibility of creating volumetrically dense structures, and a hollow spherical shell, demonstrating\nthe ability to fabricate complex, self-supporting curved geometries.\nThis hybrid capability underscores the versatility of our material system. The same ink and bath can\nbe used for both autonomous transformations to create complex frameworks and direct-write printing to\ncreate solid objects. Therefore, while the TEIW mechanism is not directly used for solid spheres, our\nplatform comprehensively addresses their fabrication.\nWe have clarified this on Page 16 of the main text: \"Furthermore, the platform supports\nconventional layer-by-layer printing on the bath substrate, enabling the fabrication of dense, volumetric\nobjects (Supplementary Fig. 19).\"\nSupplementary Fig. 19 Layer-by-layer 3D printing of structures on the substrate. a A photograph\nof a solid cube, a hollow cube, and a hollow sphere (from left to right) within the Sylgard 184 support\nbath. b Cross-sectional and c surface SEM images of the hollow sphere demonstrate complete fusion\namong filaments and absence of voids, demonstrating the ability of the method to prepare volumetric 3D\nobjects.\n(11) Would it be more appropriate to retitle the section in lines 330–339 as “Conclusion”?\nResponse:\nAs suggested, the section in lines 330–339 has been retitled \"Conclusion\" in the revised manuscript.\nComments from Reviewer #2\nThis manuscript demonstrates an intriguing concept of transforming 2D patterns into 3D structures\nwithin a bath. However, additional demonstrations and practical applications are necessary to\nsubstantiate the claims regarding the fabrication of intricate geometries and improvements in efficiency\ncompared to conventional EIW. Furthermore, several concerns about the general applicability of this\nmethod are highlighted in the comments below:\n1. The authors claimed that conventional EIW struggles with printing intricate 3D geometries,\nparticularly intersecting and overlapping paths. However, the existing path-design strategy (DOI:\n10.1126/science.adj6152) has already addressed these issues. How does the proposed method\ndemonstrate advantages over these existing strategies, and what evidence supports these advantages?\nResponse:\nWe agree that the reference mentioned has greatly improved the path-design strategy. To clarify the\nunique advantages of our TEIW strategy, we have substantially revised the Introduction to more precisely\narticulate the fundamental challenges of conventional EIW that TEIW addresses, moving the focus away\nfrom pathing limitations.\nAs now detailed in the revised Introduction, the key advantages of TEIW are not in path planning,\nbut in overcoming three intrinsic limitations of nozzle-directed EIW. (1) Rheological constraints. TEIW\nuses a Newtonian-like support bath, eliminating the stringent requirement for a high yield-stress ink to\noppose the yield stress of the bath. This greatly simplifies ink formulation and expands material choice.\n(2) Nozzle-independent structuring. The 3D structure is formed by autonomous sedimentation, not by\nthe nozzle's motion. This removes all constraints on final structural height and complexity imposed by\nnozzle length and accessibility. (3) Elimination of nozzle interference. The self-assembly process occurs\nafter printing, completely avoiding the mechanical disturbances that a nozzle introduces when passing\nnear previously deposited features in a viscous medium.\nThese conceptual advantages are robustly supported by experimental evidence throughout the\nmanuscript. The material generality enabled by relaxed rheological requirements is demonstrated by the\nprinting of various inks, including silicone elastomers (Fig. 2), conductive composites (Fig. 5a), and\nhydrogel precursors (Fig. 5d). The ability to achieve nozzle-independent 3D architectures is vividly\nillustrated by the formation of complex structures across the manuscript (such as structures in Fig. 4).\nThe high geometric fidelity attainable without nozzle interference is evidenced by Supplementary Fig.\n16, a direct comparison between the TEIW and CEIW fidelity.\nTherefore, TEIW's advantage lies not in competing with advanced pathing algorithms, but in\nproviding a fundamentally different route that bypasses the core physical constraints of conventional\nembedded 3D printing. We believe the revised Introduction and the accompanying data now make this\ndistinction and the value of our approach clear.\n2. While the authors have elucidated rheological differences between conventional EIW and the proposed\nTEIW method, comparative demonstrations of efficiency and fidelity are missing. It is recommended to\nprint identical structures using both techniques and measure differences in fabrication time and\nstructural accuracy.\nResponse:\nFollowing the reviewer's suggestion, we have conducted a direct comparison between conventional EIW\nand our TEIW method by printing identical structures (tetrahedron, vasculature, and flower patterns).\nThe results for structural fidelity and fabrication efficiency are summarized in Supplementary Fig. 16b-\nd and Supplementary Fig. 17, respectively.\nFor printing fidelity, TEIW demonstrated superior accuracy in both the in-plane (x,y-axis) and out-\nof-plane (z-axis) dimensions compared to conventional EIW, which was performed in a reported yield-\nstress support bath (ACS Appl. Mater. Interfaces 2018, 10, 23353−23361) using the same printing\nparameters as in TEIW.\nRegarding fabrication efficiency, the active printing time for TEIW is significantly shorter. The total\nprocess time for TEIW, however, includes an additional self-driven transformation period for the\nstructure to settle into its final 3D configuration. While this makes the total forming time longer, the\nabsolute extension is only on the order of several minutes. This may be considered as a practical and\nacceptable trade-off between longer total forming time and enhanced fidelity.\nThe Supplementary Fig. 16 and Supplementary Fig. 17 are as follows.\nSupplementary Fig. 16 Printing fidelity. a Z-axis fidelity of the 3D structures. b-d Comparisons\nbetween conventional CEIW and TEIW method for b the tetrahedral frame, c the branched vascular\nnetwork, and d the flower pattern. For each structure, (i) and (ii) show the top and side views of the print\nfabricated by CEIW, respectively. (iii) Comparison of the XY and Z directional fidelity between TEIW\n(blue) and CEIW (gray). The CEIW process was conducted in a yield-stress bath (Sylgard 184:1700, 7:3\nweight ratio) using the same printing parameters as TEIW. The as-printed structures via CEIW show\nsignificant fidelity loss, particularly at path crossings, under high printing speeds, and in regions\nrequiring repeated nozzle passes.\nSupplementary Fig. 17 Comparison of fabrication time between CEIW and TEIW methods.\nRevised Texts in Page 13:\n“For a direct comparison, 3D structures were also printed using the conventional EIW method in a\nreported yield-stress support bath25 (Supplementary Fig. 16b), whereas TEIW demonstrated higher\ngeometric accuracy while maintaining a comparable preparation time (Supplementary Fig. 17).”\n3. The paper employs distributions of pressure and path speed to control the settling positions of printed\nstructures, resulting in variable filament diameters as illustrated in Fig. 3. If specific channel diameters\nare required to realize functions, such as actuator chambers in robotics or biomimetic vascular systems,\nhow would the proposed method reliably achieve these precise dimensions?\nResponse:\nFirst, the filament diameter is precisely dictated by the extrusion pressure and nozzle velocity.\nQuantitative models based on fluid continuity and ink rheology (𝑑 =2√𝑄∕𝜋𝑣) allow us to accurately\ndetermine the printing parameters required to achieve a specific target diameter, ensuring high\nreproducibility (Fig. 3, Supplementary Fig. 10).\nSecond, to architect complex 3D structures with multiple filaments of different diameters, we\nemploy temporal programming of the printing sequence. Since the settling depth (D) depends on the\nterminal velocity (v) and time (D = v × t), and v is proportional to d², we can precisely control the\nt t t\nvertical positioning by introducing calculated time delays (Δt) between the printing of different filaments.\nThis enables the creation of intricate 3D architectures from a single 2D print path.\nThird, the transformation kinetics can be broadly tuned at the material level by adjusting the density\ncontrast (Δρ) and bath viscosity (η), as in the modified Stokesian model (v ∝ Δρ/η), offering an\nt\nadditional dimension of control.\nFor structures requiring extreme dimensional accuracy, we envision implementing a closed-loop\ncontrol system. This system would integrate real-time feedback on filament diameter and position to\ndynamically adjust printing parameters or material properties, ensuring strict adherence to target\ndimensions throughout the process.\n4. Regarding the printing of spherical structures, how can this geometry be fabricated effectively using\nthe proposed approach?\nResponse:\nThe self-assembly mechanism of TEIW is not ideally suited for fabricating solid, volumetrically dense\nobjects such as spheres, as the Newtonian fluid prevents the fusion of adjacent filaments during\ntransformation. However, we can effectively fabricate dense and curved geometries, including spherical\nstructures, by switching to an alternative printing modality within the same platform. Following the\nreviewer’s suggestion, we utilized the bath substrate as a support and adopted a layer-by-layer deposition\nstrategy, analogous to conventional embedded 3D printing but within our Newtonian bath environment.\nAs shown in the new Supplementary Fig. 19, we successfully printed a densely packed rectangular block,\ndemonstrating the feasibility of fabricating solid structures, and a hollow spherical shell, illustrating the\ncapability to achieve complex curved geometries.\nThis hybrid approach highlights the flexibility of our platform. The same ink–bath system can be\nused in both the autonomous TEIW mode and the direct-write layer-by-layer mode (e.g., for fabricating\nsolid or hollow dense shapes). The hollow sphere, in particular, demonstrates our ability to produce\nsophisticated spherical forms. Thus, while the self-assembly pathway of TEIW is not directly applied to\nsolid spheres, our overall platform and material strategy fully support the fabrication of such geometries.\nWe have incorporated this discussion and the corresponding results into the revised manuscript and\nsupporting information to provide a more comprehensive perspective on the capabilities enabled by our\nink–bath formulation.\nRevised Texts in Page 16:\n“Furthermore, this strategy supports conventional layer-by-layer stacking on the bath substrate,\nenabling the fabrication of dense, volumetric objects (Supplementary 19).”\nSupplementary Fig. 19 Layer-by-layer 3D printing of structures on the substrate. a A photograph\nof a solid cube, a hollow cube, and a hollow sphere (from left to right) within the Sylgard 184 support\nbath. b Cross-sectional and c surface SEM images of the hollow sphere demonstrate complete fusion\namong filaments and absence of voids, demonstrating the ability of the method to prepare volumetric 3D\nobjects.\n5. The paper emphasizes gravity and buoyancy imbalance as key factors for accurate deposition of 2D\npatterns. However, additional phenomena, such as bubble formation during nozzle movement, dynamic\nflow behaviors induced by velocity fields (DOI: 10.1021/acsami.7b19818), and viscous stresses (DOI:\n10.1126/sciadv.1500655), should also be examined to comprehensively understand the deposition\nmechanism.\nResponse: The potential roles of bubble formation, dynamic flow behaviors, and viscous stresses are\nindeed important for a comprehensive understanding of embedded printing mechanisms. In this study,\nwe focused on establishing and elucidating the gravity-buoyancy imbalance as the dominant driving\nforce in the TEIW process, a mechanism fundamentally enabled by the use of Newtonian-like support\nbaths, which distinguishes it from conventional EIW in yield-stress fluids.\n Regarding bubble formation during nozzle movement\nThe bubble formation can be a critical issue in some embedded printing systems. However, in our\nTEIW process, the Newtonian nature of the support bath, characterized by the absence of yield\nstress and negligible elasticity, along with low printing speeds and extrusion pressures, creates\nconditions that are intrinsically unfavorable for air entrapment. From a physicochemical\nperspective, such fluids exhibit minimal viscoelasticity and bubble retention under low shear rates.\nAs a further precaution, both the ink and bath were thoroughly degassed prior to printing. Consistent\nwith this, we observed no visible bubbles or related defects in any of our experiments.\n Regarding dynamic flow behaviors induced by velocity fields\nRegarding dynamic flow fields induced by the nozzle, our analysis confirms that the system\noperates deep within the Stokes flow regime (Re ≈ 3.33×10-6 << 1, see supplementary text for\ncalculation). In such regimes, velocity perturbations decay rapidly with distance from the source\n(~1/r² to 1/r³), as described in low Reynolds number hydrodynamics [John Happel, Howard Brenner,\nLow Reynolds number hydrodynamics, Springer Nature, 1985]. Consequently, any flow generated\nby the nozzle motion dissipates quickly and exerts a negligible influence on distant, previously\ndeposited filaments. The motion of each filament is thus dominantly governed by the local balance\nbetween the driving force (F ) and the viscous drag force (F ).\ndrive drag\n Regarding viscous stresses\nViscous stresses are indeed a central component of our physical model. They are explicitly\nincorporated through the viscous drag force (F ) in Equations (2) and (3), which balances F\ndrag drive\nto determine the terminal velocity (v). The modified Stokesian model accounts for end effects due\nt\nto finite filament length, providing a quantitative description for the role of viscosity. The good\nagreement between model predictions and experimental results (e.g., inverse relationship between\nv and bath viscosity η shown in Supplementary Fig. 10c, d) confirms that viscous effects are\nt\nadequately captured in our current framework.\nWe acknowledge that the mentioned factors could become more significant under an expanded range\nof printing parameters (e.g., substantially higher speeds). We therefore regard the reviewer's suggestion\nas a valuable direction for future work, where techniques such as high-speed imaging and particle image\nvelocimetry (PIV) could be employed to systematically investigate these dynamics in a broader\nparameter space.\n6. Given that deposition distance depends not only on velocity but also on duration, printing complex 2D\npatterns requiring extended fabrication times might lead to mismatches in final settling positions. It is\nrecommended that authors explore the operational window of their method and provide strategies for\neffective time management to ensure accurate deposition for arbitrary geometries.\nResponse:\nWe have included the data from these new crosslinking kinetics experiments in Supplementary Fig. 12,\nwhich clearly illustrates the temporal evolution of filament displacement under different bath conditions\n(pure and catalyzed) until complete solidification. The pure PDMS support bath achieves full\ncrosslinking under infrared (IR) irradiation within 3 minutes, while the addition of 1 wt% catalyst further\nreduces the IR-induced crosslinking time to 1 minute. In both cases, the printed filament underwent\ncontinuous motion throughout the entire duration prior to solidification of the bath. However, in the\ncatalyst-involved system, this displacement was limited to approximately 130 μm. To compensate for\nsuch displacement, initiating solidification by a time interval corresponding to the sinking velocity would\nbe an effective approach. Experimental details and results, using PF-127 ink in a silicone bath (Bath-3)\nas an example, are provided in Supplementary Fig. 12 as follows.\nSupplementary Fig. 12 Filament sinking behavior and crosslinking kinetics under different\nsupport bath conditions. a Silicone bath with 1 wt% catalyst cured in 1 min, b pure support bath cured\nin 3 mins after infrared irradiation. For each condition: (i) sinking distance of the PF-127 filament over\ntime, (ii) optical images captured during the sinking process, and (iii) state evolution of the support bath\nat different time points. The printed filament underwent continuous motion throughout the entire duration\nprior to solidification of the bath. To compensate for such displacement, initiating solidification by a time\ninterval corresponding to the sinking velocity would be an effective approach.\nRevised text in Page 10:\n“Within this low-velocity regime, defined here as the “static zone”, the filament can be stabilized rapidly\nvia curing (~1 min) before significant displacement occurs(Supplementary Fig. 12), enabling precise\nshape retention analogous to conventional EIW.”\nRevised text in Page 14:\n“The curing kinetics of the silicone elastomer in this work were tailored using additives. An inhibitor\nsecured a minimum 24-hours printing window at room temperature, while an added platinum catalyst\nfacilitated infrared-induced curing within 1 min to ensure printing accuracy.”\n7. To strengthen the current demonstrations provided in Fig. 4, a fidelity analysis comparing the printed\nstructures against the intended design models along the z-axis would significantly enhance the\nmanuscript.\nResponse:\nWe thank the reviewer for this insightful suggestion. To quantitatively evaluate the dimensional accuracy\nalong the z-axis, we have performed a fidelity analysis as recommended and included the results in\nSupplementary Fig. 16a. The analysis compared the final measured heights of five different printed\nstructures against the theoretical sedimentation depths predicted by the model (Eq. 3) for straight\nfilaments of the same diameter. The calculated z-axis fidelity across these structures ranges from 86.48%\nto 98.16%, confirming the general reliability of our method in controlling vertical architecture. The z-\naxis fidelity for the double-helix structure was indeed the lowest among the tested structures at 86.48%.\nThe primary reason for this lower fidelity is intrinsically linked to the very self-assembly mechanism of\nthe helix. As described in the manuscript, the rising motion of the low-flow (gray) side is not a result of\nits own intrinsic buoyancy, but a forced kinematic outcome. It is actively pulled upward by the torque\ngenerated at the junctions, which itself is caused by the faster-sinking, high-flow (blue) side. This\nconstrained, interdependent motion fundamentally deviates from the assumption of free, individual\ndeposition upon which the theoretical model is built.\nWe fully acknowledge that a comprehensive predictive framework for such complex structures\nrequires accounting for inter-filament forces, curvature, and non-uniform diameters. As stated in the\nconclusion, developing a multi-physics simulation that integrates these factors is one critical goal of our\nfuture work.\nSupplementary Fig. 16 Printing fidelity. a Z-axis fidelity of the 3D structures.\nRevised text in Page 12:\n“The z-axis fidelity of the above structures was quantified by comparing the as-printed heights with the\ntheoretical depths predicted by Eq. (3) for straight filaments, yielding values from 86.48% to 98.16%\n(Supplementary Fig. 16a).”\n8. To ensure reproducibility, the authors should clarify the statistical methods used in rheological\ncharacterization and parameter control sections, specifying how reliability and repeatability were\nassessed.\nResponse: All rheological measurements were performed with a minimum of n = 3 replicates for each\nformulation reported in the study. While the main text figures display a single representative curve for\nclarity, we have now created a new Supplementary Fig.1 to include all the rheological measurements.\nAll replicate measurements showed high consistency, with variability typically below 5-10%, which is\nwithin the expected range for soft viscoelastic materials.\nSupplementary Fig. 1 Rheological characterization of the inks and support baths. The crossover\npoint of G’ and G’’ was taken as an empirical indicator of the yield stress. The zero-shear viscosity (η₀)\nwas determined from the low-frequency plateau of the complex viscosity (|η*|), measured within the\nlinear viscoelastic region at a shear stress of 1 Pa.\nFor all quantitative experiments concerning printing fidelity—including filament diameter, terminal\nvelocity, and final structural dimensions—data were obtained from n ≥ 3 independent experimental\nrepeats. The methodology has been stated in the revised Methods section. Raw data for all replicates are\nsupplied in the Source Data file.\nComments from Reviewer #3\nThis work presents a novel and interesting modification of the Embedded Ink Writing (EIW), named\nTransformable Embedded Ink Writing (TEIW). The manuscript provides a thorough characterization of\nthe inks and implementation of the results to the TEIW techniques as a functional method for\nmanufacturing geometrically complex shapes. However, several revisions are needed before this\nmanuscript is recommended for publication:\n1) The introduction provides a brief overview of the method, the limitations and the research gaps. It is\nrecommended that the authors revise the introduction to better highlight the state-of-art of the work.\nMore details could be given on the extrusion-based techniques and their limitations and how the EIW\ntechnique overcomes the limitations. Also, discuss the important parameters in the EIW technique that\naffect the process (e.g., ink rheology, the ink-bath interactions) and how the proposed TEIW resolves\nthese issues. Citing more references will create a more comprehensive literature review.\nResponse:\nWe thank the reviewer for this constructive suggestion. We have thoroughly revised the Introduction to\nbetter highlight the novelty of our work. As recommended, we have expanded the discussion on the\nlimitations of existing extrusion-based techniques and EIW, and explained how TEIW effectively\nmanages them. Additional relevant references are cited to provide a more comprehensive literature\nreview.\nRevised Texts in Page 2-3:\n“In recent years, extrusion-based 3D printing, particularly direct ink writing (DIW), has emerged as a\npowerful tool for rapid prototyping of customizable soft systems5-9. In a typical DIW process, viscoelastic\nink is extruded through a nozzle onto a substrate in ambient air to build the designed structure10.\nAlthough conventional DIW is cost-effective and high scalable, its layer-by-layer printing manner often\nrequires auxiliary structures to support overhang or complex geometries, complicating the fabrication\nprocess. Moreover, structural integrity relies on the ink’s ability to solidify rapidly, which limits material\nchoices, especially for silicone elastomers that typically exhibit slow curing kinetics11,12. To overcome\nthese challenges, embedded ink writing (EIW) has been developed, wherein inks are extruded into a\nliquid bath instead of directly into air13-16. The supporting bath is typically a yield-stress liquid, which\ncan locally fluidize under shear from the moving nozzle and rapidly transition back to a solid state once\nthe shear is released17,18. In this way, it provides omnidirectional support and enabling freeform\nfabrication. As a result, EIW has demonstrated versatility across diverse applications, including strain\nsensors19, pneumatic actuators8, vascular networks20, and cell-laden scaffolds fabrication21.\nNevertheless, EIW method introduces its own challenges. Firstly, the process demands careful\nrheological compatibility between the ink and the bath material. Mismatches in yield stress or viscosity\ncould cause filament irregularities22-24. Moreover, the use of a yield-stress bath in turn requires the ink\nto possess even higher yield stress to maintain structural fidelity25. The incorporation of rheological\nmodifiers (e.g., nanoparticles) further complicates ink formulation and may impair the material’s\nproperties. Secondly, the EIW process remains heavily dependent on the extrusion nozzle26,27. The\nprintable height is constrained by the nozzle length. Longer nozzles are prone to deflection due to\nresistance from the support fluid, compromising printing accuracy. In addition, when printing near or\nacross previously deposited ink filaments, the nozzle can induce mechanical disturbances in the bath,\nmaking it difficult to achieve high geometric fidelity.\nAiming to address these challenges, this work presents a new printing strategy termed transformable\nembedded ink writing (TEIW), which enables the fabrication of 3D structures through the self-assembly\nof 2D-printed patterns via a net gravitational-buoyant force. This density-driven mechanism enables\nprinted filaments to ascend in regions of higher buoyancy or sink under greater gravity, thereby\nautonomously transforming planar precursor patterns into preprogrammed 3D architectures within\nseconds to minutes. TEIW operates within a Newtonian-like fluid support bath, which reduces the\nstrictness of rheological compatibility requirements in conventional ink-bath systems. Once the ink is\nreleased from the nozzle, TEIW circumvents the structural height limitations imposed by nozzle length\nand avoids the need for complex 3D trajectory control. Moreover, the self-assembly nature of the process\ninherently avoids distortions caused by nozzle interference. In contrast to externally stimulated 4D\nprinting28 or magnet-assisted morphing strategy29, our approach requires no specialized responsive\nmaterials and accommodates a broader spectrum of soft materials, including elastomers, hydrogels,\nphotocurable resins, and polymer composites. Building on this material generality, we demonstrate\napplications spanning customizable microelectronics, perfusable vascular networks, and\ncryptographically encoded functional devices. This strategy thus offers a simple and versatile route to\nfabricating delicate multifunctional 3D structures, opening new avenues in soft material manufacturing.”\n2) It is suggested to include the microscopic images of the ink filaments (Figure 2, supplementary file) in\nthe main text. I would suggest grouping with Figure 7 as they represent the outcome of the observed\nrheological behavior.\nResponse: We agree that the microscopic images of the ink filaments provide valuable visual evidence\nof the print outcomes and their connection to the ink's rheology. We noted a potential minor discrepancy:\nthe reviewer's comment refers to grouping with \"Figure 7\", but the intended figure for grouping was\nlikely Figure 2, which directly presents the rheological behavior of the inks. Based on this understanding,\nthe microscopic images of the filaments (previously supplementary Figure 7) have been integrated into\nthe revised Figure 2 to create a more comprehensive presentation that directly links the measured\nrheological properties with the resulting printing quality and filament morphology.\nRevised Texts in Page 7:\n“SEM images show that the cross-sections of ink filaments preserved a circular morphology after\ntransformation and solidification (inset of Fig. 2). This well-defined shape is primarily maintained by\nthe ink's own yield-stress and viscoelastic properties immediately upon deposition, with the Newtonian-\nlike bath providing negligible resistance to flow and thus minimal mechanical stress on the filament.”\nThe revised Fig.2 is as follows.\nFig. 2 Vertical displacement of ink filaments as a function of material properties. Each row, from\nleft to right, sequentially presents time-dependent vertical movement of the ink filament, shear stress-\nshear rate curve of the bath with inset SEM images of the filament cross-sections (scale bar: 100 μm),\nmodulus curves for ink and bath, and density of the materials. The ink-bath pairs are a Ink-1, Bath-0,\nb Ink-2, Bath-1, c Ink-1, Bath-2, and d Ink-1, Bath-3.\n3) In Figure 3, please revise the figure caption and add a few annotations to the panels (c), (f), (g) and\n(h) for better understanding of the reader. For example, in panels (g) and (h), the concept of blue and\ngreen plots is unclear to the reader.\nResponse:\nWe thank the reviewer for these constructive suggestions to improve the clarity of Figure 3. We have\nthoroughly revised the figure and its caption accordingly.\n(ⅰ) Regarding Figure 3, panels (c)\nBased on the reviewers’ suggestions, the original panels c, d, and e have been moved to the supporting\ninformation and are now presented as Supplementary Fig. 10. The revised caption is as follows:\nSupplementary Fig. 10 a Relationship of filament diameters with extrusion pressure and printing speed\n(nozzle diameter 610 μm). b Plot of volumetric flow rate versus filament diameter for the Ink-1/Bath-1\nsystem, demonstrating precise control over the extruded filament's dimensions. c Experimental and\ntheoretical terminal velocity (v) of Ink-1 filament as a function of volumetric flow rate (Q) in Bath-1.\nt\nSolid lines represent model predictions from Eq. (3). As C was set to 0.84, a correlation coefficient\nconst\nof 0.97 was obtained, with a p-value of <0.001, confirming a strong linear relationship. d v vs. Q for\nt\nInk-1 in a lower viscosity bath (Ecoflex 00-30+5 wt% Thinner). With C maintained at 0.84, the\nconst\nresulting correlation coefficient was 0.88, with a p-value of <0.001. The increased slope demonstrates\nthat reducing bath viscosity accelerates the shape transformation kinetics, as predicted by the inverse\ndependence of v on bath viscosity (η).\nt\n(ⅱ) Regarding Figure 3, panels (f), (g) and (h), now as panels (d,e,f), we have directly annotated the plots\nto eliminate any ambiguity. The diameters of the printed filaments (680 µm and 640 µm) are now clearly\nlabeled on the graphs in their respective colors (blue and green). The caption has been updated to state:\nFig. 3 d Deposition distance versus time of a 660 µm ink filament. Synchronized deposition of 640 µm\n(green) and 680 µm (blue) filaments, e achieving the same depth by introducing a time delay Δt and f\ncreating a designed depth difference ΔD . All experiments were conducted using Ink-1/Bath-1 and 610\nμm nozzle.\nIn the main text, we have added a detailed explanation to elaborate on the concepts of\nsynchronization control and time-dependent deposition. This text explicitly describes how the model\nenables precise control by compensating for slower sinking rates with a time delay (Fig. 3e) and contrasts\nit with the pronounced offset resulting from simultaneous printing (Fig. 3f).\nRevised Texts in Page 10:\n“Based on the above framework, the temporal evolution of the filament's z-position can be quantitatively\npredicted. Given that the ink filament sinks at an essentially uniform velocity, the deposition distance D\nis effectively approximated by 𝐷 =𝑣 ×𝑡 , where t is the duration. This predictive capability was\nt\nvalidated by the close agreement between the experimental data and the theoretical prediction for a 660\nµm diameter filament, as shown in Fig. 3d. Furthermore, this model enables synchronization control.\nBy deliberately delaying printing by a time Δt of a thinner filament to compensate for its slower sinking\nrate, two filaments with a 40 µm diameter difference were synchronized to reach the same depth\nsimultaneously (Fig. 3e). Conversely, printing 680 µm and 640 µm filaments simultaneously resulted in\na pronounced vertical offset of 1.5 mm (Fig. 3f). These results show that the filament diameter variations,\nencoded via printing parameters, can be translated into time-dependent deposition differences.”\n4) As there are various inks used in this study, it would be better to consistently label all the graphs with\nthe specific ink system. This would make it easier for the reader to follow the results without needing to\ncross-reference the text.\nResponse:\nAs suggested, to improve readability, we have compiled all material compositions and properties in a\nnew Table 1. And we have standardized the use of these labels (e.g., Ink-1, Bath-2) across all figures and\nthe results narrative. This systematic approach will greatly assist the reader in tracking the materials used\nin each part of the study.\nTable 1 Ink and bath information\nMaterials Density Viscosity Note\n(g/cm3) (Pa.s)\nInk-1 SE 1700 1.016 3.60×104 Yield-stress ink\nInk-2 6 wt% SiO /Ecoflex 00-30 0.990 2.36×103 Yield-stress ink\n(weight ratio 7:3）\nHydrogel ink PF-127 hydrogel 1.020 1.88×104 Yield-stress ink\nConductive ink graphite/inorganic 1.450 1.35×106 Yield-stress ink\naluminosilicate\nFluorescent ink 6 wt% SiO / 1.010 3.22×103 Yield-stress ink\n2\n1 wt% fluorescent powder/\nSylgard 184\nBath-0 2 wt% Thivex/Ecoflex 00-30 0.977 1.70×102 Yield-stress bath\nBath-1 Ecoflex 00-30 0.998 2.90 Newtonian-like\nbath\nBath-2 Ecoflex 00-10 0.998 9.20 Newtonian-like\nbath\nBath-3 Sylgard 184 0.966 4.18 Newtonian-like\nbath\nThermochromic 0.5 wt% Thivex/0.1wt% 0.982 1.27×102 Newtonian-like\nsupport bath thermochromic bath\npowder/Sylgard 184\n5) In section “3D structural construction” the results are pretty descriptive, please describe the more\ncomplex mechanical transformation happening in different structures (e.g., such as in tetrahedron) in\nmore detail. I would suggest summarizing the key points from “Deformation-Dependent Deposition\nBehavior of Heterogeneous Filaments” section of the supplementary material to provide a detailed\nexplanation on the mechanisms. Also, it is recommended that the authors incorporate a summary of the\nkey findings from Supplementary Figure 11 into the main results section.\nResponse:\nWe have implemented the following changes.\n（ⅰ）Regarding the “3D structural construction” section\nWe have expanded the discussion of the mechanical transformations, including the tetrahedron, focusing\non the role of localized stress and deformation.\nRevised Text in Page 12:\n“With reference to computer-aided design (CAD) blueprints, a 3D helix was fabricated via printing a\nplanar spiral pattern with graded printing pressures (P >P >P >P ), which induces diameter variations\n4 3 2 1\nalong the continuous filament (Fig. 4a). Thicker, high-pressure segments sank faster than thinner, low-\npressure regions, establishing a continuous curvature gradient along the spiral. The deformation arose\nfrom the relative motion between adjacent turns. The faster-sinking outer segments dragged the slower\ninner segments downwards, while the slower-sinking inner sections restrained the outer ones, resulting\nin smooth, continuous helical geometries. Similarly, by alternating the nozzle velocity, a segmented linear\nfilament transformed into a waveform pattern (Fig. 4b). The faster-sinking segments descended ahead of\nthe slower-sinking ones, forcing the straight filament to buckle periodically in the vertical plane,\ntransforming it into a stable, undulating 3D structure.\nDual helical structures were realized by printing a continuous filament in a serpentine pattern with\nprogrammed flow rate variations (Fig. 4c). Each section of the pattern exhibited a high-flow side (blue)\nand a low-flow side (gray), and adjacent sections had this orientation reversed. During transformation,\nthe high-flow side descended faster, thereby generating a localized torque at the junctions and lifting the\nlow-flow side upward. The systematic reversal of the force gradient along the path caused these torques\nto alternate in direction, prompting the entire structure to twist and coil into a stable, double-helical\nmorphology. The rapid self-assembly (≤10 s) demonstrates programmable kinetic control through\nfilament-level force modulation.\nThe tetrahedral structure, a closed three-dimensional architecture, was achieved via velocity-\ngraded triangular motifs (Fig. 4d). The central high-flow-rate region (v = 3 mm/s) exhibited a larger\n3\ndiameter and higher driving force compared to the peripheral low-flow-rate segments (v , v , v = 7, 5,\n1 2 4\n10 mm/s). This systematic heterogeneity established an asymmetric force distribution across the\ntriangular pattern. During sinking, the high-drive central region experienced preferential descent, but\nits motion was constrained by mechanical connectivity to the slower peripheral arms. This constraint\nconverted the vertical force imbalance into a distributed bending moment, triggering simultaneous\nupward folding along three pre-defined edges. The entire structure underwent coordinated large-\ndeformation, evolving into a stable tetrahedron within 5 mins. Structural integrity was maintained\nthrough dynamic force equilibrium during the transformation, without nozzle-induced disturbances\naffecting the structure.\nTo explore bioprinting potential, CAD-designed 2D bifurcation patterns were printed using colored\nInk-1 (Fig. 4e). By assigning different printing velocities, differential deposition between slow trunk\nsegments and fast terminal branches introduced a controlled force imbalance. This programmed\nkinematic imbalance drove spontaneous 3D vascularization, inducing out-of-plane bending to yield\nvessel-like structures that mimic natural arteriovenous branching networks. This mechanism overcomes\nfilament interference challenges inherent in conventional 3D branched printing.”\n（ⅱ）Regarding the Supplementary Figure 11 (now Fig.13)\nWe have summarized the core mechanisms from the “Deformation-Dependent Deposition Behavior of\nHeterogeneous Filaments” section into the main text in Page 10 as follows.\n“Experiments with non-uniform and curved filaments reveal that the sinking velocity is dictated by fluid-\nstructure interactions arising from their geometry (Supplementary text and Fig.13). A heterogeneous\nfilament sinks slower than a uniform filament of the same maximum diameter, as the mechanical coupling\nbetween segments of different diameters restrains the overall motion. Similarly, greater filament\ncurvature leads to a slower descent. These findings form the basis for a rational workflow proposed to\nguide the optimization of the TEIW printing process by addressing key factors such as the ink-bath system\nand printing parameters (Supplementary Fig. 14).”\nAdditionally, the corresponding discussion in the Supplementary text has been revised for clarity.\nRevised text in Supplementary Page 16:\n“Deposition Behavior of Heterogeneous Filaments\nTo investigate filaments with spatially varying diameters, dual-segment filaments were prepared where\neach segment was printed at constant extrusion pressure but different nozzle speeds (v = 4, 5, 6, 7 mm/s)\n(Supplementary Fig. 13a). Experimental results show the heterogeneous filaments exhibited lower\naverage sinking velocities than mono-diameter filaments printed at the minimum speed (v = 4 mm/s).\nThe cross-sectional mismatch led to distinct sinking dynamics. Filaments with larger diameter disparities\nexhibited greater intra-filament velocity differences, with the 4–5 and 4–7 filament pairs showing velocity\ngaps of 0.10 and 0.29 mm/min between their thick and thin ends, respectively (Supplementary Fig. 13b).\nCompared to uniform controls, the thick segment of the 4–7 filament sank at 1.73 mm/min, only 0.06\nmm/min faster than the uniform 4 mm/s control, indicating its behavior approached that of a uniformly\nthick filament. In contrast, the thin segment of the 4–7 filament sank significantly slower (1.54 mm/min)\nthan its uniform counterpart. These results demonstrate that increasing diameter contrast amplifies\ninternal velocity gradients during settling. Since the filament descends as a single rigid body, each\nsegment cannot reach its natural terminal velocity, which should be considered for predicting\ndeformation and improving 3D architectural precision.\nThe effect of bending angle was systematically evaluated by printing V-shaped filaments with\ncontrolled angles (Supplementary Fig. 13c-e). The sinking velocity decreased monotonically with\nincreasing bending angle (15°, 30°, 45°, 60°), attributed to a redistribution of the gravitational force.\nFor straight filaments (0°), gravitational acceleration acts uniformly along the longitudinal axis. In\ncontrast, curvature introduce geometric asymmetry, redirecting a component of gravity perpendicular to\nthe local filament cross-section. This results in reduced net downward force as the bending angle\nincreases, consistent with the observed velocity decline. By encoding spatial variations in deposition\nspeed and geometric curvature, local sinking velocities can be systematically modulated, enabling\nsystematic modulation of local sinking kinetics for transforming 2D patterns into 3D architectures with\nhigh shape fidelity.”\n6) It is suggested to include Supplementary figure 1 regarding the ink and bath rheology in the main text\nto better support the discussion and the findings related to the material behavior.\nResponse:\nAs suggested, we have created a new Table 1 that compiles the key properties, including the rheology of\nall ink and support bath systems. This table is placed at the beginning of the Results section, providing a\ndefinitive reference that significantly reduces the need for cross-referencing and improves the\nmanuscript's readability. Further information regarding the ink and bath rheology can be found in the\nnew Supplementary Fig. 1.\n7) Please provide a clearer explanation on how the Time-dependent vertical displacement profiles, z-\npositions and other experiments were used to design the printing process parameters. Please explain the\nimportance of these experiments for designing the process.\nResponse:\nThe time-dependent vertical displacement profiles and z-position measurements were essential as\nthe quantitative foundation for designing the printing process. The importance of these experiments lies\nin their role in transitioning our approach from a trial-and-error process to a predictable, engineering-\ndriven workflow.\nBy tracking the z-position of filaments with known diameters over time, we obtained the\nexperimental data necessary to determine the system-specific constant C in Eq. 3. This calibration\nconst\nensured the model's accuracy in predicting terminal velocity (v) across a range of viscosities and\nt\ndiameters.\nThe validated model enables rational, target-oriented printing. To fabricate a filament at a specific\ndepth (D ), we first calculate the required terminal velocity as v = D / t. The model then directly\ntarget t target\ninforms the necessary filament diameter (d) to achieve this velocity. Finally, the printing parameters\n(pressure P, speed v) are set using the calibrated flow rate-diameter relationship.\nIn summary, these experiments allow us to start with a desired 3D geometry and systematically\ndetermine the 2D printing parameters and material properties required to achieve it, significantly\nenhancing the method's precision, reliability, and practical utility.\nTo visually summarize the printing workflow, we have added a new schematic as Supplementary\nFigure 14.\nSupplementary Fig. 14 Rational design workflow for the TEIW printing process. The process begins\nby defining a target depth (D), from which the required terminal sinking velocity (v) is calculated. This\nt\nvelocity is then used in the validated physical model (Equation 3) to determine the necessary filament\ndiameter (d). Finally, the required volumetric flow rate (Q) and corresponding printing parameters\n(nozzle pressure P and speed V) are determined using the established relationship between flow rate and\nfilament diameter.\n8) Please add a short description of the rheology results and their importance in the conclusions sections.\nResponse:\nWe have revised the Conclusion section to include a concise description of the rheology results and\ntheir critical importance. We now explicitly state that the distinct rheological profiles of the yield-stress\nink and the Newtonian bath were fundamental to enabling the TEIW process, as this contrast is what\npermits planar printing and subsequent spontaneous 3D transformation.\nRevised Texts in Page 17-18:\n“This study presents a TEIW method which utilizes planar printing of yield-stress inks and their\nautomatous assembly within Newtonian-like fluid baths. By applying a modified Stokesian framework\nthat quantitatively couples the net buoyancy force arising from density contrast with the viscous drag\nforce governed by bath viscosity, TEIW achieves precise control over filament deposition through simple\nprinting parameter adjustments, effectively bridging the gap between the simplicity of 2D patterns and\nthe complexity of 3D structures. Furthermore, it allows for concurrent assembly of functional\ncomponents such as fluidic, electrical, and structural elements within a single printing session, opening\na route toward next-generation integrated systems with spatiotemporal material control. Future\nenhancements aimed at the development of a multi-physics simulation, alongside the integration of\ncomputational algorithms for predictive control and a multi-inlet system for real-time density control,\nwill further expand the precision and compositional versatility of TEIW. This strategy could pave the way\nfor the on-demand fabrication of increasingly sophisticated and intelligent devices.”"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have thoroughly addressed all the concerns raised in the previous review. The manuscript has been\nsignificantly improved through the addition of new experiments, clearer explanations, and enhanced figures. I recommend\nthe manuscript be accepted for publication.", "reviewer_2": "The reviewers have addressed all the comments.", "reviewer_3": "I have carefully reviewed the revised version of the manuscript titled \"Up and down: A transformable embedded ink writing\nstrategy for soft 3D architectures\". The authors have addressed all of my previous comments accurately and thoroughly. The\nrevisions have improved the clarity, rigor, and overall presentation of the work.\nI find no remaining concerns and recommend the manuscript for acceptance in its current form."}, "author_response": ""}]

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