Triboelectric 'electrostatic tweezers' for manipulating droplets on lubricated slippery surfaces prepared by femtosecond laser processing

Figure 1(h) shows the process of preparing a superhydrophobic surface and a lubricated slippery surface in our experiment. A polydimethylsiloxane (PDMS) sheet with a thickness of 1 mm was chosen as the substrate because of its intrinsic hydrophobicity and excellent compatibility with silicone oils (the most commonly used lubricant). The characteristics of ultrashort pulse width and ultrahigh peak power have made femtosecond (10⁻¹⁵ s) lasers one of the most important tools in modern extreme and ultraprecision manufacturing [48–52]. Femtosecond laser processing was utilized to create the required microstructures on the PDMS surface, as shown in figure S2 (supporting information). After the laser treatment, uniform rough coral-like hierarchical micro/nanoscale structures were formed on the PDMS surface (figures 1(i) and S3 in the supporting information). There are abundant cracks and porous structures between the coral-like microstructures. Although slight oxidation and carbonization occur with laser ablation, the low-surface-energy C–H₃ and C–H₂ groups still dominate the ablated surface [53, 54]. Superhydrophobicity can be directly achieved after laser processing without any chemical modification (figures 1(h) and (i)). A water droplet on the resultant surface is spherical with a contact angle (CA) of (154.3 ± 2.1)° and can roll away easily at a sliding angle (SA) of (1.2 ± 0.8)° (figure 1(j) and movie S2 in the supporting information). A falling droplet can bounce multiple times on the resultant surface, indicating that the surface also has low vertical adhesion to the droplet (figures S4(a) and (b) and movie S2, supporting information). The vertical adhesive force between the structured surface and the water droplet was only (18.7 ± 4.7) μN (figure S4(c), supporting information). The excellent superhydrophobicity and ultralow water adhesion are ascribed to the synergistic effect of the inherent hydrophobicity of the PDMS substrate and the laser-induced rough surface microstructure. This synergistic effect allows the water droplet to touch only the top of the superhydrophobic microstructures (i.e. the so-called Cassie contact state) (figure 1(h-ii)) [55–57].

Lubricant infusion is needed to turn the laser-structured surface into a lubricated slippery surface. The lubricant used needs to have excellent electrical insulation so that it is not significantly changed by electrostatic interactions. As shown in figure 1(h-iii), electrically insulating silicone oil with a dielectric constant of ∼2.7 and a resistivity of 10¹¹–10¹² Ω·m was used as the lubricant and poured onto the PDMS surface. Since silicone oil molecules have a chemical structure similar to that of cross-linked PDMS, they can not only fill between the rough microstructures of the PDMS surface but also partially penetrate the PDMS network [58]. This excellent compatibility allows the silicone oil to be firmly locked into the PDMS substrate. When the excess oil is removed, a smooth and ultrathin lubricant layer is formed on the PDMS surface. The water droplets are nearly hemispherical with a CA of 95.4 ± 1.8° on such a lubricated slippery surface (figure 1(k)). Despite the large contact area between the droplets and the slippery surface, their lateral adhesion is very small. Figure 1(l) and movie S3 (supporting information) show that a water droplet slides down on the slippery surface at a tilt angle of 5° (the average SA of the droplet on the slippery surface is only 0.8°). The slippery surface also exhibited excellent liquid repellence because the trapped lubricant layer prevents the droplet from making effective contact with the solid substrate (figure 1(h-iv)).

The manipulations of liquid droplets on the superhydrophobic surface and lubricated slippery surface by TET were compared. A glass rod with a diameter of approximately 7 mm becomes positively charged when rubbed against the silk. The TCR is moved close to the droplet until the droplet begins to move. The manipulation of droplets with a volume of 10 μl on superhydrophobic surfaces is shown in the supporting information (including the description and figure S1). The droplet rolling speed is particularly fast under electrostatic attraction, even above 100 mm·s⁻¹. It takes only 137 ms for the droplets to start moving and attach to the TCR (movie S4, supporting information). Such swift motion makes the droplets difficult to control. In addition to moving in the direction parallel to the surface, we also try to move the TCR from an oblique height closer to the droplet. Unfortunately, the droplet can easily separate from the superhydrophobic surface and fly toward the high-altitude TCR because of the very low adhesion of superhydrophobic surfaces to water droplets in the direction perpendicular to the substrate surface (movie S5, supporting information). The small adhesive force cannot resist the electrostatic force in the vertical direction. When a negatively charged water droplet was previously placed on the superhydrophobic surface and a positive TCR gradually approached the droplet, the droplet became deformed but firmly adhered to the surface. This reveals that the droplet is difficult to move, even though the electrostatic force on the charged droplet is stronger than that on the neutral droplet. The negatively charged droplet can induce positive charges on the surface of the PDMS substrate due to electrostatic induction. The attractive electrostatic force of the polar opposite charges exerts a downward pull on the liquid surface near the solid surface, causing the droplet to partially penetrate into the rough surface microstructure. Therefore, the charged droplets strongly adhered to the superhydrophobic surface (figure S5, supporting information) because the charged droplets were in the highly adhesive Cassie–Wenzel transition state [57]; thus the charged droplets were not easily moved by electrostatic interactions. Therefore, there are many limitations to manipulating droplets on superhydrophobic surfaces by TET.

The characteristics of a lubricated slippery surface can easily eliminate the abovementioned difficulties associated with superhydrophobic surfaces. Figure 2(a) and movie S4 (supporting information) show the motion of a 10 μl neutral water droplet on the lubricated slippery surface attracted by a +5.5 kV charged glass rod. The changes in droplet position and velocity with time are depicted in figure 2(b). The distance (d) between the droplet and the TCR gradually decreases with time as the droplet approaches the charged rod. The droplet initially slides at a very low velocity (v), approximately moving forward at a constant speed. However, when approaching the near-glass rod, v suddenly increases. This motion process can also be reflected in the relationship between the droplet motion velocity/acceleration and d (figure 2(c)). The results also reveal that the closer the droplet is to the TCR, the more attractive it is. There is a critical distance, d₀, between the droplet and the TCR, which allows the droplet to overcome the adhesion of the substrate and begin to move. Figure 2(d) shows the measured results of d₀ under the different electrostatic potentials of the TCR. d₀ is positively correlated with the applied potential of frictional static electricity on the TCR within the error range. A higher potential results in a larger d₀, so the control distance can be longer; in other words, a larger electrostatic potential can manipulate droplets farther away. For droplets of different volumes, d₀ increases with increasing droplet volume when the volume is less than 10 μl (the droplets can be considered approximately spherical because their diameters are smaller than the capillary length) and roughly reaches saturation for larger droplets (the droplet deformation is quite serious), as shown in figure 2(e).

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In contrast to a superhydrophobic surface, a lubricated slippery surface has high adhesion to droplets in the vertical direction, although the adhesion is still low in the lateral direction [59]. The vertical adhesion ensures that the droplets cannot break away from the slippery surface. As shown in figure 2(f) and movie S5 (supporting information), when a TCR is gradually moved to approach the water droplet from above, the droplet always stays on the solid surface, although the droplet is stretched upward due to electrostatic attraction. Even when the distance between the rod and the droplet reaches the minimum limit at which an electrical discharge occurs, the water droplet remains on the slippery surface. The vertical adhesion between droplets and slippery surfaces makes it possible to manipulate droplets without gravity. For example, in a space station, astronauts or scientists can use electrostatic forces to move droplets on a lubricated slippery surface without separating the liquid droplets from the solid surface or flying into the air.

The contact state between the droplet and slippery surface is very different from that of Cassie contact on superhydrophobic surfaces, which relies on the air cushion trapped beneath the droplet [41, 57]. The space between the droplet and the solid surface is filled with lubricant on a slippery surface, stabilizing this contact state. The contact state is not changed by pressure, disturbance, or even charging of the droplet. Electrostatic forces can also drive charged droplets to slide on a slippery surface. When the charges of the TCR have the opposite polarity to the charges carried by the droplet, the TCR attracts the droplet to move (figure 2(g)). In contrast, when the TCR is charged to the same polarity as the droplet, the charged rod repels the droplet (figure 2(h)). For example, figure 2(i) shows the process of a negatively charged droplet being attracted (pulled) forward by a positive TCR, and figure 2(j) shows the process of a positively charged droplet being repelled (pushed) forward on a lubricated slippery surface by a positive TCR. Notably, negative TCRs can also achieve droplet manipulation on a slippery surface (figure S6, supporting information).

The TCR can directly and remotely exert force on droplets, similar to tweezers, to move a droplet on a slippery surface. This technique for droplet manipulation can be specifically referred to as 'triboelectric electrostatic tweezers (TETs)'.

The charges on the TCR generate an electrostatic field around the rod, as shown in figure 2(k). When an electrostatic field is applied to a droplet, electrostatic induction will cause redistribution of the charges in the droplet, i.e. the polarization process [37, 60–62]. The induced charges contribute to the electrostatic Coulomb force between the droplet and the TCR. The electrostatic force, F _e , acting on an object is the sum of the Maxwell stress working on the surface of the object, and such a surface force is the integral of the surface of the object. For a liquid droplet under an electrostatic field, the electrostatic force can be expressed as [63, 64]:

$$\begin{align}{{\boldsymbol{F}}_e} = \oint {\left[\varepsilon {\boldsymbol{E}}\left({\boldsymbol{En}}\right) - \frac{\varepsilon }{2}{{\boldsymbol{E}}^2}{\boldsymbol{n}}\right]} {\text{d}}S\end{align} \tag{ 1 }$$

where is the permittivity of the droplet ( = _r0, _r is the relative permittivity of the liquid, and ₀ is the permittivity of air), E is the electric field intensity, n is the surface unit normal, and S is the surface area of the droplet. The Coulomb force can be quantified by the following formula in tensor form [37, 65, 66]:

$$\begin{align}&{{\boldsymbol{F}}_e} = \oint {{T_{e,ij}} \cdot {\boldsymbol{n}}} {\text{d}}S, \nonumber\\ & {\text{with}}\;{T_{e,ij}} = {\varepsilon _0}\left({E_i}{E_j} - \frac{{{\delta _{ij}}}}{2}{E^2}\right),i,j = x,y,z\end{align} \tag{ 2 }$$

where T _e is the Maxwell stress tensor applied on the droplet, δ_ij is the Kronecker delta function, and E is the magnitude of the electric field intensity. The distributions of T _e in the lateral direction (T_x ) and vertical direction (T_z ) can be calculated through finite-element analysis using COMSOL Multiphysics simulation, as shown in figures 2(l) and S7 (supporting information), respectively.

Taking a positively charged rod as an example, under the influence of the electrostatic field generated by the TCR, the induced negative charges gather on the droplet surface near the TCR because of electrostatic equilibrium. In contrast, the positive charges gather on the side farthest from the TCR. Therefore, the electrostatic force on the droplet consists of two parts ( F _e = F _e,a + F _e,r ): the attraction force ( F _e,a ) on the negative charges and the repulsion force ( F _e,r ) on the positive charges (figure 2(m)). Although the charges are not uniformly distributed, we can treat them as a point charge for simplicity, with a total charge of q. The polarization charge due to electrostatic induction can be written as [20, 62]:

$$\begin{align}q = \left({\varepsilon _r} - 1\right){\varepsilon _0}\left| {\nabla {\boldsymbol{E}}} \right|.\end{align} \tag{ 3 }$$

According to Coulomb's law, the net electric force can be approximated as:

$$\begin{align}{{\boldsymbol{F}}_e} = {\boldsymbol{E}}q = \left({\varepsilon _r} - 1\right){\varepsilon _0}\left| {\nabla {\boldsymbol{E}}} \right|{\boldsymbol{E}}\end{align} \tag{ 4 }$$

where ${\boldsymbol{E}} = - \nabla V$ (V is the electric potential). The intensity and variation of the electric field are depicted in figure 2(k). The further away the charged rod is, the smaller the electric potential and the smaller electric field strength. Therefore, the attraction where the negative charges accumulate is greater than the repulsion at the side where the positive charges accumulate. That is, the attraction of the negatively induced charges (near the TCR) to the droplet is dominant (figure 2(l)). The direction of the resultant electrostatic force on the droplet is toward the TCR. This electrostatic force provides the driving force for droplet motion.

The dynamic behaviors of droplets on slippery surfaces are determined by the resultant force acting on the droplet. As shown in figure 2(m), there are four main forces acting on the droplet: the electrostatic Coulomb force (F_e ), the gravitational force of the droplet (G = mg, where m is the mass of the droplet and g is the acceleration of gravity), the lateral adhesive force (F_ad,x ), and the vertical adhesive force (F_ad,z ). We only consider lateral droplet manipulation. The horizontal composition of the electrostatic force and lateral adhesive force could be responsible for the propulsive movement of droplets on a horizontal surface. The net force F driving the droplet can be expressed as:

$$\begin{align}F = {F_e}{\text{cos}}\alpha -{F_{ad,x}}\end{align} \tag{ 5 }$$

where α is the angle between the electrostatic force and the horizontal direction. This relation provides a fundamental understanding of droplet motion in an electrostatic field. The lateral adhesive force can be expressed as F_ad,x = kwγ (cosθ_r –cosθ_a ), where k, w, γ, θ_r , and θ_a are the shape correction coefficient, width of the droplet, surface tension of the droplet, receding CA, and advancing CA, respectively [67, 68]. Since slippery substrates have very little lateral adhesive force to water droplets, when the TCR is close enough to the droplet, F_e can be greater than F_ad,x . When F > 0, the droplet begins to move, which is driven forward by electrostatic forces. When the droplet slides on a surface lubricated by silicone oil, it will be affected by motion resistance, mainly caused by viscous force (F_μ ). According to the experimental results of Aizenberg et al, F_μ can be approximated as [69–71]:

$$\begin{align}{F_\mu }\sim \pi {\gamma _{wo}}RC{a^{2/3}}\end{align} \tag{ 6 }$$

where γ_wo is the water–oil interfacial tension, R is the droplet radius, and Ca is the capillary number $Ca = {\mu _0}v/{\gamma _{wo}}$ (μ₀ is the oil viscosity and v is the motion velocity of the droplet). Thus, the equation of motion of the droplet can be described as follows:

$$\begin{align}{F_e}\text{cos} \alpha - {F_\mu } = ma = m\frac{{dv}}{{dt}}\end{align} \tag{ 7 }$$

where a is the acceleration of the droplet and t is the time. Therefore, by moving the charged rod and maintaining the proper distance between the droplet and the rod, the droplet can be guided to move uniformly on the slippery surface. The motion velocity can be adjusted from low to high by controlling the proper distance from the rod.

The characteristics of the lubricated slippery surface enable the TET to have the dexterous ability to manipulate droplets. Figure 3(a) and movie S6 (supporting information) show that a 10 μl water droplet attracted by a TCR slides upward along the inclined slippery surface. Due to the vertical adhesion of the slippery surface to liquid droplets, the droplets will not fall off the slippery surface even if the surface is turned over. This property allows TETs to manipulate suspended droplets. Suspended droplets can also be attracted remotely through electrostatic interactions (figure 3(b) and movie S6 in the supporting information). In contrast, manipulating suspended droplets on superhydrophobic surfaces is impossible because droplets cannot hang on superhydrophobic surfaces. The electrostatic repulsion between a TCR and a charged droplet of the same polarity can push a tiny droplet to climb vertically against gravity on a vertical slippery surface (figure 3(c) and movie S6 in the supporting information).

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In addition to water, electrostatic forces can manipulate a variety of other liquids on slippery surfaces. For example, common fluids (e.g. milk, coffee, cola, and juice) during life are repelled by slippery surfaces and thus can be easily moved with the TCR (figure S8 and movie S7, supporting information). The slippery surface is resistant to corrosion because the lubricant layer can prevent corrosive liquids from effectively contacting the substrate surface [72]. Therefore, the manipulation of corrosive droplets is allowed on slippery surfaces. As shown in figure 3(d) and movie S7 (supporting information), corrosive droplets composed of acid HCl solution at pH = 2 (figure 3(d-i)), alkali NaOH solution at pH = 12 (figure 3(d-ii)), and 10% NaCl salt solution (figure 3(d-iii)) can be driven to slide by electrostatic interactions. The slippery surface is also able to repel low-surface-tension liquids, so droplets with low surface tension, such as ethanediol (figure 3(e-i)), propanediol (figure 3(e-ii)), 50% ethanol (figure 3(e-iii)), and ethanol (figure 3(e-iv)), can also be transported on the slippery surface (movie S7 in the supporting information). The surface tension of these droplets is as low as 22.3 mN·m⁻¹ (figure 3(f) and table S1 in the supporting information). In contrast, due to Cassie contact state failure, superhydrophobic surfaces are usually wetted by liquids with low surface tension (figure S9, supporting information), preventing these liquids from being moved by electrostatic forces on superhydrophobic surfaces. Surprisingly, in addition to liquids, small air bubbles (figure 3(g-i)) and solid plastic balls (figure 3(g-ii)) can also be attracted by the TCR to move forward on the slippery surface (movie S8, supporting information). Induced charges are also generated on the surfaces of the bubbles and the solid balls, causing the bubbles and plastic balls to move under the action of electrostatic forces.

The deformability of fluids allows droplets to pass through narrow slits. Figure 3(h) and movie S9 (supporting information) show the process of a positively charged 20 μl droplet being remotely pushed through a slippery narrow slit with a width of 2 mm by a positively charged metal rod. The bottom and sidewalls of the slit are composed of femtosecond laser-structured slippery microstructures. The bottom diameter of the droplet on the slippery surface is approximately 3.3 mm, which is less than the width of the narrow slit. When the droplet entered the slit, it elongated and squeezed in the slit. Finally, the droplet successfully passed through the narrow slit whose width is 1.7 times smaller than the droplet diameter. This flexibility allows the droplet to act as a soft robot that can be controlled remotely by a TET to perform specific tasks in a confined space.

A slippery surface usually has high stability and good self-repairing capability [41]. Even if subjected to multiple bending, friction, and droplet scour treatments, the slippery surface prepared by the femtosecond laser can maintain liquid repulsion for a long time [41, 44]. As shown in figure 3(i-i) and movie S10 (supporting information), even if a knife scratches the slippery surface, the TCR can guide liquid droplets to slide over the scratch. This outstanding performance is due to the spontaneous repair of the damaged area by the lubricant (figures 3(i-ii)–(i-iv)). The lubricant on the slippery surface and the lubricant filled inside the PDMS network quickly flowed to the damaged area and filled the scratches (figure 3(i-iii)), ensuring the smoothness of the surface lubricant layer. Thus, the damaged area still allows the droplet to slide through (figure 3(i-iv)). In contrast, droplets stick to scratches on superhydrophobic surfaces because of the high adhesion of the damaged area to the liquid (figure S10, supporting information).

In addition to PDMS, slippery surfaces can be prepared on various substrates, such as polytetrafluoroethylene (PTFE), aluminum, silicon, and glass. As shown in figure S11 and movie S11 (supporting information), droplets can also be manipulated on these slippery substrates by TET. The substrates include both electrically conductive and electrically insulating materials. The successful movement of droplets on different substrates demonstrated that electrostatic droplet manipulation on slippery surfaces is a universal method and does not depend on the type of solid substrate.

TETs not only enable contactless, flexible, and precise droplet manipulation on slippery surfaces but also exhibit many dexterity capabilities. As shown in table 1, manipulating liquid droplets on a slippery surface based on a TET has many advantages over manipulating liquid droplets on a superhydrophobic surface.

The remote and flexible manipulation of droplets with TETs enables various practical applications ranging from motion guidance, motion switching, droplet-based microreaction, surface cleaning and surface defogging to liquid sorting. For example, a droplet on a slippery surface can be dragged remotely in any direction under electrostatic attraction by a TCR. TET can even guide droplets out of complex maze patterns, as shown in figure 4(a) and movie S12 (supporting information). Small droplets can carry chemical reagents. Contact between different droplets can trigger reactions between different chemical reagents, also known as droplet microreactions. Figure 4(b-i) and movie S13 (supporting information) show the process of guiding a 10 μl aqueous droplet of AgNO₃ to merge with a FeCl₃ droplet on a slippery surface. When the two droplets come into contact, a precipitation reaction (Ag⁺ + Cl⁻ → AgCl↓) occurs, forming a white precipitate inside the merged droplet (figure 4(b-ii)). As the merged droplet continues to move and comes into contact with another phenol droplet, the newly merged droplet turns purple because of the color reaction (6C₆H₅OH + Fe³⁺ → [Fe(C₆H₅O)₆]³⁻ + 6H⁺) (figure 4(b-iii)). It should be noted that the reaction can also be carried out by moving the phenol droplet to other droplets. Both inorganic and organic reactions based on droplet manipulation have been demonstrated on slippery surfaces. In contrast, achieving an organic droplet reaction on a superhydrophobic surface is difficult because low-surface-tension organic liquids (e.g. phenol) usually wet the surface (figure S12, supporting information). The TET can be used for motion switching to control the sliding and pinning state of the droplet on a slippery surface, as shown in movie S14 (supporting information). When a TCR is suspended above the slippery surface, droplets sliding on the surface by gravity stop below the TCR due to electrostatic attraction (figures 4(c-i) and (c-ii)). The droplet is pinned on the slippery surface without the TCR touching it directly. Once the TCR is removed, the droplet will continue sliding downward (figures 4(c-iii) and (c-iv)). Therefore, droplet motion can be remotely switched between sliding and pinning states in a noncontact manner.

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There are no restrictions on the direction or travel distance for electrostatic droplet manipulation, which makes it possible to remotely and precisely clean contaminants on a slippery surface with a TET. When the droplet slides forward, foreign objects on the surface can be picked up. As shown in figure 4(d) and movie S15 (supporting information), a slippery surface contaminated with tiny spray drops is cleaned by a large droplet guided by a TCR. The clean droplet is driven to slide along an 'M'-shaped route, during which all contaminants are removed (figure 4(d-ii)). By controlling the motion of the droplets, the cleaning path can be precisely programmed. Inspired by the windshield wiper, the charged rod swung from side to side to clean fog drops on the slippery surface without direct contact (figure 4(e-i)). Tiny droplets are attracted to both sides of the slippery surface, keeping the surface clear (figures 4(e-ii) and (e-iii)).

Under the electrostatic attraction of a TCR, different droplets can be guided to different sliding routes remotely to achieve liquid sorting (movie S16, supporting information). As shown in figure 4(f) and figure S13 (supporting information), a droplet can slide down slowly by gravity on an inclined slippery surface (step-1). When the droplet reaches the vicinity of the TCR, the height of the TCR is decreased to generate a stronger electrostatic force on the droplet (step-2). Then, if the TCR is moved laterally, the droplet will move with it (step-3). Once the droplet slides to the designated route, the TCR will be lifted to reduce electrostatic attraction. After that, the droplet continues to slide downward and toward the liquid collection zone (step-4). Figures 4(f-i) shows the process of a red droplet being assigned to the left collection tank via electrostatic interactions. Following the same process, blue and green droplets were distributed to the middle and right collection tanks, respectively (figures 4(f-ii) and (f-iii)).

The TET can be assembled into a mechanical control system to achieve more accurate control of droplets. As shown in figure 5(a), the TCR is vertically fixed on a three-dimensional mobile platform. As the TCR moves directly above the droplet and then decreases to a suitable height, the droplet will be bound by the electrostatic force. When the TCR moves laterally, the droplets on the slippery surface will move with it, always under the rod (figure 5(b)). It is like manipulating droplets with a VET. Figure 5(c) reveals the underlying mechanism of the ability of the VET to move droplets. The electrostatic force acting on the droplet directly below the TCR is symmetric in the horizontal plane; thus, there is no lateral force on the droplet (figures 5(c-i) and (c-ii)). Once the TCR is moved forward and the droplet is not directly below the TCR, the electrostatic force on the droplet will be asymmetrical in the horizontal plane and stronger along the center of the rod (figures 5(c-iii) and (c-iv)). The asymmetrical electrostatic force pointing to the TCR will drive the droplet to slide to a position directly below the TCR, again achieving horizontal electrostatic symmetry. As a result, the droplet is always below the TCR and can be moved remotely by the VET. The control strength of the VET is affected by the distance between the TCR and the droplet. When the distance between the TCR and the droplet is close, the droplet deformation is more serious, indicating that the VET strongly binds the droplet (figure 5(d)). A strong binding force can accelerate droplet manipulation. However, too small a distance can easily lead to disruptive discharge. By mechanically moving the TCR horizontally, the droplet can slide back and forth on the slippery surface (figure 5(e) and movie S17 in the supporting information). It should be noted that there is a small position delay between the droplet and the rod during droplet movement because the motion of the droplet is affected by viscous resistance (figure 5(f)). The measured displacement delay and time delay are 2.1 mm and 1.0 s, respectively, at a velocity of 2 mm·s⁻¹. Despite the motion delay, the droplet can eventually reach the position directly below the rod, meaning that it can obtain its target position precisely.

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VET strongly binds droplets, so droplets of different volumes can be manipulated (movie S18, supporting information). As shown in figure 5(g), even water droplets much smaller in diameter than the TCR (e.g. a 100 nl water droplet) or enormous pie-shaped droplets (e.g. a 0.5 ml water droplet) can be transported by the VET. Unlike other reported methods of droplet manipulation that require a predetermined pathway [73, 74], the guided mode of mechanically assisted VET allows the droplet to move in any desired direction. Figure 5(h) and movie S19 (supporting information) show the use of the VET to remotely move a droplet along a handwritten Chinese character-shaped track (meaning 'happy') on a slippery surface. The droplet faithfully followed the tweezers. By controlling the mobile platform through a computer program, we can more precisely control or design the motion path of the droplets. In addition, compared with reported ETs with ultrahigh applied voltages [37], TETs based on frictional static electricity are safer and more portable.

The ability of the VET to remotely transport droplets allows us to manipulate liquids in an enclosed system, as shown in figure 5(i-i). As a demonstration, a water droplet on the slippery surface was placed into a disposable Petri dish (the most common cell culture plate) and covered. We succeeded in moving the droplet from outside the closed system (figure 5(i-ii) and movie S20 in the supporting information). The noncontact manipulation of droplets in an enclosed system from the outside is difficult to achieve via other methods. In some special applications, such as biomedicine, the remote operation of liquids in enclosed systems is highly useful. For example, figure 5(j) shows a simple cell labeling experiment in which the VET manipulates a droplet containing HeLa cells to merge with a PBS aqueous droplet containing SYTO-16 stain to stain the cell nucleus in an enclosed Petri dish. The cells were labeled with green fluorescence without opening the culture system. In this process of manipulating cells, the closed space ensures that the cells are not polluted by the external environment and that the gaseous environment of the cell culture is not changed. TETs provide a low-cost, contactless, highly controllable, and portable way to move and merge droplets isolated from the external environment.

Solid PDMS was prepared by mixing the Sylgard 184 liquid prepolymer (Dow Corning Corporation) and its curing agent at a volume ratio of 10:1. The mixture was then poured on a glass substrate, followed by heating at 80 °C for 4 h. As a result, cured PDMS sheets with a thickness of 1 mm were adhered to the glass substrates. The glass rods, rubber rods, silks, and furs used to generate static electricity by friction were purchased from online stores. PTFE and aluminum substrates were purchased from YuanDongLi Internet Corporation. Silicon wafers were purchased from SILICON WAFER Corporation. The glass substrates used were ordinary microscope slides (CITOTEST). Silicone oil (PMX-200, 10 cSt) was purchased from Dow Corning. Pure milk, coffee, Coca-Cola, and orange juice were purchased from a local supermarket. HCl, NaOH, NaCl, ethanediol, propanediol, ethanol, AgNO₃, FeCl₃, and phenol were purchased from Sinopharm Chemical Reagent Co., Ltd. Deionized water was used as the main measured liquid droplet.

A femtosecond laser (Spectra-Physics, USA) was used to generate the required microstructure on the PDMS surface. As shown in figure S2 (supporting information), the laser pulses (pulse duration = 75 fs, central wavelength = 800 nm, repetition rate = 1 kHz, pulse energy = 500 μJ) were guided into a high-speed galvanometer scanner (s-9210d, Sunny Technology, China) and further focused onto the PDMS surface by an f–θ lens (focal length = 160 mm) with a spot diameter of ∼30 μm. The laser scanning speed and scanning space were set at 10 mm·s⁻¹ and 30 μm, respectively, under line-by-line scanning. The laser-treated samples were carefully cleaned with ethanol and deionized water under ultrasonication. The laser-structured PDMS surface directly exhibited superhydrophobicity. To obtain a lubricated slippery surface, silicone oil was used as the lubricant and poured onto the sample surface, allowing the silicone oil to fill the rough microstructures of the PDMS surface. Excess oil was removed by standing the sample upright. The method for preparing superhydrophobic and slippery surfaces on PTFE, aluminum, silicon, and glass substrates is similar to the above process, except that the laser-treated aluminum, silicon, and glass surfaces require a low-surface-energy modification.

A glass rod with a diameter of approximately 7 mm was positively charged by rubbing it against the silk. Similarly, a rubber rod was negatively charged by rubbing it against the fur. The electrostatic potential on the surface of the charged rod was measured by an electrostatic voltage tester (FMX-003, Xiangruide Corp.). The induced electrostatic potential can be adjusted (0 ∼ (±6) kV) by the strength and speed of friction. The charged rod was moved close to the droplet until the droplet began to move. Unless otherwise specified, the volume of droplets used to achieve manipulation was 10 μl. The charged rod was then moved to guide the droplet forward, and the droplet was kept at a suitable distance from the charged rod.

The charged rod with frictional static electricity was vertically fixed on a three-dimensional mobile platform. The rod was first moved to the position above the droplet. Then, the height was decreased to a suitable height so that the charged rod could exert a strong binding force on the droplet. Through the movement of the mobile platform, the droplet moves with the rod and stays below the charged rod.

HeLa cells were grown in cell culture medium (Process, China) at 37 °C and 5% CO₂. When the cells reached 90% confluence, they were washed, treated with trypsin, centrifuged, and resuspended to produce a cell suspension. Then, a droplet containing the HeLa cells was transferred to the enclosed system (i.e. a closed Petri dish). The droplet was remotely moved to merge with another aqueous PBS droplet containing 2 μl·ml⁻¹ SYTO-16 (KeyGEN, KGA260) for 30 min to stain the cell nucleus. After this, the fluorescence images of the droplets were observed by a fluorescence microscope (Leica, DMI8).

Finite element analysis (COMSOL Multiphysics, MA, USA) was used to calculate the surface potential, electric field, and electrostatic force for droplet manipulation. In the simulation setup, electrostatic field physics was used in an air environment. The physical characteristics of the shapes and dimensions of the charged rod and the liquid droplet, as well as the initial surface potential, were chosen as in the measured experiments. The droplet deformation was small and therefore negligible in our simulations.

The surface microstructure of the PDMS substrates after femtosecond laser ablation was observed by a scanning electron microscope (GeminiSEM 500, Carl Zeiss). The wettability of the as-prepared superhydrophobic surface and slippery surface was measured by a contact-angle instrument (CA100C, Innuo). A digital camera (D7100, Nikon) was used to record the processes of electrostatic droplet manipulation. In particular, extremely fast droplet motions were captured by a high-speed camera (Chronos 2.1-HD, Kron Technologies) at 1000 fps.