Directional liquid dynamics on natural creature surfaces
Studying nature to reveal the directional liquid dynamics on the surfaces of biological organisms is the most effective way to design and fabricate artificial materials (22–27). Selected examples of biological surfaces with directional liquid transport behaviors are shown in Fig. 1. To survive in harsh conditions, organisms living in arid areas have always evolved surfaces with special wettability and topography to collect fog or water vapor from the air (9–11). For example, desert beetles have patterns of hydrophobic troughs and hydrophilic bumps on their backs (22). On surfaces with periodic chemical wetting gradients, the liquid tends to move to the area with a higher surface energy. In this process, small fog droplets first nucleate on the non-waxy hydrophilic regions and then form fast-growing droplets and slide down the wax-coated hydrophobic slopes. The driving force, FC, caused by the chemical wetting gradient can be inferred as FC~Wγ( cos θr − cos θa), where W is the drop width and θa and θr are the advancing and receding contact angles of the microdroplet on the gradient surface, respectively.
Compared with surface chemical composition gradients, the driving force caused by the structure gradients is more notable. For example, as shown in Fig. 1, spider silks can collect and transport fog from hydrophilic wet-rebuilt periodic spindle knots to joints (9). Cacti use the conical spine of the stem to move condensate drops to collect water for survival (10). In both species, the Laplace pressure difference,
, induced by the cone structure is the main driving force for directional liquid transport (23–25), where γ is the surface tension of the liquid and R1 and R2 are the orthogonal radii of curvature. The transport velocity is tens of micrometers per second (Fig. 3A and table S1). To achieve fast liquid transport, in addition to the driving force, the resistance force (FR) should be reduced. Sarracenia trichomes use a unique hierarchical microchannel structure to achieve ultrafast water transport (26). The water transport velocity is three orders of magnitude faster than that on the cactus spine (Fig. 3A). This difference is because around the trichome cone, a rapid thin film of water is formed inside the multiple channels, notably decreasing the moving resistance of the transporting water. In the same way, we can often observe on rainy days; a water strip typically slides along the previous water strip on the windshield (27). Compared with a dry surface, water tends to slide along the wet surface at a much faster speed.
In rainy tropical regions, plants also need to use surface structures to direct water directional transport for survival. Pitcher plants rely on prey-trapping pitcher organs for nourishment (28). The overlapping anisotropic V-shaped microcavities on the peristome can transport the secreted lubricant from the inner side to the outside at a speed of several millimeters per second (13). The self-constructed lubricating water layer on the peristome surface can slip insects into the bag when the insect walks on the peristome (29). A smaller condensate drop size means a small driving force for directional liquid dynamics. These measures may be effective for tiny insects and plants but are not suitable for animal drinking requirements (30–32). Shorebirds use the repeated opening and closing of their V-shaped beak for directional drinking and capturing (30). Briefly, by the repeated tweezer-like motion, birds move water from the tip of their beaks to their mouths in a stepwise ratcheting fashion. The droplet in the hydrophilic beak will form two concave liquid levels (Fig. 1). During this process, assisted by the Laplace pressure difference, contact angle hysteresis drives the drop motion directionally.
In addition to dropwise motion, continuous water directional motion can be triggered by capillary rise behavior (Fig. 1). Plants use their vessel system to transport and uplift water from the soil to leaves (31). Many animals use their mouthparts, proboscises, or tongues for drinking and ingesting enough energy (32). For example, Texas horned lizards use their skin texture with half tubes to transport water from the ground to their mouths at a speed of several millimeters per second (33). Then, by means of capillary rise, water droplets are imported into their mouths (34). In addition, numerous and complicated branching networks of tubes in the lung airway of humans and animals are of vital importance for the blood recycling and gas exchange process to promote a smooth respiratory system (8, 35). The study of the capillary rise phenomenon can be traced back to the Renaissance period. Leonardo da Vinci first recorded the capillary rise phenomena. In the following centuries, researchers have gradually concluded the detailed physical mechanism underlying the capillary rise process, summarized as the “Lucas-Washburn equation,” combining the interactions of the surface tension force, viscous drag force, inertial force, and gravity (36). The equation can be written as the following formula
, where ρ is the liquid density, η is the liquid viscosity, γ is the liquid surface tension, r is the capillary radius, g is the gravity acceleration, h is the capillary rise height,
is the one-order derivative of height h, and
is the second-order derivative of height h.
Besides water collection for survival, there are also many creatures using their unique structures to expel water directionally for preventing pollution, keeping dry, and walking quickly (7–12, 37–39). For example, a butterfly wing obliquely inserted with periodic anisotropic nanotips can orientally expel raindrops to prevent wetting (37). In detail, the direction-dependent arrangement of wings with flexible overlapping microscales with nanotips causes an anisotropic adhesive force; this force acts on the droplets, causing them to easily roll along the radial outward direction but tightly pinning them in the opposite direction. Water striders can walk rapidly on a water surface because of the special hierarchical structure on their legs, which are covered by large numbers of oriented tiny microsetae with fine nanogrooves (38). In addition, the condensed microdroplets could spontaneously bounce off the two V-shaped superhydrophobic microsetae structures directionally. This is the result of a combination of two factors: the self-penetration effect and the sweeping effect along individual cones caused by the stiffness gradient (39).
The exploration of these natural phenomena is important for developing artificial materials with similar properties to meet the different needs of our daily life and industry (12–17, 25–27). For example, researchers have constructed the bump or cone-shaped structures mentioned above by simple chemical etching or masking methods with similar or better liquid directionally manipulation ability than the surface of natural organisms (12–15, 29, 30). In recent years, researchers have successfully produced biomimetic surfaces via three-dimensional (3D) printing technology, which has excellent directional liquid transport capability (3–5, 7, 13–17). These works not only realized the unification of the structure and function of biomimetic materials but also developed some new functions beyond nature, such as the separation of oil and water microdroplets (3, 6, 25, 40).
External field–induced gradient for directional liquid dynamics
To achieve controlled and fast liquid directional transport for applications in relevant fields, an external stimulation, such as heat, light, magnetic, and electric, is performed to trigger drop motion (Fig. 2). Thomas Young proposed the cohesion of fluids in 1805, where the existence of forces is equivalent to the tension of the surface of a liquid that is uniform in all directions (41–43). In practice, the tensile force is not the same if the drop contains different liquids, such as the “tears of wine” phenomenon, or the drop deposits on thermal gradient surfaces. Today, this phenomenon is called the Marangoni effect or the Gibbs-Marangoni effect (42, 43). A liquid with a surface tension field flows along its gradient, which can be built by thermal interaction directly or indirectly. The vapor emitted by neighboring two-component droplets of miscible liquids constructs a “long-range attraction” and “short-range chasing” style. In response to the evaporation-induced surface tension gradients, neighboring droplets move autonomously and directionally (41). Cooperating with surface modifications, thermocapillary convection can perform more efficiently. Induced by the thermal interaction, the property and morphology of surfaces can be changed (42, 43). Adaptive superamphiphilic organohydrogels with a reconfigurable surface topography was developed and showed a self-healing capacity for programmable liquid transport (14).
The levitation of drops away from the surface is an effective way to reduce friction (Fig. 2). A volatile drop can levitate above its own vapor on a solid with a much higher temperature than the boiling point of the drop, which is commonly referred to as the Leidenfrost effect (44). Because the vapor vitally influences the behavior of the Leidenfrost drop (45, 46), the ratchet is a typically used asymmetric structure to investigate and manipulate the rapid motion and directional transport of the Leidenfrost drop by its close influence on vapor (47). The transport speed of a droplet is typically tens or hundreds millimeters per second (Fig. 3B and table S2). In the absence of external asymmetry, a millimeter-size Leidenfrost droplet was observed to rotate in a manner similar to wheels and then spontaneously propel in the wheel direction after detachment because of a ratchet-like mechanism caused by its imbalanced rapid internal flow (48). In addition, topographically patterned surfaces were fabricated to create two concurrent thermal states, the Leidenfrost region and contact-boiling region, to achieve the directional transport of high-temperature Janus droplets (49).
Unlike the energy sources from heating or evaporation, the energy originating from photoirradiation can be absorbed and converted to thermocapillary, chemical compositional, or photoelectrowetting gradients (Fig. 2). There are two typical compounds that are responsive to light (50–54). TiO2 under ultraviolet (UV) light can change the surface wettability from hydrophobic to amphiphilic, as reported by Wang et al. (50), and azobenzene dyes can change between cis- and trans-configurations under the radiation of different wavelengths, leading to surface wettability changes (51). Compared with other methods, as shown in Fig. 3B, the motivation time is quite long and typically takes over 30 min of irradiation by UV light (52). Since then, much effort has been devoted to investigating and improving the photo-induced directional motion of objects at interfaces (53). The combination of microfluids and photocontrol has generated a new field of research interest, called optofluidics, and has wide applications in labs-on-chips, microreactors, and actuators (54). To date, there are generally three ways to control directional movements caused by light: (i) surface modifications, such as azobenzene compounds and rotaxane decoration; (ii) introducing additives into liquids to change the stimuli-responsive properties; and (iii) deformable polymers that can bend under light irradiation.
In the case of additives, photothermal effects are used for changing liquid properties, which can achieve direct optical-to-hydrodynamic energy conversion (55–61). Photothermal nanoparticles dispersed in liquids can generate heat when focused illumination is at the liquid/air interface, which turns a liquid into vapor and thus accelerates the directional liquid motion (55). The surface tension gradient caused by the photothermal effect also works via propulsion and drives oil motion at the liquid-liquid interface (known as the chromocapillary effect); even the deformation of polydimethylsiloxane membranes can facilitate directional liquid transport (56). A stronger photothermal effect results in plasmonic heating–induced vapor flow; for example, this approach was applied to fabricate a motor by coating a piece of floating paper with a gold nanoparticle film. This new propulsion can directionally drive and control object motion on a liquid under light irradiation. The other way to achieve directional liquid transport is by introducing additives, such as liquid marbles, which was proposed by Aussillous and Quéré (57). Coated with hydrophobic particles, a droplet cannot be wetted by a liquid or a solid. Light-induced Marangoni flow can drive the liquid marble to move with and against it (58), the speed of which is several millimeter per second (Fig. 3B and table S2). In addition to directional liquid transport, materials contained in the liquid marble can also be precisely released at the target.
Recent research carried out by Kwon et al. (59) has overcome the shortcoming that UV light is necessary for a wettability change, where a dye-sensitized TiO2 surface is fabricated and can be engineered to have its wettability state optically modulated upon illumination by visible light owing to the electrical potential difference established between the surface and the liquid upon incident illumination. Except for traditional materials, a light controllable paraffin-infused porous graphene film was reported in 2018 by Wang et al. (60), which provides programmable wettability pathways to guide liquids directionally. In 2018, multiresponsive surfactants based on functionalized nanoparticle dimers were synthesized, which integrated all responsive properties into one system (61).
Photomechanical polymers, usually prepared by a single film of a liquid crystal network containing azobenzene, can bend directly under light (27, 62). In 2016, this photodeformable material was used as a tubular microactuator, which can change asymmetrically via light irradiation, and liquid slugs inside the deformed conical tube can transport spontaneously. By incorporating azobenzene derivatives with fast cis-trans thermal relaxation, this photoactive liquid crystal network–formed polymer can exhibit continuous, directional, macroscopic mechanical waves under light illumination (27, 63).
Among all the drop motion driving strategies, magnetic actuation has unique merits, including noncontact, real-time control, fast response, free of specific environmental requirements, and excellent compatibility with current biomedical technologies (Fig. 2). The design principles of the magnetoactuation of liquid droplets can be extended to two different categories: adding magnetic particles into droplets and surface deformations by the magnetic field (64–70). Commonly, a superparamagnetic liquid droplet, which can be magnetic in itself or embedded with magnetic particles, can move in response to an external magnetic field. Deformable magnetoresponsive surfaces can manipulate droplet motion directionally (64). Under a gradient magnetic field, superparamagnetic liquid droplets are attracted to the high–magnetic field region (64–66). Magnet-actuated droplet manipulation methods, such as droplet movement, coalescence, and splitting on the hydrophobic surface, provide a general means for manipulating and monitoring small volumes of liquids without the use of pumps, valves, or a microfluidic container (65–67). Compared with hydrophobic surfaces, superhydrophobic surfaces can reduce friction (Fig. 3B). For example, superparamagnetic microdroplets and ferrofluid droplets can generate controlled motion behavior on superhydrophobic ratchets and surfaces at a high motion speed (65). At the same time, the manipulation of paramagnetic liquid oxygen and ferrofluid under an external magnetic field has also been reported (67).
Magnetoresponsive surfaces are an emerging magnet actuation technique that does not necessarily incorporate magnetic particles into the liquids. Magnetoresponsive surfaces provide a flexible and controllable fluidic control platform and may greatly expand the application fields of magnetoresponsive microfluidics (68–72). To obtain magnetic responsive surfaces, researchers embedded magnetic particles into a soft matrix. For example, Zhu et al. (68) reported the real-time manipulation of the spreading directionality, fluid drag, and optical transmittance of a liquid through magnetically tunable micropillar arrays with uniform, continuous, and extreme tilt angles. In addition, Lei et al. (72) manipulated liquid droplets in a magnetic tubular microactuator by an adjustable capillary force generated by magnetism-induced asymmetric deformation. This work achieved a speed of 10 cm/s, representing the highest speed of liquid motion driven by an external stimulus–induced capillary force in a closed tube found to date (Fig. 3B and table S2). Magnetic liquids are also used to fabricate magnetically responsive surfaces (72). Wang et al. (70) developed ferrofluid-impregnated surfaces and realized topographical reconfiguration with spatial and temporal dynamics and numerous functions.
Sessile drops of water can change shape or “dance” on the dielectric surface in the presence of an alternating current electric field. Upon the application of 700-V, 50-Hz electric voltage on the solid, the water drop started to experience a wetting-dewetting state and was directionally transported at a speed of 0.15 mm/s (73). The electrowetting method to trigger liquid transport is typically relayed on patterning electrodes on the substrate (74–76). This wetting behavior is approximated by the well-known Young-Lippmann equation cos θw = cos θ + εiε0V2/(2γlvt), where γlv, θw, and θ are the relatively large liquid-vapor surface tensions and the wetted and static contact angles, respectively; εi and ε0 are the dielectric permittivities of the insulator and vacuum, respectively; V is the applied voltage; and t is the thickness of the insulator (77). The advantage of this method is that the direction and path of the droplet movement can be well controlled. Liquids are suitable for a wide range of applications without the need for additives to achieve directional liquid transport. The disadvantage is that electrowetting requires complex material processing and construction. In addition to the need to manufacture the electrodes, it is also necessary to build the circuit of the electrodes. To improve the accuracy, the number and accuracy of electrode patterns need to be improved, which increases the complexity of the overall operation (78–82).
A charged object can attract an uncharged object to move on the substrate surface. During this process, the traction of charged droplets is induced by the use of triboelectricity on the electrodes or by light (18). Printing surface charges to perform a pattern on the substrate can direct the movement of droplets on the substrate (78). The use of a nonuniform electric field distribution can suddenly direct the trajectory of droplet movement (79). Adding additives or injecting a charge into the liquid can reduce the complexity of manipulation, which can realize the attraction or repulsion of liquid droplets (80–83). A better understanding of the physics of droplet actuation is derived from electrodynamic analysis, which explains the phenomenon of electrical forces generated on the free charges in a droplet meniscus (in the case of conductive liquids) or on dipoles inside of the droplet (in the case of dielectric liquids). These forces can be calculated by integrating the Maxwell-Stress tensor, Tij,
, over any arbitrary surface surrounding the droplet, where i and j refer to pairs of x, y, and z axes, δij is the Kronecker delta function, and E is the electric field surrounding the droplet. Unlike electrowetting, this formulation explains the motion of dielectric liquids and liquids that do not experience a change in the contact angle. This method not only can realize the sudden reversal of the direction of the droplet in the 2D plane (82) but also can realize the directional trajectory of the droplet in the 3D space (81).
There are currently several ways to implement droplet drives using electricity. The speed of the droplet’s movement is subject to various restrictions. One restriction is a fast speed and a short moving distance. For example, traditional electric infiltration has a high instantaneous speed when electricity starts to trigger, but the duration is relatively short. One restriction is a slow speed, but the distance traveled is relatively long (18). Another restriction is a fast speed and a long moving distance. For example, in the work driven by the charge method (81) and the electric field (82), the electrostatic force that the charged droplet receives in the electric field is continuous.
