Electrostatic self-cleaning gecko-like adhesives

Abstract

This paper describes the use of the electrostatic element of an electrostatic/gecko-like adhesive to repel dust particles, which have been shown to significantly affect adhesion and reliability. The result is a non-destructive, non-contact cleaning method that can be used in conjunction with other cleaning techniques, many of which rely on physical contact between the fibrillar adhesive and substrate. The paper focuses on experimental evaluation of the repulsion of 100 μm glass beads as a function of wave shape, frequency, phase number and electrode direction in relation to the gecko-like features. Results show that a two-phase square wave with the lowest practically feasible frequency can remove 100 μm glass beads from a directional gecko-like adhesive with up to 70% efficiency. Finally, using the optimized electrostatic cleaning properties, results show an approximately 25% recovery in shear stress on a rough glass for three contaminated directional gecko-like adhesives after contact with a dusty table.

1. Introduction and background

Gecko-like adhesives have been developed as an approach for adhering to flat surfaces [1,2], manipulating micro-sized objects [3] and providing the adhesive interface that allows robots to climb [4] or perch [5] on walls, among others. Research in the field has focused on increasing the overall adhesion force [6,7], controllability, (i.e. the ability to easily attach and detach from substrates) [8] and durability [9].

Despite the abundance of research, most experiments are still done under relatively controlled laboratory conditions where surfaces have been carefully cleaned before testing; little experimental work has been performed in field conditions.

One of the major reasons for the lack of experiments in field conditions is the detrimental effect of dust and other contaminants, which our experiments have shown can decrease the shear stress by up to 100% (figure 1). This prevents researchers from obtaining reliable and repeatable results outside of a controlled laboratory setting. Thus, to improve the practicality of gecko-like adhesives, solutions must be enacted that minimize dust adsorption or enable cleaning.

Figure 1.

(a) An SEM image of a directional gecko-like adhesive contaminated with dirt particles filtered to be less than 63 μm in size. The particle size was chosen based on the ISO 14688-1:2002 standard. (b) Experimental results of the effect of contaminants on shear stress (1550 Pa normal pressure) for the directional gecko-like adhesives on a glass substrate. Shear stresses measured before and after contamination for six samples. To contaminate pads, filtered dirt was dropped by hand from approximately 3 cm above the pads. The pads were then shaken gently to remove extra dirt.

In response, this paper introduces a method to mitigate dust on gecko-like adhesives using electrostatic forces. The method takes advantage of the electrodes found in electrostatic/gecko-like adhesives, which have been previously demonstrated to increase shear stress beyond the sum of its parts and adhere to substrates with a wide range of surface properties [10]. The paper characterizes, both through experiments and simulations, wave shape, frequency, phase number and electrode direction in relation to the gecko features for directional gecko-like adhesives [9]; however, most of the results would also be applicable to non-directional gecko-like adhesives [7].

1.1. Cleaning fibrillar adhesives

There has been a large body of research on the fabrication and testing of gecko-like¹ adhesives [6,8,9,11–13]. Microstructured surfaces are generally considered more resistant to contamination compared to flat surfaces [14]; however, cleaning them has not received as much attention. In spite of that, there are several notable studies on the subject.

One approach is to create adhesives that minimize dust adsorption such that extensive cleaning is not necessary. This can be done by creating features smaller than the size of the contaminants, using stiff materials with low surface energy [15], and increasing the surface roughness [16]. Unfortunately, a low surface energy or high surface roughness can reduce the adhesive's ability to adhere to the substrate, and small features or stiff materials can decrease the ability of the fibrillar wedges to conform to any surface irregularities. Thus, one must be careful in balancing adhesion to the substrate with dust adsorption.

The second general approach involves removing adhered dust particles. To date, there have been two general methods to accomplish this: wet cleaning and dry-contact cleaning. Each is described below before we present a third method, electrostatic repulsion, in this paper.

In wet cleaning, microfibres on the adhesive make the surface hydrophobic. Water droplets can then capture and remove contaminates as the water rolls off of the surface, sometimes referred to as the lotus effect [17]. This method may work in some terrestrial situations where access to water is readily available, but it is not practical in places where water is inaccessible such as space environments, where gecko-like adhesives have shown significant promise [18].

Dry self-cleaning is a technique used by geckos to clean their feet [15]. Experimental studies of geckos revealed that higher pull-off velocity increases particle shedding [19] and digital hyperextension can increase the cleaning rate [20]. For artificial gecko-like adhesives, dry self-cleaning works well [21], but requires a clean surface with which to work. Another important limitation is that small particles (≈1 μm) may be adsorbed, which damages wedges and decreases adhesion [22].

Still other work has tried to increase the efficiency of dry contact cleaning. One method created high-aspect ratio fibrillar arrays from polypropylene, which has a Young's modulus similar to the β-keratin of a gecko's foot (E ≈ 1.5 GPa) [23]. The design was able to clean 1.5 μm gold microspheres from the adhesive by dragging the adhesives in contact with clean glass to reach 33% of the pre-contamination shear force after 20–25 steps. Unfortunately, the method did not work for particles greater than 3 μm. Another method used relatively stiffer carbon nanotubes for the gecko-like adhesives [24].

Making smaller pillars is another way to improve contact-based cleaning. Studies of adhesives comprised of polypropylene (PP) and PDMS (Sylgard 170) with different wedge sizes show that relatively harder materials with relatively smaller pillars leads to better self-cleaning [22]. Other research focused on contact cleaning of spheres, which could be enhanced by using low normal loads and low drag rates to effectively reduce the rolling resistance of the particles [25]. Finally, adding lamellae-inspired grooves can increase cleaning by providing a channel that also reduces rolling resistance [21].

All of the above-mentioned dry contact cleaning techniques have been proven to work relatively well if provided access to a clean surface. However, this caveat may be difficult to achieve in field environments. Furthermore, it is also possible that dry contact cleaning can lead to wedge damage.

1.2. Electrostatic cleaning

In contrast to dry contact and wet cleaning methods, this paper utilizes a new approach, electrostatic repulsion, which is enabled through the use of an electrostatic/gecko-like adhesive [10]. Electrostatic repulsion is a non-destructive technique that does not require any mechanical contact with external inputs like clean surfaces or water. Moreover, the use of electrostatic repulsion does not preclude the use of wet or dry cleaning methods. Thus, electrostatic repulsion can be used in addition to any of the aforementioned techniques, if desired. Furthermore, in cyclic robotic applications, electrostatic cleaning can occur during periods where the robot is moving but no adhesion is needed, such as the flight phase of a legged climbing robot, or the time between releasing one part and picking up another for an industrial gripper. This can improve efficiency by eliminating the need to interrupt operation for cleaning.

Transporting particles with electrostatic forces has been studied before. One of the earliest efforts was done to control dust in manufacturing settings [26]. Since then, a variety of applications have been proposed, such as separating small particles suspended in liquid by mass and charge [27], cleaning solar panels [28], moving liquid droplets [29] and transferring blood cells [30]. In the method described here, a voltage is applied to a set of parallel electrodes embedded in a dielectric to induce an electrostatic force on neighbouring particles. Investigation of the frequency and phase-lag effects on three-phase signals (the most commonly studied phasing) demonstrated that low frequencies generate relatively higher vertical displacement on particles [31]. Analysis of wave shape for a three-phase electrostatic actuator for particle handling showed that square waves are the most effective for particle transportation [32,33]. However, wave shape and frequency effects have not been studied for two-phase electrostatic excitation, both of which are addressed here in the context of particle removal.

There has been less of a research focus on standing waves (one- and two-phase) compared to travelling waves (three-phase) because standing waves can only repel particles, as opposed to moving them in a particular direction [26]. In one research study, a single-phase standing wave coupled with gravity was used to remove sand from inclined solar panels [34]. Other work involves electrophotography, where studies focused on identifying the electrode geometry as a function of the dielectric constant and charge distribution of the particle to be repelled [35,36].

With regard to scaling, there are no specific difficulties in applying the electrostatics to a large area. However, there are issues with scaling gecko-like adhesives in general [37]. Moreover, the power consumption during cleaning is less than 1 W (high voltage, but low current) and no specific controller is required, which makes this method practical for many applications.

1.3. Contributions and organization

This paper applies electrostatic forces for cleaning gecko-like adhesive pads and evaluates the method's performance. The effects of parameters including wave shape, phase number, frequency and electrode direction in relation to the gecko-like features on cleaning efficiency in selected conditions are experimentally investigated.

The paper is organized as follows: §2 explains the principles of electrostatic particle repulsion as a function of fluctuations in the electric field; §3 describes the fabrication process for the electrostatic/gecko-like adhesives and the test procedure; §4 details the experimental and simulation results. Finally, §5 presents concluding remarks and highlights potential areas of future work.

2. Principles of electrostatic particle removal

The van der Waals forces, F_V, and electrostatic (electrostatic, F_E; Coulomb, F_C and dielectrophoretic, F_D) forces acting on a particle on the surface of an electrostatic/gecko-like adhesive are described in this section. To illustrate the forces, a cross-sectional view of an electrostatic/gecko-like adhesive coupled with a particle is shown in figure 2a, while figure 2b shows an SEM image of several 100 μm glass beads on the surface of the adhesive. As silicon dioxide is a major component of dust [38], glass beads were used as a contaminant; however, note that the shape of the glass beads is not the same as random dust, which may contain sharp edges. These edges may result in some errors in experiments due to charge concentration on edges and non-uniform contact areas with the gecko-like adhesives.

Figure 2.

(a) Cross-sectional view of an electrostatic/gecko-like adhesive underneath a particle. The electrode width and gap between adjacent electrodes are not drawn to scale. (b) An SEM image of a directional gecko-like adhesive contaminated with 100 μm silicon dioxide particles. (Online version in colour.)

The van der Waals forces act to adhere the particle to the adhesive. The magnitude of the van der Waals force is proportional to the inverse of the distance to the power of two between the particle and microstructured adhesive as well as the surface energies of the particle and adhesive [39,40].

Electrostatic forces arise from the difference between the particle's charge and the external applied electric field [41]. Charges on the particle are created mostly through collisions among particles and between the particle and adhesive. The particle charge induces a mirror charge on the substrate that will generate an electrostatic adhesion force, F_E, between the particle and adhesive surface.

Applying an external electric field will exert a Coulomb force, F_C, on the particle due to the charge of the particle. This force adheres or repels the particle from the surface of the electrostatic/gecko-like adhesive depending on the polarity of the charge.

If the electric field is not uniform, an induced dipole moment on a particle creates a dielectrophoretic force, F_D. In this work, as the permittivity of the glass beads (SiO₂, ≈ 5) is greater than the permittivity of air and the gecko-like adhesives (Dow Corning Sylgard 170, ≈3.5), the dielectrophoretic force acts to adhere the glass beads to the surface [42]. However, as the electric field switches polarity during cleaning, the direction of the electric field will change quicker than the dielectric relaxation time of the particle, which ultimately results in repulsion.

Figure 3a shows a particle in a non-uniform electric field with forces acting on the particle in the Y-direction. Since we cannot control the charge on the particle, for the work presented here, we assume that all particles on the surface of the adhesive have the same negative charge due to prior collisions among particles and the adhesive. The negative and positive signs on the sides of the particle represent induced negative and positive charges due to the presence of the electric field, respectively. Note that there are more signs on the left side of the particle because of non-uniformity of the electric field (electric field lines are denser on the left). In figure 3a, all forces adhere the particle to the surface. In figure 3b, the electrodes' polarity has been gradually changed in a time period longer than the dielectric relaxation time of the particle, as if the electrodes are excited with a low-frequency sinusoidal wave. This results in a dielectrophoresis force that adheres the particle to the surface. Particle repulsion results only from the Coulomb force. In figure 3c, the electrodes' polarity has been changed (approx. 3.0 × 10⁻⁴ s) in less time than the dielectric relaxation time of the particle. This changes the direction of the electric field; however, the particle polarization does not change. The dielectrophoretic force changes direction and, along with the Coulomb force, repels the particle. Thus, it is critical to both maximize the dielectrophoretic force and change the polarity of the induced electric field quickly enough so that the dielectrophoretic force adds to the repulsive force rather than to the adhesion force.

Figure 3.

A particle, assumed to have a negative charge due to collisions with other particles and the substrate, has induced charges on the surface due to polarization in non-uniform electric field with forces acting on it in the Y-direction. (a) van der Waals (F_V), electrostatic adhesion (F_E), Coulomb (F_C) and dielectrophoretic (F_D) forces adhere the particle to the surface. (b) Gradually changing the electrodes' polarity in a longer time than the dielectric relaxation time of the particle causes van der Waals (F_V), electrostatic adhesion (F_E) and dielectrophoretic (F_D) forces to adhere the particle to the surface, while the Coulomb force (F_C) repels the particle. (c) Quickly changing the polarity of the electrodes in a shorter time than the dielectric relaxation time of the particle causes the van der Waals (F_V) and electrostatic adhesion (F_E) forces to adhere the particle to the surface, while the Coulomb (F_C) and dielectrophoretic (F_D) forces repel the particle. (Online version in colour.)

With regard to the dielectric relaxation time of the Sylgard 170, due to the small contact area between 100 μm particles and wedges, this effect is ignored. (However, it needs to be studied in future work, especially when the contact area is bigger.) Regarding particle–particle repulsion effect, as this parameter affects all samples (we covered the entire samples' surface with particles), its effects were the same for all tests, so it does not change the conclusion. Also, it should be considered that it is hard to distribute particles on the surface of samples without any contacts.

3. Experimental procedure

This section describes the electrostatic/gecko-like adhesive fabrication process and test procedure.

3.1. Adhesive fabrication

The description of the fabrication process is divided into three parts: the electrostatic adhesive, the gecko-like adhesive and finally, the combination of the two.

3.1.1. Electrostatic adhesive

To fabricate an electrostatic dry adhesive pad (figure 4), a ‘comb’, or ‘inter-digital’ [43,44], electrode pattern is printed on toner transfer paper using a laser printer. A laminator transfers the ink to the 9 μm-thick copper side of a 25 μm thick Kapton sheet. Copper that is not coated with ink is removed by etching in a ferric chloride bath for approximately 15 min. Any remaining ink is removed with acetone and then cleaned with isopropyl alcohol. The result is a set of 400 μm wide electrodes with a 600 μm gap between adjacent electrodes (figure 4a). A thin, approximately 20 μm, layer of DYMAX Multi-Cure 9-20557 resin is painted onto the surface to insulate the electrodes. Another layer of 25 μm thick Kapton is added to act as a high-dielectric insulator to decrease the risk of a voltage short between electrodes.

Figure 4.

(a) Electrostatic pad (without gecko-like adhesive) and (b) cross-sectional SEM image of an electrostatic/gecko-like adhesive to highlight its layers. (Online version in colour.)

3.1.2. Gecko-like adhesive

To create gecko-like adhesive wedges, Sylgard 170 (Dow Corning) is prepared according to manufacturer's specification and degassed in a vacuum chamber at 30 inch.Hg until no air bubbles appear. A spin-coating machine creates a flat thin film of Sylgard 170 on the surface of a negative wax mould of the gecko-like adhesive wedges [45]. The gecko-like adhesive consists of triangular wedges 15 μm at the base, approximately 46 μm tall and 200 μm wide, with a spacing of 25 μm between each wedge (figure 5).

Figure 5.

Geometry of the gecko-like adhesive wedges. (Online version in colour.)

3.1.3. Combination electrostatic/gecko-like adhesive

To combine the two parts, first, Dow Corning PR-1200 RTV Prime Coat Red is brushed on the surface of the Kapton to create a bond between the Kapton and gecko-like adhesive. Second, the electrostatic pad is placed on the Sylgard 170 and a 50 g weight is rolled across the electrostatic pad to remove any air bubbles that may have been trapped between the electrostatic pad and Sylgard 170. This rolling process also helps create a uniform thickness in the gecko-like adhesive. Last, the gecko-like/electrostatic adhesive is cured in an oven at 60°C for 60 min followed by 150°C for 30 min. The pads before (a) and after (b) attaching the gecko-like adhesive can be seen in figure 4. Note that due to the hand-made fabrication process, there is high variance in cleaning efficiency among different electrostatic/gecko-like adhesive pads. This variance comes from differences in the thickness of different layers and variations in the moulds over time.

Figure 6 depicts the electrode arrangement and signal connections for single, two and three-phase configurations when excited by square waves. The right side of the figure also shows the voltage waveforms and electrode states. For single-phase excitation, one set of electrodes is connected to the ground and the other to the signal's source, resulting in two possible states. For two-phase excitation, electrode sets are connected to signals 180° out of phase, which also results in two possible states. For three-phase excitation, three sets of electrodes receive signals with a 120° difference in phase. This results in six possible states.

Figure 6.

The arrangement of electrode array, connection to signal source and voltage waveform in one cycle in (a) single-phase, (b) two-phase and (c) three-phase configurations. Note that the electrode width and gap between adjacent electrodes are not drawn to scale. (Online version in colour.)

3.2. Experimental test platform

The experimental test platform includes a PC with Labview 2013 v. 13.01f2 and data acquisition card (National Instruments USB-6211) to create a multiphase voltage profile. Generated signals are amplified (Ultra Volt, 5HVA24-BP1-F) 500× to yield a peak-to-peak voltage potential of 3 kV. In this set-up, the output voltage, phase number, frequency, wave shape, duty cycle and phase lag can be adjusted.

To simulate dust, glass beads (Crystal Mark company, item 600-007-155) were filtered in both no. 140 and no. 170 sieves such that the remaining particles were 90–106 μm in diameter. The glass beads were dropped by hand from approximately 3 cm above the surface to cover the entire area of the adhesive. The adhesive pad was then gently shaken to remove any extra particles such that only one layer of glass beads remained on the surface. The adhesive covered with glass beads was examined under a microscope with 6–10× magnification. An 18 MP photograph was taken before and after cleaning without moving the pad.

The ability to remove particles is defined as the cleaning efficiency:

3.1

where N₁ and N₂ are the number of particles in each frame before and after excitation, respectively. The number of particles in the frame was determined using the imfindcircles command in Matlab v. 7.0. The function is based on detecting a particle's circular edge using a circular Hough transform [46]. For accuracy, each processed image was also checked visually to ensure that the algorithm correctly identified each particle. Figure 7 depicts an example of the particles detected before and after the cleaning process, respectively.

Figure 7.

(a): The gecko-like adhesive covered with 90–106 μm glass beads. (b) The gecko-like adhesive cleaned with a two-phase square wave at a 5 Hz frequency for 30 s. The images are of the gap between electrodes, which would lie to the left and right of each image. (Online version in colour.)

4. Results and discussion

This section details the results of 376 tests designed to evaluate the wave shape, phase number, frequency, electrode direction versus gecko-like features and cleaning time.

4.1. Wave shape and phase number

Four wave shapes were investigated to identify the best for particle repulsion: sinusoidal, square, sawtooth and triangular. The frequency, duty cycle and running time were set at 5 Hz, 50% and 30 s, respectively. The median cleaning efficiency for each wave profile when excited with single-, two- and three-phase signals is shown in figure 8. Ten samples were tested for each combination of wave shape and phase number for a total of 120 tests. The error bars show upper and lower quartiles. For one-way analysis of variance, when wave shape is the independent variable, F = 19.690 and p = 0.00001. When the independent variable is phase number, F = 32.182 and p = 0.00001.

Figure 8.

Cleaning efficiency versus wave shape and phase number for a frequency of 5 Hz. (Online version in colour.)

The results indicate that the square wave has the highest cleaning efficiency regardless of phasing. The sinusoidal wave yielded the poorest results for the single-phase signal, but it was better than the triangular and sawtooth waves for two- and three-phase signals. Finally, the sawtooth waveform has the lowest efficiency for two-phase and three-phase signals. These observations can be explained by the distribution of the electric field on the surface of the pad during the cleaning time. The square wave creates a relatively larger electric field with a longer charging time than the other waveforms. This equates to a higher repulsive force, which leads to better cleaning. As described in §2, when square waves are used, changing the polarity of the electrodes happens quicker than the dielectric relaxation time of the particles. As the polarization of the particles does not change as fast as the change in the electric field direction, the repulsive electric field strength is the sum of both the Coulomb and dielectrophoretic forces (figure 3).

With regard to phase number, the two-phase waveform has the best cleaning efficiency for all wave shapes, followed by the three-phase waveform. The single phase has a comparably far weaker cleaning efficiency. To understand why this occurs, Comsol Multiphysics v. 5.3 was used to study repulsive forces acting on particles when electrodes are excited with two- and three-phase square waves.

Figure 9 shows the magnitude of the Coulomb force acting on the particles in state 1 (figure 6, right, for a graphical representation of the electrode states) for the three-phase is higher than the two-phase configuration. Thus, the dielectrophoretic repulsive force of the two-phase design must have a significant impact.

Figure 9.

Repulsion Coulomb force acting on particles as a function of position along the electrodes when two- and three-phase square waves are applied with the assumption that all particles have the same amount of negative charge due to collision between particles and adhesives (as shown in state one in figure 6). (Online version in colour.)

The magnitude of the dielectrophoretic force depends on the magnitudes of the particle polarization and applied electric field. The former is induced by applying an electric field over time; however, there is a saturation limit (of the order of several tens of seconds) [47]. Figure 10 shows the induced polarization (dipole moment) on a particle due to the applied electric field in state 1 for two- and three-phase square wave signals, where the polarization is modelled as [48]:

4.1

where ɛ_m is the dielectric constant of the medium, r is the radius of the particle, f_CM is the Clausius–Mossotti factor and E is the magnitude of the applied electric field. The Clausius–Mossotti factor indicates the relative polarizability of the particle with respect to the surrounding medium and is given as

4.2

where ɛ_p is the dielectric constant of the particle. Note that the maximum polarization for the three-phase signal is higher than the maximum polarization for the two-phase signal; however, the dielectrophoretic force is proportional to both the polarization of the particle, P and magnitude of the applied electric field, E.

Figure 10.

Polarization (dipole moment) of a 100 μm diameter glass bead due to the electric field as a function of position for two- and three-phase square waves (state 1 in figure 6). (Online version in colour.)

The resulting (normalized) dielectrophoretic force acting on a particle is thus shown in figure 11. The repulsive force over the length of the cross-sectional surface of a two-phase electrostatic adhesive is much higher than the force generated by a three-phase signal, except for a small section at approximately 2.7 mm along the X-direction. In the three-phase signal, the dielectrophoretic forces result from a changing electric field from state 1 to state 2. As the electrodes change to states 3–6, the repulsive forces essentially move along the electrodes. Thus, they are only present at one particular electrode for a relatively small portion of time. In contrast, the dielectrophoretic forces for the two-phase configuration are always present at each electrode due to the fact that the two-phase signals only have two states. Additionally, for the two-phase configuration, there are more cycles in a given time for a given frequency than in a three-phase configuration. Therefore, particles in a two-phase field are exposed to three times the number of cycles of the three-phase configuration.

Figure 11.

Normalized dielectrophoretic forces acting on a 100 μm glass bead in state 2 as a function of position along the electrodes when two- and three-phase square waves are applied. (Online version in colour.)

4.2. Electrode direction versus gecko-like features

Because the electrostatic field is not uniform, the angle between the electrodes and gecko-like features can affect dust mitigation. To understand the effect, we experimentally investigated the cleaning efficiency for electrodes parallel and perpendicular to the gecko features (figure 12) for a two-phase square wave running at 5 Hz for 30 s (nine samples). Results are shown in figure 13, which demonstrates that electrodes that are parallel to the gecko-like features have a better cleaning efficiency compared with perpendicular (F and p for one-way analysis of variance are, respectively, 6.47 and 0.021).

Figure 12.

(a) Perpendicular electrodes to gecko-like features and (b) parallel electrodes to gecko-like features. (Online version in colour.)

Figure 13.

Cleaning efficiency versus electrode direction in two-phase pad excited with square wave. A box-and-whisker plot is used to present the data where the band inside the box is the median. Bottom and top of the box are bars represent lower and upper quartiles and dot represents the outlier. (Online version in colour.)

Note that to be able to use the same gecko-like adhesive sample on the same electrostatic pad sample, we did not follow §3.1.3. Instead, after spin-coating the mould with Sylgard 170, the mould was put in an oven to cure at 60°C for 60 min without rolling the aforementioned 50 g weight and using PR-1200 RTV Prime. This allowed us to use double-sided tape (Polymer Science 1340 double-sided PET Silicone Tape) to attach the gecko-like adhesive to the electrostatic pad. This made it possible to remove the gecko-like adhesive from the electrostatic pad after testing the ‘parallel’ configuration, rotate the gecko-like adhesive 90°, reattach it and test the perpendicular configuration. Unfortunately, this process increases the thickness of the gecko-like adhesive by approximately 120 μm, which decreases the effectiveness of the electrostatic element. Thus, the overall cleaning efficiency is reduced in the results shown in figure 13. Nevertheless, the difference between the two orientations is clear.

To understand why this occurs, we modelled the situation in Comsol Multiphysics v. 5.3 finite-element analysis (FEA) software. As the PDMS' deformation under a single particle's weight is less than 2 μm, we assume an incompressible linear elastic material with a Young's modulus of 1.6 MPa and a Poison's ratio of 0.5. Furthermore, we assume a penalty-based contact boundary condition to establish the contact between the particle and the gecko wedges. The contact boundary condition incorporates a built-in adhesion boundary condition that uses the conventional cohesive zone model (CZM) [49] for the FEA analysis. The work of adhesion for Sylgard 170 was taken to be 0.03 J m⁻². Simulations are displacement oriented, i.e. the particle is brought in contact with the wedges in the normal direction (illustrated in figure 14) and then separated from the wedges in multiple different angles, while the reaction forces and the principal stress distributions are being analysed.

Figure 14.

FEA simulations results showing the von Mises stress distribution (Pa) when a particle is in contact with the gecko wedges. (Online version in colour.)

The simulation results, shown in figure 15, confirm that particle separation requires less force when the displacement occurs in the X-direction (electrodes parallel to the gecko wedges). Moreover, as the angle of decohesion approaches the normal to the surface (90°), the separation forces in the X- and Z-directions (electrodes parallel and perpendicular to the gecko wedges features, respectively) become identical. The difference in particle separation forces can be explained by the contact area between a particle and the adhesive during the separation process and decreases over time as the particle is separating from the adhesive.

Figure 15.

Normalized particle separation force versus separation angle in the X-direction (electrodes parallel to the gecko wedges' features) and Z-direction (electrodes perpendicular to the gecko wedges' features) for the FEA simulation. (Online version in colour.)

4.3. Frequency

To evaluate the effect of square wave frequency on two-phase cleaning efficiency, five frequencies (0.5, 1.0, 5.0, 10.0 and 20 Hz) were studied. The number of the cycles was held constant at 200. This caused the running time to vary from 10 to 400 s for frequencies between 0.5 and 20 Hz. A total of 12 samples on three pads were cleaned two times, once with ascending frequencies and once with descending frequencies. Figure 16 shows the average cleaning efficiency and standard deviation for each pad separately. The difference in cleaning efficiency among pads is a result of high variance in the fabrication method. One-way analysis of variance on each pad displays a statistically significant difference in cleaning efficiency due to a change in frequency. For pads 1, 2 and 3, F and p values are F₁ = 4.135, p₁ = 0.006; F₂ = 2.695, p₂ = 0.046; and F₃ = 3.856, p₃ = 0.017. Results indicate that the cleaning efficiency increases at lower frequencies; however, it takes more time (figure 16). This phenomenon is due to the fact that lower frequencies have a longer charging time, which allows the particles to attain a relatively higher polarization [47].

Figure 16.

Cleaning efficiency versus frequency for a fixed 200 cycles (two-phase square wave). (Online version in colour.)

For some practical applications, such as climbing robots [50], it may be unreasonable to run a cleaning cycle for extended periods of time, such as 400 s. Thus, multiple frequencies (0.5, 1, 5, 10 and 20 Hz) were tested (24 samples) with a two-phase square wave for a fixed 30 s running time, resulting in a different number of cycles for each frequency. Figure 17 shows the cleaning efficiency average and standard deviation for each frequency. Results indicate that 5 Hz has the highest cleaning efficiency for 30 s of two-phase square wave electrostatic cleaning (F = 7.39204 and p = 0.00002 for one-way analysis of variance). In this case, increasing the frequency decreases cleaning time due to an increased number of cycles; however, it also simultaneously decreases the cleaning efficiency because the particles are exposed to a shorter charging time. These two opposing phenomena demonstrate why there is an optimum frequency, 5 Hz, for a 30 s running time.

Figure 17.

Cleaning efficiency versus frequency for a 30 s run (two-phase square wave). (Online version in colour.)

4.4. Cleaning time

Owing to the importance of the cleaning time, as described in §2, the required cleaning time for a two-phase square wave at 5 Hz is shown in figure 18. Cleaning efficiency was calculated for frames captured at 30 Hz. After approximately 8 s, the cleaning efficiency reaches its maximum (≈80%). Interestingly, there is a drop in the cleaning efficiency between 2 and 7 s. This is due to particles from neighbouring areas passing through the camera's frame. After 8 s, the cleaning reaches a steady state.

Figure 18.

Cleaning efficiency versus time when electrodes are excited with a 5 Hz two-phase square wave, and electrodes are parallel to gecko-like features. (Online version in colour.)

4.5. Experimental results summary

Experimental results show that the two-phase square wave with lower frequency has the best cleaning after 200 cycles. However, note that by decreasing the frequency, the running time should be subsequently increased to allow for enough cleaning cycles to occur. For a 30 s running time, a 5 Hz signal shows the best cleaning. Also, parallel electrodes to gecko-lines have higher cleaning efficiency compared with perpendicular ones. Cleaning time for two-phase square wave excitation of electrodes with a 5 Hz frequency is approximately 8 s.

4.6. Electrostatic dust mitigation

To understand the efficiency of the optimized electrostatic cleaning method on contaminated gecko-like adhesives with real dust, shear stresses were measured for a glass substrate (1.2 μm roughness) with a 1550 Pa normal pressure for three samples when they were fresh, contaminated by contact with a dusty table (figure 19) and after electrostatic dust mitigation.

Figure 19.

An SEM image of a directional gecko-like adhesive contaminated with real dust by contact with a dusty table.

In figure 20a, shear stresses for fresh samples are considered to be 100%. As can be seen, after contact with a dusty table, shear stresses for pad 1, 2 and 3 dropped to 30%, 45% and 54%, respectively. By running the optimized electrostatic dust mitigation for 30 s (two-phase square wave, 5 Hz frequency, parallel electrodes to gecko-like features), approximately 28%, 34% and 15% recovery was observed for pads 1, 2 and 3, respectively.

Figure 20.

(a) Shear stress for fresh, dusty and electrostatic dust-mitigated (30 s, 5 Hz two-phase square wave when electrodes are parallel to gecko-like features) gecko-like adhesives contaminated with real dust by contact with a dusty table. (b) Same as (a), but without electrostatic dust mitigation. (Online version in colour.)

Repeating the same procedure without running electrostatic dust mitigation (figure 20b) demonstrates that the observed recovery in figure 20a results solely from electrostatic dust mitigation (error bars show the standard deviation).

5. Conclusion

This paper introduced a electrostatic/gecko-like adhesive that uses electrostatic forces not only for adhesion but also for dust repulsion. The paper outlined the physics involved in dust repulsion using electrostatic forces and experimentally investigated wave shape, frequency and electrode orientation as a function of the gecko wedges orientation, phase number and cleaning time. The results show that cleaning efficiency can approach approximately 70% for 100 μm glass beads, which compares favourably with previously reported cleaning methods. Also, optimized electrostatic cleaning properties show an approximately 25% recovery in shear stress on a rough glass for three contaminated directional gecko-like adhesives after contact with a dusty table. More importantly, the electrostatic cleaning method can be used in conjunction with other methods and in situations (e.g. space environments, contaminated factories) where the wet and dry-contact cleaning methods are impractical or impossible. In future work, we are investigating the effect of electrode geometry, particle size and material properties on dust mitigation.

Data accessibility

This article has no additional data.

Author's contributions

V.A., M.M. and M.S. conceived the experiments and interpreted data. V.A. and M.S. wrote the manuscript. S.M.J.M.A. performed the FEA simulation for §4.2. All the authors reviewed the manuscript.

Competing interests

We have no competing interests.

Funding

This work is supported by NASA Early Stage Innovations grant no. NNX16AF05G and NASA SBIR grant no. NNX15CP47P.