Introduction

Oil spill disasters may occur anywhere the oil is drilled, processed, stored and transported1,2,3. Oil spills can contaminate surrounding waters thousands of times their volume, resulting in widespread and long-lasting social, economic, environmental and ecological impacts1,2,3. It is common practice to use oleophilic adsorbent materials for in-situ capture of spilled oil. For example, in the accidents of the 2010 Deepwater Horizon and the 2023 MT Princess Empress, spilled oil was collected by using adsorbent booms modified by oleophilic polymers such as polysiloxanes, organosilanes, polypropylene and polyurethane4,5. To expand the oil-solid interface, functionalized trawl nets6, separator-skimmers7 and floating wells8 are applied under static mode. However, a common challenge faced by these technologies is their sensitivity to water-flow fluctuation. This will lead to severe performance loss in terms of mechanical robustness, interfacial mass transfer and oil capture efficiency, as a consequence of inhomogeneous, unstable and uncontrollable hydrodynamic behaviors of oil-capture matrixes. Such issues are commonly encountered for oil-in-water emulsion in the case of pipeline leakage and offshore industrial discharge. Therefore, there is a strong incentive to develop effective solutions for dynamic robust cleanup of spilled oil under complex hydrodynamic conditions.

Nature may offer inspiring solutions. A large number of previous studies reported bio-inspired strategies for oil-water separation. For example, cobwebs9, marine mussels10, cat-tongues11, and nepenthes-peristomes12 provided inspirations for designing superhydrophobic materials and interfaces. Manta rays inspired the nanofiberous membrane for oil-water separation by non-clogging ricochet filtration13,14, and filter-feeding fish inspired the helical, cross-step filter for collecting harmful algae15. However, these works mainly focused on modifying interfacial properties and mass transfer modes for oil-adsorbing materials (e. g. hydrophobicity/hydrophilicity and oleophobicity/oleophilicity), but their hydrodynamic stability remains unclear. Low hydrodynamic robustness would result in low oil-capturing efficiency, time delay and oil escape, especially under turbulent flow.

In nature, deep-sea glass sponge (e. g. E. aspergillum or Venus’ flower basket)16,17,18 attracts our interest because its exceptional structures are closely connected with what we are searching for with respect to spilled oil capture. Unlike shallow-water sponges that benefit from nutritious photosynthetic algae, feeding of deep-sea sponges is quite challenging in the deep sea with complex flow, scarce nutrients and shallow anchorage. E. aspergillum can achieve filter feeding with high effectiveness, high selectivity and high robustness, originating from its mechanical architecture16. Specifically, E. aspergillum has the multi-layered skeleton-flagellum architecture as illustrated schematically in Fig. 1a and Supplementary Fig. 119,20. As water stream flows through the sponge body of E. aspergillum, the multi-angle struts create 3D streamlines with frequent collision, deflection, convergence and separation. Then, the macro-scale turbulent flow is dissipated, resulting in small-scale low-speed vortical flow within the body cavity over subcritical and critical regimes (Re<5×103)17. The swirling flow patterns hold the key to reducing hydrodynamic load, capturing nutrients by flagellums and maintaining mechanical stability. This allows the E. aspergillum to thrive via aeons of natural selection at depths ranging from 100 to 1000 meters in the Pacific Ocean and around Antarctica 18.

Fig. 1: Bio-inspired design for vortex-anchored filter (VAF).
Fig. 1: Bio-inspired design for vortex-anchored filter (VAF).
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a Skeletal motifs of deep-sea E. aspergillum, whose food particles shared similarity with oil droplets46,47. b Front and top views of bio-inspired VAF with bio-inspired hollow cylinder (BC) skeleton and flagellum-adsorbent. c Models of oil-capture matrixes for different skeletons, including solid plate (SP), solid cylinder (SC), grid hollow cylinder (GC), chequerboard hollow cylinder (CC), helical ridge-grid hollow cylinder (HC), and BC (more details in Supplementary Text 2). d–f Impact of skeletal motifs on (d) the flow pattern at supercritical regime, (e) the magnitude of flow velocity and (f) the pressure at discrete nodes in adsorption region under different Re numbers. Note: The thickness is 0.1 L for horizontal, vertical, and diagonal elements in the grids of GC, CC, HC, and BC. Source data are provided as a Source Data file.

The anatomy of E. aspergillum provides an elegant biophysical inspiration for designing the skeletal architecture of oil capure filter toward high mass transfer and hydrodynamic stability. By mimicking the filter-feeding patterns of deep-sea glass sponge during oil capure, the vortex-anchored flow pattern would be expected over subcritical to supercritical regimes. Theoretically, this would realize (i) enhanced interfacial mass transfer of oil adsorption as low-speed vortical flow can promote field synergy between concentration gradient and velocity, thereby oil can be captured more effectively by increasing residence time when water-oil mixture is filtered, and (ii) increased hydrodynamic stability of the oil-capture matrix through dissipating water-flow kinetic energy and thus attenuating the drag force in nearly quiescent wake flow, which makes it highly resistant to bending stress generated by boundary-layer separation of viscous fluid. Drawing inspiration from biophysical similarities to skeletal features and filter-feeding patterns of deep-sea glass sponge, we attempted to develop a vortex-anchored filter (VAF) that may be applicable for in-situ, dynamic and robust oil cleanup under turbulent flow.

Results

Bio-inspired design for vortex-anchored filter

Inspired by the filter-feeding pattern of E. aspergillum, we propose the principle for designing vortex-anchored filter (VAF) by mimicking the structure of E. aspergillum in terms of outer skeleton and inner flagellum (Fig. 1b). The primary function of outer skeleton, made of helical ridge and chequerboard lattice, is to create slow vortex field in the cavity and quiescent regions in the wake17, so that mass transfer and hydrodynamic stability can be achieved under turbulent flow. The inner flagellum-shaped adsorbent provides a large interfacial area oil adsorption. To this end, hydrophobic melamine resin21 (total length of 2 cm and diameter of 0.1 cm; Supplementary Fig. 2) was embedded onto the inner wall of skeleton that was 3D-printed by stainless steel (Supplementary Fig. 3).

The helical-ridge and chequerboard-lattice structure are believed to play the central role in the VAF design. Therefore, prior to 3D printing of VAF, we performed lattice Boltzmann simulation of the structural feature of skeletal motifs in terms of grid width (L) and strut position (S/L; Fig. 1c) to gain mechanistic insights. First, the skeleton motif was designed with the 16-L height and 10-L diameter, in which the helical ridge was designed as a diagonal ring structure consisting of semi-octahedra with L-width (Fig. 1c and Supplementary Fig. 3). Second, two optimization problems were formulated to identify the value of L and S/L that resulted in the highest flow vorticity inside cavity and lowest flow velocity in wake. The two optimization problems were solved under supercritical regime (i.e., Reynolds number of 105) by using Covariance Matrix Adaptation Evolution Strategy algorithm (CMA-ES)22 (Supplementary Text 1). Standard bounce-back procedure was used to deal with the coupling between fluid and solid (i.e. skeleton and flagellum). For structural optimization, we varied L and S/L one by one while keeping the other parameter constant. As shown in Fig. 1d and Supplementary Fig. 4, the skeleton motif was of extreme importance to the hydrodynamic feature. Indeed, some undesirable motifs not only impeded the generation of internal vortex, but also disrupted the stabilization of wake flow, even leading to vortex street shedding23 (Fig. 1d). On the contrary, grid width (L) had a less significant impact on the flow pattern under each Re value (Supplementary Fig. 4), indicated by the fact that changes of L only led to a maximum change lower than 27% in vorticity. Based on above consideration, we design VAF with L=5 mm and S/L=0.3, accounting for total geometric size of 5-cm diameter and 8-cm height, which emulated the vortex-anchored flow patterns behind the filter-feeding pattern of E. aspergillum.

Smoothness and uniformity of flow field

Flow pattern is vital for dynamic oil cleanup using adsorbents. To examine the flow pattern at adsorption region on a quantitative basis, we compared six kinds of skeleton architectures (Fig. 1c), i.e., solid plate (SP), solid cylinder (SC), grid hollow cylinder (GC), chequerboard hollow cylinder (CC), helical ridge-grid hollow cylinder (HC), and bio-inspired hollow cylinder (BC) skeleton, with details of these geometries given in Supplementary Text 2. For each skeleton architecture, the velocity (V, cm s−1) and pressure (P, Pa) field were modeled at Re value of 102, 103, 104 and 105. The flow field analysis was conducted on a horizontal cross-section at the mid-height of VAF. The adsorption region was the cavity area for hollow structures, peripheral area for solid structures, circular ring for SC (outer diameter 7.08 cm, inner diameter 5 cm) and rectangular ring for SP (outer dimensions 3.36 × 7.36 cm, inner 1 × 5 cm). This setup enabled equal adsorption areas (Supplementary Fig. 6). In these adsorption regions, the smoothness of flow pattern was evaluated based on the distribution of V and P at discrete nodes. In addition, the uniformity was assessed by the coefficient of variation (CV) for V and P where dimensionless CV was defined as the ratio of standard deviation to mean value24. A larger absolute value of CV means a greater dispersion for data distribution.

We summarized the magnitude of velocity and CVv surrounding the adsorbent under different Re values. As shown in Fig. 1e, the BC skeleton with open pores reduced the velocity by almost one order of magnitude compared with that for SC and SP skeletons. Even for Re=105 (V=350 cm s−1) in supercritical regime, the BC could still attenuate turbulence with velocity decay to the level as low as 23 cm s−1 inside the cavity, indicating minimal disturbance to flagellum-shaped adsorbent. The velocity reduction is attributed to the interlaced fluid-alleyways and high-permeability pore network25, which prevented the flow from being accelerated when passing the cylinder or plate structures. In addition, much more uniform velocity field was obtained for BC compared with that for SC and SP skeletons, even in supercritical regime. For example, when Re value was increased from 102 to 105, the CVv for SC skeleton was increased from 0.8 to 1.5, implying discrete and non-uniform velocity distribution (Fig. 1e and Supplementary Fig. 7). In contrast, the BC exhibited a substantially more uniform velocity, with CVv being as low as 0.15 (Supplementary Fig. 7). Likewise, uniform flow field was not achieved for other hollow skeletons (i.e., GC, CC and HC), because disassembling the helical ridge and chequerboard lattice resulted in a significant loss of reversing streamline in the half space of cavity (Fig. 1d). This led to an almost 3-fold increase in CVv for CC (0.5) and HC (0.4) compared with that for BC (Supplementary Fig. 7). This suggested the smooth and uniform flow field via vortex-anchored mechanism for E. aspergillum.

The BC skeleton exhibited a vortex-induced negative pressure distribution inside the cavity (Fig. 1f), which physically attracted oil to move onto the adsorbent. In comparison, the SP and SC structures produced both positive and negative pressures, potentially leading to insufficient oil-solid contact and inefficient usage of the adsorbent materials. Because the pressure field included both positive and negative values, we used the absolute value of CVp to describe the uniformity of the flow field. Compared with the discrete pressure distribution around SC with |CVp|=78.2 for Re=102 and 3.0 for Re=105, respectively, uniform pressure distribution was observed for BC (|CVp|<0.2). Replacing BC skeleton motif by other hollow structures (i.e., GC, CC and HC) resulted in sparse vortices and non-uniform pressure distribution (|CVp|>1.0; Fig. 1f and Supplementary Fig. 8). Hence, combination of helical ridge and chequerboard lattice learned from E. aspergillum’s skeletal motif created a suitable hydrodynamic condition for stable oil capture by the adsorbent over Reynolds numbers from subcritical to supercritical regimes.

Enhancement of mass transfer

We next investigated the mass transfer during oil capture by VAF under different oil-water states, i.e., dissolved oil, floating oil, and emulsified oil, for an oil volume fraction of 1%. The mass transfer pathway for floating oil was experimentally observed in a flume at water-flow velocity in the range of 0–350 cm s−1, and that for dissolved and emulsified oils were theoretically simulated by using Lattice Boltzmann method. Considering the inertial-flow effects, we simulated the mass transfer of dissolved and emulsified oils at Re=102, 103, 104 and 105 based on single-phase flow and multi-phase flow modeling26, respectively (Method and Supplementary Text 3).

Fig. 2a-e show the pattern of mass transfer for floating and emulsified oils. Based on modified Shan-Chen algorithm developed by Falcucci et al.27,28 and Dollet et al.29 who used both repulsive and frustration forces to stabilize the droplets, the simulation could accurately capture droplet distribution in the wake region. Unlike the SC and SP structures around which oil droplets bypassed and flowed away, negative hydrodynamic pressure driven by vortical flow in the cavity of BC directly attracted the oil droplets for enhancing oil-solid interfacial contact. This appeared to be in line with the attraction of buoyant particles towards vortices reported by Fujiki et al.30. This suction effect accounted for almost 100% utilization for adsorbents (Fig. 2d, j), compared with that of 30% for SP and 20% for SC, respectively (Fig. 2e, 2j and Supplementary Fig. 9). As a result, the BC was found to capture more than 97% of emulsified and floating oil at each Re value, with <3% being leaked into the quiescent region downstream (Fig. 2f). In contrast, the capture efficiency for SC was lower than 54% at Re=102, and the values were further declined to 46% at Re=103 and 22% at Re=105. That is, BC could be highly resistant to water-flow fluctuation over a wide Re number ranging from subcritical to supercritical regions. Owing to non-uniform distribution of vortex field and negative pressure, GC, CC, and HC without helical ridge or chequerboard lattice were shown to capture only 27–32%, 43–47% and 30–35% of emulsified oil at Re=102–105 (Fig. 2f).

Fig. 2: Comparison of mass transfer for different skeletons.
Fig. 2: Comparison of mass transfer for different skeletons.
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a–c Volume fraction of emulsified oil at the wake flow for (a) solid cylinder (SC), (b) grid hollow cylinder (GC) and (c) bio-inspired hollow cylinder (BC) skeleton. d, e Optical images of oil distribution for (d) SC skeleton and (e) BC skeleton. f-g, Simulated oil capture efficiency (Ce) for (f) emulsified and (g) dissolved oil. h Simulated Sherwood number (Sh). i, Dimensionless residence time (tNon) at supercritical regime. j Simulated Material utilization (Mu). k Schematic illustration of vortex-anchored flow pattern for VAF. Source data are provided as a Source Data file.

To quantify the mass transfer of dissolved oil, we calculated the Sherwood number (Sh) in accordance to inner concentration field of dissolved oil (Eq. 9). Sh value obtained for BC (5-6) filled with vortices was approximately two folds of that obtained for SP (3.3–4) and SC (2.5–3.5; Fig. 2h). This accounted for capture efficiency of 98% obtained for BC at Re=105, the value being 4-fold and 6-fold of that observed for SP (28%) and SC (16%), respectively (Fig. 2g). These results suggested enhanced mass transfer by extra inertia effect associated with the uniform vortex-anchored field inside BC cavity of VAF whose oil cleanup was independent on oil-water states. For other hollow skeletons without helical ridge and chequerboard lattice (i.e., GC, CC, and HC), there was no extra inertial effect requisite for preventing dissolved oil from escape. Thus, the capture efficiencies for GC, CC, and HC were decreased to lower than 30% even for subcritical regime (Re=102 and 103) (Fig. 2g), which were even lower than that for SP and SC. This clearly demonstrated vortex-anchored flow pattern to be responsible for enhanced mass transfer and oil capture.

Additionally, residence time is another essential factor that exerts major influence on mass transfer and adsorption delay31. We further derived dimensionless residence time from vorticity field according to Eq. 11, as a measure of the time available for oil to dwell within the skeleton cavity. Figure 2i and Supplementary Fig. 10 show the normalized frequency for each non-dimensional residence time (tNon). Compared with SC whose maximum tNon was shorter than 1.6 at Re=105, BC exhibited an order of magnitude increase in maximum tNon (9.8). This phenomenon could be further supported by the slow vortex field observed in both optical images (Fig. 2d) and simulated flow fields (Fig. 1d). The maximum tNon observed for CC, GC and HC was only 5.3, 2.6 and 2.3, respectively, indicating the dependence of residence time on vortex-anchored flow pattern associated with helical ridge and chequerboard lattice. Notably, such mass transfer mechanism was fundamentally applicable by analogy to the stirring frequently observed for beakers in laboratory32. That is, the VAF with BC skeleton shifted the mass transfer from conventional macro-scale intercept mode to in-situ stirring mode driven by discrete small-scale vortex.

Hydrodynamic robustness

Hydrodynamic stability holds the key to robust oil cleanup under complex water-flow environments. The loss in hydrodynamic stability not only leads to inflexible and imprecise operation but also irreversibly lower mass transfer and oil capture efficiency3. We examined the hydrodynamic stability in terms of pressure drop (ΔP), drag coefficient (Dc) and experimentally measured swing angle (θsw) of different matrixes in the flume shown in Fig. 3a at Re=102–105. To decouple the impact of rotational inertia, each skeleton was designed with identical weight, size, and loading mode during the tests, as detailed in the Method section and Supplementary Fig. 11.

Fig. 3: Comparison of hydrodynamic robustness.
Fig. 3: Comparison of hydrodynamic robustness.
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a Optical images of velocity flume. b Posture of solid cylinder (SC) and bio-inspired hollow cylinder (BC) skeletons under supercritical regime at Re=105 (Supplementary Movies 1–4). c Simulated pressure drop (Dp). d Simulated drag coefficient (Dc). e, Measured swing angle (θsw) over subcritical, critical and supercritical regimes. Source data are provided as a Source Data file.

The BC structure remains stably vertical across subcritical, critical, and supercritical flow regimes due to lower pressure drop (ΔP) and reduced drag coefficient (Dc) (Fig. 3b). In detail, variation of ΔP for BC (0.007–800 Pa) was at least one order of magnitude smaller than that for the solid SC skeleton (0.3–50000 Pa) as Re was increased from 102 to 105 (Fig. 3c). Thus, the BC exhibited the most remarkable drag reduction, indicated by a Dc value as small as 1.2–0.4, which was almost half of that for SC (1.8 to 1.6) (Fig. 3d). In contrast, the higher Dc and ΔP led the solid SC to sway by θsw=20° (Re=102) to θsw=50° (Re=105) along the flow direction (Fig. 3b, e). Notably, the vortex shedding behind the SC was apparently visible under turbulent flow (Re=104–105; Movies S1–S3).

We next investigated the impact of skeletal motifs on hydrodynamic robustness of hollow-structured skeletons. As shown in Fig. 3c, the skeletons without chequerboard lattice (i.e., GC and HC) were subjected to much higher ΔP (0.08–5000 Pa) compared with that of CC (0.005–700 Pa) and BC (0.007–800 Pa) for all Re values. This led to the re-rise in drag for the GC and HC, especially for strong turbulent flow (Re=104–105), indicated by Dc of GC and HC being higher than 1.5 (Fig. 3d). Thus, these simple grids were not able to achieve stable hydrodynamic responses during oil capture. Removing helical ridge from BC resulted in a slight decrease in Dc for CC by an amplitude of 0.1, suggesting the insignificant contribution of helical ridge to fluid resistance of VAF (Fig. 3d). However, such minor impact on Dc was unlikely to compromise the hydrodynamic robustness, as BC was always kept vertical and stable under all tested Re (Fig. 3b). Considering the structural stability benefited from the helical ridge plus enhanced mass transfer, the trade-off between hydrodynamic robustness, mass transfer and structural stability could be well addressed for BC under laminar, transition and turbulent flow conditions.

Hydrodynamic mechanisms

We next elucidated the mechanisms that enabled mass transfer and hydrodynamic robustness of BC inspired by the predation strategy of E. aspergillum. Our previous study verified that the vortices could reduce the intersection angle between velocity vector and concentration gradient, thereby physical field synergy was realized for enhanced mass transfer33. Thus, we hypothesize that the vortex-anchored mechanism was also responsible for the excellent performance obtained for BC within the context of physical field synergy.

To verify this hypothesis, we first examined the relationship between vorticity field, Sh value and physical field synergy (Supplementary Text 4 and Fig. 4a, b). For all the six structures tested herein, high vorticity implied small local synergic angle (θs) for water flow surrounding the adsorbents (Fig. 4a). Moreover, the Sh value was positively correlated with the volume-weighted average θs (i.e., volumetric average synergic angle, θV). As θV was declined from 65° to 15°, Sh was increased from 3 to 7.5 for BC under all the Re values (Fig. 4c). This offered the most likely explanation to the reason for enhanced mass transfer by modifying flow pattern to achieve physical field synergy.

Fig. 4: Effect of skeletal morphology on flow pattern, field synergy, and energy dissipation at Re=105.
Fig. 4: Effect of skeletal morphology on flow pattern, field synergy, and energy dissipation at Re=105.
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a Vorticity and local synergic angle (θs). b Schematic illustration of physical field synergy. c Relationship between Sh and volumetric synergic angle (θV). d Proportion of local synergic angle (θs). e–g Time evolution of velocity fluctuation and Reynolds stresses (Rs) at point A under (e) x component, (f) y component and (g) z component. Zoomed-in view of streamline for (h) bio-inspired hollow cylinder (BC) and (i) chequerboard hollow cylinder (CC) skeletons. j, Energy dissipation rate (EDR) along flow direction for different skeletal motifs. Note: Kolmogorov microscale (Km=[(vk)3/EDR]1/4; μm) is the smallest scale of energy dissipation accounting for the smallest sized vortex in turbulent flow37. Source data are provided as a Source Data file.

We next assessed the field synergy of different skeletons. For solid SC, the vortex with θs<45° tended to form behind the skeleton at a large Kolmogorov microscale (Km)34 of 425 μm where oil was difficult to access due to flow deflection (Fig. 4a and Supplementary Fig. 12). Although θs<45° accounted for approximately 30% of the total adsorption sites (Fig. 4d), the SC was subjected to ineffective mass transfer at supercritical flow (Re=105). On the contrary, the BC evoked remarkably uniform distribution of vortices at small Km of 85 μm within the cavity, allowing 70% of total adsorption regions with small θs (<45°) from laminar to turbulent flow environments. This difference provided a plausible explanation for the higher mass transfer of BC owing to more sufficient adsorbent utilization in comparison with SC during water-flow transitions. On the other hand, inside the hollow skeletons without chequerboard lattice (i.e., GC and HC), there was no observation of apparent vortex and small θs (<45°) regions over all the Re values (Figs. 4a, 4d and Supplementary Figs. 13–15), suggesting the importance of chequerboard-like structure for vortex formation and realization of physical field synergy. For hollow skeletons with chequerboard lattice but lacking helical ridge (i.e., CC), vortices with 259 Km were only generated in the front half of cavity. In this case, poor mass transfer was encountered in the latter half part with only 25% small-θs regions (θs<45°) that occurred under supercritical regime (Supplementary Figs. 13–15). The current study shows that mass transfer was enhanced inside the BC cavity by the slow vortex field and physical field synergy driven by synergistic contribution of chequerboard lattice and helical ridge, beyond the previously known benefit of increased residence time 16.

Next, mechanistic insights into drag reduction were also elucidated by modeling the hydrodynamic field downstream through monitoring the velocity fluctuation and Reynolds stresses (Rs) at three Cartesian directions at the center of recirculation region (point A) of cylinder wake. (Fig. 4a). This point A was located at the symmetry axis of skeletons along the flow direction, and 2.5D downstream from the skeleton (D is the diameter of BC). Figure 4e–g reveal the final ~1% of time evolution within the statistical steady state of the given fluid regime. As fluid alleyways penetrated into the recirculation region, two solid skeletons (i.e., SC and SP) were characterized by intense velocity fluctuation and high Rs at all three directions35, ranging from −180 to 200 cm s−1 and 1.3–4.4 kPa, respectively. By contrast, even at supercritical flow (i.e., Re=105), the helical ridge of BC disturbed the recirculation in wake flow (Fig. 4a and Supplementary Figs. 17) and exhibited negligible fluctuation at point A with velocity components nearly approaching constant 0 cm s−1, leading Rs to be only 0.002–0.04 kPa. This clearly demonstrated the capability of BC to stabilize the flow field, thereby both pressure drop and drag could be sustained quasi-statically. Moreover, other hollow skeletons without chequerboard lattice (i.e., GC) failed to avert unstable recirculation in wake flow in three-axis velocity directions (fluctuation amplitude of −120 to 180 cm s−1, Rs of 1.3–1.9 kPa; Fig. 4e-g and Supplementary Fig. 18). Those with chequerboard lattice but without helical ridge (i.e., CC) were found to only stabilize the velocity and Rs in the vertical direction, whereas fluctuation in horizontal direction remained as great as −100 to 100 cm s−1 and 0.06–0.7 kPa (Fig. 4e-g). That is, only BC had the capability of wake stabilization among all the structures tested herein.

To shed light on mechanistic insights into such hydrodynamic behavior, we examined the evolution of flow pattern with respect to increased complexity of skeleton from simple grid structure (GC) to complex BC structure. Compared with GC across which all streamlines traversed the cavity directly (Supplementary Fig. 19), abundant vortices were generated via more intensive interaction and reversion of streamlines behind the chequerboard lattice of CC (Fig. 4h). The reversing streamlines resulted from the difference in orientation and velocity of water flow in 2D plane induced by multi-angle struts25 of chequerboard lattice (Fig. 4h). Nonetheless, the streamline reversal disappeared in the latter half of CC cavity led to insufficient distribution of vortices (Fig. 4h). Vertical guidance for the streamlines employed by helical ridge allowed them to collide, deflect, converge and separate in broader 3D space (Fig. 4i). As a result, the BC reinitiated the missing streamline reversal, followed by creating the low-speed and small scale (Km of 85 μm at supercritical regime) vortices that filled the cavity extensively (Fig. 4i). Furthermore, energy dissipation rate (EDR, W kg−1) was calculated by velocity distribution along flow direction according to Eq. 12. As shown in Fig. 4j, the kinetic energy of turbulent flow was converted to rotational energy with the EDR of 20–70 W kg−1 inside BC cavity for Re=102–105, thereby EDR was decayed to 0–5 W kg−1 in the quiescent region downstream (Fig. 4j and Supplementary Fig. 20). Notably, for solid skeletons and simple-grid structures (CG and HC), high-EDR regions were found to be located in the wake flow (25–90 W kg−1) rather than in the cavity (5–15 W kg−1) over a wide Re numbers. This resulted in considerable performance loss in terms of hydrodynamic stability and mass transfer. Taken together, the chequerboard grid was likely to be essential for generating vortices in the 2D plane, while the helical ridge played the role of re-constructing flow velocity, vortex scale, and vortex distribution in the 3D space. Our results highlighted the importance of helical ridge and the chequerboard lattice for dissipation and redistribution of water-flow energy, which was in good consistence with that reported in previous studies on biophysical mechanisms for hydrodynamic stability offered by E. aspergillum18. Physical field synergy provided the most likely explanation for the reason why enhanced mass transfer and filter-feeding efficiency were improved by vortex-anchored flow pattern.

Oil cleanup by VAF under turbulent flow

To further verify the applicability of VAF for dynamic robust cleanup of spilled oil, we performed experimental investigations on capture efficiency (Ce) for floating oil, underwater oil and emulsified oil with Si100 and Si20 (e. g. silicone oil) under Re=102–105 (Method). The results obtained for floating oil were compared with those reported in previous studies8,36,37,38, and those for underwater and emulsified oils were compared with the SC matrix.

The capture of floating oil, underwater oil and emulsified oil is illustrated by using VAF (Fig. 5a) and conventional interception matrixes (Supplementary Fig. 9). The SC matrix was unable to adsorb all three kinds of oils immediately, i.e., adsorption delay1,7, and the oil was aggregated to dispersed droplets on the surface of adsorbent (Supplementary Fig. 12). In comparison, these oils could be retained and anchored by low-speed small-scale vortices generated in the cavity of VAF matrix (Fig. 5a), which prevented secondary leakage. As a result, the SC device only captured 50% of floating Si20, 40% of underwater Si20, and only 7% of emulsified Si20 even under laminar flow (Re=102; Fig. 5b-d). Under strong turbulent flow (Re=105), these values were further declined to 7%, 5% and 1%, respectively, as a consequence of oil escape via streamline deflection. With increase in oil viscosity (Si20-Si100, 19–97 mPa s), the SC device only captured 40% of floating Si100, 21% of underwater Si100, and 6% of emulsified Si100 at Re=102, indicating the sensibility to adsorption delay. In fact, the Ce did not exceed 90% for conventional interception based on similar SC and SP skeletons, unless the Re was lowered down to 5000 (V<17 cm s−1; Fig. 5e)8,36,37,38. Remarkably, the VAF demonstrated the excellent performance for capturing all the types of oil with efficiency higher than 97% (Fig. 5b-d), even at supercritical regime (Re=104 and 105). More importantly, the adsorbent utilization reached almost 100% during oil-cleanup (Fig. 5f) in favor of enhanced mass transfer and long residence time. Taken together, the VAF demonstrated capability of dynamic robust oil cleanup by alleviating adsorption delay, oil escape and hydrodynamic instability over subcritical, critical and supercritical regimes.

Fig. 5: In-situ oil cleanup and potential applications.
Fig. 5: In-situ oil cleanup and potential applications.
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a Robust oil cleanup by vortex-anchored filter (VAF) at Re=105. b–d Effect of oil viscosity and Re number on Ce for (b) floating oil, (c) underwater oil and (d) emulsified oil. e Floating-oil capture efficiency as function of Re by making comparison with reference data for oils with viscosities of 39.3–111.9 mPa·s (i.e., ISO 32, SAE 5W-20, SAE 5W-30, SAE 10W-40, SAE 30). f Comparison of material utilization (Mu) between solid cylinder (SC) and bio-inspired hollow cylinder (BC) skeletons. g–i Three typical application of VAF for (g) flexible oil cleanup integrated to mobile vehicles, (h) real-time cleanup by serving as ballast for buoys and (i) vertical barrier for long-term cleanup at source. Source data are provided as a Source Data file.

We also tested the Ce of VAF for crude oil with much higher viscosity of 1200 mPa·s. At room temperature (25 °C), Ce<10% was observed due to blockage of the pores by paste-like, low-fluidity crude oil. When the crude oil was dispersed into droplets by raising temperature to 65°C and stirring, Ce could reach 80% for all the Re values (Supplementary Fig. 21). This necessitated the coupling of VAF to heating process (e. g. photothermal or electrothermal module) for capture of crude oil.

In light of above results, the bio-inspired VAF can be applied for dynamic robust cleanup of spilled oil with adaptability, flexibility and sustainability in several practically relevant scenarios. For example, the VAF can be well-suited to be integrated to mobile vehicles such as boat and ship, which realizes real-time decentralized pinpoint-positioning cleanup of floating, underwater and emulsified oils wherever they are spilled (Fig. 5g). In addition, the VAF can find application by serving as ballast for buoys, which allows timely cleanup in quick response to accidental oil-spill emergencies (Fig. 5h). Moreover, by virtue of superior hydrodynamic robustness and permeability, VAFs can be also used in interconnected way so as to build up long-term vertical barriers that accomplish prevention of oil spill at source (Fig. 5i). The VAF could be operated in a stationary position in turbulent flow, or positioned at the front or rear of a vessel by optimizing geometric configuration, materials and connections. For practical applications, the scale-up of VAF could be achieved by two modes, i.e., (i) principle of similarity based on relevant similarity criterions such as Reynolds number (Re), Euler number (Eu), Weber number (We) and Sherwood number (Sh), and (ii) numbered-up strategy to make scalable arrays by increasing the quantity of VAF modules (Supplementary Text 5).

From the life-cycle point of view, the devices after oil capture need to be disposed properly1,3. Hence, building-block assembly of VAF allows the used flexible adsorbents to be recycled, and the rigid skeleton to be reused by simply replacing new adsorbents. In the meantime, adsorbed oil together with the flagellum-adsorbent can be treated in the centralized manners such as burning, recycling and landfill. Cyclic tests validated the retrievability of both adsorbent materials and oil (Supplementary Fig. 23). Compared with commercial booms, skimmers, and chemical methods for oil-cleanup, the VAF developed by bio-inspired vortex-anchored flow pattern demonstrates several advantages for in-situ, dynamic robust oil cleanup under turbulent flow. This study provides insights into biophysically inspired development of all-in-one strategies for cleanup of spilled oil, benefiting from flexibility and adaptability, easy-to-handle operability and scalability, environmental compatibility and life-cycle sustainability.

Discussion

Drawing inspiration from skeletal features and filter-feeding patterns of deep-sea glass sponge E. aspergillum, we developed a vortex-anchored filter (VAF) that was practically applicable for in-situ, dynamic and robust oil cleanup under complex hydrodynamic conditions. The VAF could retain external turbulent-flow kinetic energy in small-scale low-speed vortical flow, leading to enhanced interfacial mass transfer by physical field synergy beyond previously known residence time increment. It improved hydrodynamic stability by attenuating the Reynolds stresses in wake flow. The VAF was able to realize >97% capture of floating, emulsion and dissolved oil over subcritical, critical and supercritical regimes, even under strong turbulent flow (Re=105). The present interdisciplinary study lies on the interface of environmental engineering, fluid mechanics, biophysics and bionics, which not only highlights the importance of hydrodynamics for oil capture, but also represents a paradigm shift to advance biophysically inspired strategies for in-situ, dynamic and robust cleanup of spilled oil. Besides that, our work will have broader implications that extend to bio-inspired design for advanced systems coupled with photothermal, electrothermal and electrochemical modules that are more applicable, more economical and more sustainable for environmental remediation39,40 and resource recovery41 under practically relevant hydrodynamic conditions.

Methods

Modeling

To model velocity, pressure and oil volume fraction during oil cleanup, 3D Shan-Chen multi-component lattice Boltzmann framework was developed on the basis of four assumptions: (i) the solid phase was stationary and non-deformed, (ii) the fluid phase satisfied no-slip condition at the fluid-solid interface, (iii) the computational domain was saturated by fluid components without air, and (iv) the oil droplet trajectory terminated when intercepting the adsorption region42. The dynamics of two-phase fluid were modeled by using the entropic lattice Boltzmann (ELBM) method43, accounting for both momentum conservation and continuity equation. Interaction between oil and water phase was described by the Shan-Chen pseudopotential approach, and the Shan-Chen force was coupled in source term 26,29.

$$\begin{array}{c}{f}_{i}^{k}({{\bf{s}}}+{{{\bf{c}}}}_{i}\varDelta t,t+\varDelta t)={f}_{i}^{k}({{\bf{s}}},t)+\alpha \beta [{f}_{i}^{k,eq}(\rho,{{\bf{V}}})-{f}_{i}^{k}({{\bf{s}}},t)]\\+[{f}_{i}^{k,eq}(\rho,{{\bf{V}}}+\varDelta {{\bf{V}}})-{f}_{i}^{k,eq}(\rho,{{\bf{V}}})]+{{{\bf{F}}}}^{k}({{\bf{s}}})\end{array}$$
(1)
$${f}_{i}^{k,eq}={\rho }^{k}{w}_{i}\left[1+\frac{{{{\bf{c}}}}_{i}\cdot {{\bf{V}}}}{{c}_{s}^{2}}+\frac{{({{{\bf{c}}}}_{i}\cdot {{\bf{V}}})}^{2}-{{\bf{V}}}\cdot {{\bf{V}}}}{2{c}_{s}^{4}}+\frac{{({{{\bf{c}}}}_{i}\cdot {{\bf{V}}})}^{3}-3({{{\bf{c}}}}_{i}\cdot {{\bf{V}}})({{\bf{V}}}\cdot {{\bf{V}}})}{6{c}_{s}^{6}}\right]$$
(2)
$${{{\bf{F}}}}^{k}({{\bf{s}}})= -\frac{{G}_{AB}}{{\rho }_{0}^{2}}{\rho }^{k}({{\bf{s}}})\sum_{i=1-18}{w}_{i}({|{{{\bf{c}}}}_{i}|}^{2}){\rho }^{k{\mbox{'}}}({{\bf{s}}}+{{{\bf{c}}}}_{i}){{{\bf{c}}}}_{i}-{G}_{AA,1}{\psi }^{k}({{\bf{s}}})\sum_{i=1-18}{w}_{i}({|{{{\bf{c}}}}_{i}|}^{2}){\psi }^{k}({{\bf{s}}}+{{{\bf{c}}}}_{i}){{{\bf{c}}}}_{i} \\ -{G}_{AA,2}{\psi }^{k}({{\bf{s}}})\sum_{i=1-54}{p}_{i}({|{{{\bf{c}}}}_{i}|}^{2}){\psi }^{k}({{\bf{s}}}+{{{\bf{c}}}}_{i}){{{\bf{c}}}}_{i}$$
(3)

where fik(s, t) was the probability density function for component k (i.e., water or oil) at site s and discrete time t (s), moving along the ith lattice direction; ci (cm s−1) the lattice velocity vectors; Δt (s) the time step; α the characteristic collision frequency calculated by entropy minimization (see details in Eq. 4); 0 < β < 1 a parameter related to the fluid’s kinematic viscosity vk (cm2 s−1), defined as vk=(β−1-1)cs2/2; fik,eq the local Maxwellian equilibrium, expressed as a third-order Mach-number expansion of the continuum Maxwell-Boltzmann distribution; wi the weights associated with each lattice velocity direction; cs the speed of sound within the lattice framework (commonly 3-0.5 in lattice units)26; ρk the hydrodynamical densities for both components defined as, ρk = ∑i fik; V the macroscopic velocity given by V = (∑k, i fikci)/(∑k ρk); Fk(s) the modified Shan-Chen model that included repulsive and frustration forces; GAB the interaction strength parameter for repulsive force between two components; GAA,1 and GAA,2 the interaction strength parameters for short-range self-attraction and long-range self-repulsion within a single component, respectively; pi the weights associated with each lattice velocity direction for long-range self-repulsion; ψk the pseudopotential function given by \({\psi }^{k}\left({{\bf{s}}}\right)={\rho }_{0}(1-{{{\rm{e}}}}^{-{\rho }^{k\left({{\rm{S}}}\right)/{\rho }_{0}}})\); ρ0 the reference density. Detailed description could be found in refs. 26,29,43.

The parameter α in Eq. 1 was key to maintaining the entropy balance in the relaxation step at each node and could be obtained as the nontrivial root of the equation.

$$H[{f}_{i}^{k}+\alpha ({f}_{i}^{k,eq}-{f}_{i}^{k})]=H({f}_{i}^{k})$$
(4)

where H = ∑i fik ln(fik/wi).

For single-phase flow with dissolved oil, the discrete Boltzmann equation with single relaxation time (SRT) was

$${f}_{i}({{\bf{s}}}+{{{\bf{V}}}}_{i}\varDelta t,t+\varDelta t)={f}_{i}({{\bf{s}}},t)-\frac{1}{{\tau }_{f}}({f}_{i}-{f}_{i}^{eq})({f}_{i},{{\bf{s}}},t)$$
(5)
$${g}_{i}({{\bf{s}}}+{{{\bf{V}}}}_{i}\varDelta t,t+\varDelta t)={g}_{i}({{\bf{s}}},t)-\frac{1}{{\tau }_{g}}({g}_{i}-{g}_{i}^{eq})({g}_{i},{{\bf{s}}},t)$$
(6)
$${f}_{i}^{eq}={w}_{i}\sum_{i}{f}_{i}\left[1+\frac{{{{\bf{c}}}}_{i}\cdot {{\bf{V}}}}{{c}_{s}^{2}}+\frac{{({{{\bf{c}}}}_{i}\cdot {{\bf{V}}})}^{2}}{2{c}_{s}^{4}}-\frac{3({{\bf{V}}}\cdot {{\bf{V}}})}{2{c}_{s}^{2}}\right]$$
(7)
$${g}_{i}^{eq}={w}_{i}\sum_{i}{g}_{i}\left(1+\frac{{{{\bf{c}}}}_{i}\cdot {{\bf{V}}}}{{c}_{s}^{2}}\right)$$
(8)

where fi(s, t) and gi(s, t) were the probability density function for fluid and dissolved oil, respectively; fieq and gieq the local Maxwellian equilibrium; τf and τg the relaxation time related to fluid’s kinematic viscosity vk (cm2 s−1) and dissolved oil’s diffusion coefficient D (cm2 s−1), defined as vk = cs2(τf -0.5)Δt and D = cs2(τg -0.5)Δt.

Equations 1–4 were used to address two-phase flow problems, including the oil capture efficiency and oil phase distribution. Equations 5–8 were applied to single-phase flow problems, covering analysis of flow pattern, mass transfer, and field synergy. The simulation was performed by using LBMPY and waLBerla44. All the coefficients were obtained from the software (Supplementary Table 1). We employed 19 discrete speed (i = 0,…,18) scheme along the three spatial dimensions, which was also known as D3Q19 lattice. Standard bounce-back procedure was used to deal with the coupling between fluid and solid (i.e., skeleton and flagellum-shaped adsorbents). The details in the method were described in the prior literatures45. More detailed descriptions on structure construction and initial/boundary conditions were available in Supplementary Text 3.

Design and construction of VAF

The VAF with BC skeleton was fabricated by using 3D printing on a commercially available machine EOS M290 (EOS GmbH, Germany) equipped with a maximum 400 W single-mode ytterbium fiber laser. Fabrication was carried out at laser power of 370 W, scanning speed of 650 mm s−1, hatching space of 0.11 mm, and layer thickness of 30 μm. The build chamber was maintained at a low oxygen content (<0.1 vol%) by aerating with Argon gas. Subsequently, the samples were carefully separated from the build platform via a wire Electrical Discharge Machining (wire-EDM, DK 7732). Prior to uses, ultrasonic-cleaning was performed to wash off the powder residues by immersing the samples into alcohol solution (95%) 31. The outer surface of the chequerboard hollow cylinder was coated with photosensitive resin to prevent structural damage and abrasion during installation.

Oil capture tests

The oil capture and hydrodynamic stability were tested using an open flume that was 4 m long, 45 cm tall and 45 cm wide tilted 0° from horizontal, featuring glass sidewalls and a bottom to facilitate visualization (Fig. 3a). The water flow was generated by a pump equipped with a variable frequency at the maximum flow rate of 150 L s−1 and a resolution of 1.31 L s−1. Flow rates were measured with a magnetic flow meter. The water depth was kept constant at 10.0 ± 0.5 cm using an adjustable tailgate. At the upstream end of the flume, the water passed through a flow straightener to reduce lateral velocities and make the velocity distribution as uniform as possible. The experimental section was located 1.5 m downstream of the flume entrance (Fig. 3b and Supplementary Fig. 9).

Prior to oil injection, we assessed the hydrodynamic stability of oil capture matrix by measuring their posture and swing angle (θsw) under Re=102–105 at flow velocities of 0.35, 3.5, 35, and 350 cm s−1. Each skeleton was suspended 2 cm above the flume’s base by a flexible wire attached to a fixed point, ensuring that the skeletons were submerged in the water flow and had enough freedom to sway with the flow (Fig. 3b). During the tests, each skeleton shared the same weight (Supplementary Fig. 9) and suspension setup (Fig. 3b).

We then evaluated the oil capture under three kinds of oil-water mixture, i.e., floating oil, emulsified oil and underwater oil. The emulsified oil was prepared by using 30 min 10000 Hz ultrasound with an oil-water volume ratio of 1:99. The floating oil and underwater oil were pure oil. The three kinds of oil were dyed in red color by using Oil-Red-O at mass fraction of 1%. The oil spill source was modeled by two 1×10−2 L injection syringes located 10 cm upstream of the oil-capture device. The syringes were driven by an injection pump at a rate of 1×10−3 L s−1 to ensure that all the oils reached the adsorption zone without bypassing it (Supplementary Fig. 10). For floating oil, the injection syringes were located above the water surface, while for underwater oil and emulsified oil, the injection syringes were positioned 3 cm below the water surface. We recorded the weight difference of the adsorbents before and after the test to calculate the weight of oil captured (Oc).

Calculations and analysis

Derived from simulated distribution of dissolved oil, mass transfer from bulk flow to adsorbent surfaces was calculated by using Sherwood number (Sh) according to

$${{\rm{Sh}}}=\frac{\sum {{{\bf{n}}}}_{i}\cdot D\nabla {C}_{i}}{{A}_{{{\rm{int}}}}({\langle C\rangle }^{f}-{\langle C\rangle }^{w})}\frac{L}{D}$$
(9)

where Aint (cm2) was the mass transfer area for adsorbent (i.e., 100 cm2 for hollow skeleton; 126 cm2 for solid skeleton); <>f and <>w was the average in the fluid region and the adsorbent surfaces; L (0.5 cm) the characteristic length and D (cm2 s−1) the diffusion coefficient for dissolved oil.

Hydrodynamic resistance was quantified by calculating the drag coefficient Dc as

$${D}_{C}=\frac{2{F}_{drag}}{A{\rho }_{{{\rm{inlet}}}}{V}_{{{\rm{inlet}}}}^{2}}$$
(10)

where Fdrag (N) was the total drag force acting on the oil capture matrix computed at the statistically steady state along flow direction; ρinlet (g cm−3) and Vinlet (cm s−1) the fluid density and velocity at the domain inlet and A (cm2) was the area of the transverse section being perpendicular to the fluid flow (i.e., 40 cm2).

Non-dimensional residence time tNon19,28 and energy dissipation rate (EDR, W kg−1) were calculated on the basis of flow velocity V (cm s−1) and vorticity ω (s−1) as

$${t}_{Non}=\frac{|{{\bf{V}}}\cdot \omega |{d}_{path}}{{u}_{inlet}^{2}}$$
(11)
$${\mbox{EDR}}={v}_{k}\sum _{i,j=1}^{3}{\left(\frac{\partial {V}_{i}}{\partial {x}_{j}}+\frac{\partial {V}_{j}}{\partial {x}_{i}}\right)}^{2}$$
(12)

where dpath was the length of flow path through adsorption region. Adsorption region was defined early in Section “Smoothness and Uniformity of Flow Field” (Supplementary Fig. 6). For the hollow structure, the flow path passed through the cavity, whereas in SC, it bypassed the adsorption region (Supplementary Fig. 6). Therefore, dpath for hollow structure was calculated as diameter (5 cm), and for the solid structure, it was half of the outer diameter plus a quarter of the outer circumference (9.1 cm). vk (cm2 s−1) was the kinematic viscosity of water, subscript i and j the direction of flow velocity (i.e., x, y and z).

Reynolds stress (Rs) was calculated at three Cartesian directions to assess the turbulent fluctuations in wake flows33, representing the covariance of the fluctuating velocity components as

$${R}_{si}={\rho }_{inlet}\left(\frac{1}{t}\int _{0}^{t}{({V}_{i}-\overline{{V}_{i}})}^{2}dt\right)$$
(13)

where Rs (Pa) was the Reynolds stress, subscript i the Cartesian direction (i.e., x, y and z) and \(\bar{u}\) the time-averaged velocity.

Oil capture performance was evaluated experimentally in terms of capture efficiency (Ce) as

$${C}_{e}=\frac{{{{\rm{O}}}}_{{{\rm{c}}}}}{{{{\rm{O}}}}_{0}}\times 100\%$$
(14)

where Oc (g) and O0 (g) was the weight of captured oil and the total oil, respectively.

Material utilization (Mu) was assessed from the optical images of the adsorbents before and after use as

$${M}_{u}=\frac{{{{\rm{A}}}}_{{{\rm{red}}}}}{{{{\rm{A}}}}_{{{\rm{total}}}}}\times 100\%$$
(15)

where Ared (cm2) and Atotal (cm2) was the area of dyed adsorbent and total adsorbent in the optical images, respectively. The areas were measured by using ImageJ software.