Particle Rolling on a Fibrillar Interface Uyiosa Abusomwan, Metin Sitti Carnegie Mellon University Pittsburgh, Pennsylvania, 15213, USA [email protected] Introduction Despite the significant progress made towards the design and fabrication of fibrillar adhesives and the successful demonstration in several potential application areas such as in robotics, manufacturing and biological devices, a notable success has not been seen in the use of fibrillar adhesives in real-world environments (1-3). One of the major hindrances to practical application of fibrillar adhesives is the presence of particle contaminants in the environments which have been shown to drastically reduce the adhesive strength and overall performance of fibrillar adhesives. Recently, dry contact-based cleaning procedures have been successfully demonstrated as a more practical method of recovering some or all of the initial adhesive strength of contaminated fibrillar adhesives (4). The cleaning procedure involves cycles of loading, shearing and unloading the contaminated sample against a rigid smooth substrate. The success of the procedure has been attributed partly to particle rolling or sliding at the fibrillar interface. In this work, we further investigate shear-based contact cleaning to unearth the main mechanism of dry contact cleaning. Load-drag-unload cleaning experiments are conducted for adhesive samples contaminated with a single contaminating particle. An analytical model of particle rolling which fits well with the experimental data is also presented. Experiments The experiments were conducted on elastomer microfibers with mushroom-shaped tips, which were fabricated using a published lithographic technique (5). The diameter of the microfibers tip was 95 μm, with an aspect ratio (tip diameter to height) of 1. The samples were made from polyurethane elastomer (ST-1060, BJB Enterprises) with Young’s modulus Ef of 2.9 MPa and work of adhesion to glass Wpf of 93 mJ/m2. Glass microspheres (Potters Industries, ‘type 1922’) were used as contaminants. The cleaning experiments were performed on a custom designed 2-axis force measurement system, consisting of automated linear actuated stages (MFA-CC and VP25XA, Newport) for motion control, manual rotational stages (GON40-U, Newport) for angular alignment, and load cells (GSO-50 and GSO-10, Transducer Techniques) for force measurement. The setup was mounted on an inverted microscope and a colored digital video camera (DFW-X710, Sony) was used to capture the visual data during the experiment. A customized software was used to control the system and to record time-stamped visual and force data. During the experiments, a clean and smooth glass slide was brought into contact with the contaminated samples and compressed to a desired preload. When the preload is reached, the glass slide was moved horizontally (parallel to the substrate) at a constant speed, while keeping the preload constant. The distance travelled by the particle δ was manually obtained from post-analysis of the recorded video frames. The recorded force data from the load cells were analyzed using a custom MATLAB code. By varying the normal load Fz, we studied the effect of preload on the particle displacement, and observed the mechanism (rolling vs sliding) of the particle motion. In this work, two sets of experiments were conducted: In Experiment I, the dry-contact cleaning of a particle larger than the diameter of the fiber tip was studied, using a 240 μm diameter particle as the contaminant on a microfiber array. In this study, the particle makes contact simultaneously with more than one microfiber. The particle was loaded with Fz ranging from 0.5 mN to 200 mN, and the substrate was moved at a constant speed of 20 μm/s for 2mm. In Experiment II, the dry contact cleaning of a particle smaller than the diameter of the fiber tip was studied. In this case, the particle is in contact with only one microfiber tip at a time. Subsequently a JKR contact was assumed. In this study a particle was sandwiched between a glass substrate and a flat polyurethane mold. The choice of using a flat polyurethane substrate in place of a single microfiber was due to the limitation of our force sensor to measure the sub-milliNewton rolling force of particles much less than the fiber tip. However, we believe that the physics and mechanism are the same. A large 500 μm radius particle was used as contaminant in the experiment to further magnify the rolling resistance force. The polyurethane mold was made by soft cast molding against a smooth and flat acrylic to obtain a smooth polyurethane elastomer surface. Similar to Experiment I, a clean glass substrate was brought into contact with the contaminated polyurethane sample and preloaded to a desired normal load. The glass substrate was then displaced horizontally at a constant speed while keeping the normal load constant. Results and Discussion For a spherical particle sandwiched between a glass substrate and an adhesive sample, three cases of particle motion are possible, when a shear force is applied to the substrate: in Case 1, the particle slides along the substrate without moving relative to the adhesive; in Case 2, the particle slides along the adhesive without moving relative to the substrate; and in Case 3, the particle rolls with respect to the two surfaces. A combination of any two or all three cases is also possible. We define the relative displacement of the particle, ρ as ρ = 2δ / Δ, (1) where δ is the total the particle moves when the substrate is moved by a distance Δ. Under pure rolling motion (Case 3), the contaminating particle will move a distance equal to one-half the applied displacement, so that ρ = 1. However, for Case 1, ρ = 0; and ρ = 2 for Case 3. Evidently, ρ is a measure of the cleaning performance under a given normal load. We will declare that a value of 1 or greater indicates a good cleaning cycle. In Experiment I, we measured the total distance traveled by the 240 μm diameter particle along the microfiber array, when the substrate is moved a distance Δ = 2 mm, at a drag velocity of 20 μm/s and for various normal loads. Figure 1 shows a graph of relative displacement plotted against Fz. From the graph and recorded video, it is observed that at normal loads less than 10 mN, the value of ρ is slightly greater than 1 and the particle rolls on the microfiber tips with seldom slipping across the tip. As the normal load increases up to about 50 mN, the particle indents the microfibers and rolls across the microfiber sides with infrequent sliding on the glass substrate, with ρ approximately equal to 1. ρ decreases to 0.8 at 200 mN as sliding on the glass substrate becomes more frequent. Beyond a normal load of 200 mN, some microfibers in the array make contact with the substrate, and the particle slides on the glass surface. These results suggest that low normal loads favor dry contact cleaning. Secondly, from our visual analysis, it is observed that particle rolling dominates the cleaning process. A graph of the measured shear force Fc for the various normal loads is also shown in Fig. 2. As expected, we observe an increasing rolling resistance force as the normal load is increased. However, Fc is almost linearly proportional to the applied normal load. From Experiment II, the particle is sandwiched between a rigid glass substrate and a flat polyurethane elastomer sample. Experiments were conducted at normal loads reaching up to 153 mN. A visual post-processing of the experimental videos show that the particle rolling dominates at all the preloads tested. The results of the measured shear force at various normal loads are shown in Fig. 3. The results show a steady increase in the measured shear force as the normal load is increased. Using on the JKR theory, Dominik and Tielens (6) derived the rolling resistance moment M at the interface of two contacting particles as M=6πRWξ, (2) where ξ is the critical rolling displacement before a readjustment of the contact zone, and W is the work of adhesion of the interface. In the present study, the particle is in contact with two surfaces so that the total rolling resistance is given as MT=6πR(Wpfξpf+Wpsξps), where the subscripts ‘ps’ and ‘pf’ refers to the particle fiber and particle substrate interfaces, respectively. The critical drag force Fr required to roll the particle can be obtained as Fr=3π(Wpfξpf+Wpsξps). (3) In the present analysis, Wpfξpf is over an order of magnitude greater than Wpsξps so that we can safely drop the later parameters from Eq. 3 and the critical drag force is given as Fr=3πWpfξpf. (4) Generally, the value of ξ ranges from the interatomic distance (ε=0.2 nm) to the interface contact radius r such that 0.2 nm < ξ < r (7). However, since r is a function of Fz, we assume that ξ = function(Fz). By setting ξ = 0 at no load, and fitting Eq. 4 to the experimental results in Fig. 3, we obtained ξpf = 0.2 nm + 0.0028Fz. This result suggests that the critical rolling distance is linearly proportional to the applied normal load. Conclusions The experimental results show that particle rolling dominates the cleaning process under most normal loading conditions. The preload force applied during cleaning is shown to also play a major role in dry contact cleaning, where small normal load is favorable for cleaning. An analytical model presented suggests that the critical rolling distance is linearly proportional to the applied load. These results take us closer to obtaining design parameters that can be implemented to achieve self-cleaning of fibrillar adhesives in various real-world application environments. References 1. 2. 3. 4. 5. 6. 7. A.T. Asbeck et al., IEEE Int Conf Robot Autom, 2009, pp 2675-2680. H.E. Jeong et al., Proc Natl Acad Sci USA, 2009, 106, pp 5639-5644. M.K. Kwak, H.E. Jeong, K.Y. Suh, Adv Mater, 2011 23, 3949-53. A.G. Gillies, et al., ACS Appl. Mater. Interfaces, 2013, 13, pp 6081-6088. B. Aksak, M.P. Murphy, Langmuir, 2007, 23, 33223332. C. Dominik, A.G.G.M. Tielens, Philos Mag A, 1995, 72, 783-803. LO. Heim, J. Blum, Phys. Rev. Lett, 1999, 83, 33283331. Relative Displacement 1 0.8 1 0.6 0.9 0.4 0.8 0.2 0 0 0.7 0 10 20 50 100 30 150 40 200 50 Normal Load [mN] Figure 1. Relative displacement of a 240 μm particle sandwiched between a glass substrate and a microfiber array and sheared at various normal loads. Each data point and error bar represents the mean and standard deviation respectively, of two cleaning experiments with a drag distance of 4 mm. Shear Force [mN] 25 20 15 10 5 0 0 50 100 150 200 250 Normal Load [mN] Figure 2. Experimental sheat force measured for various normal loads. Each data point and error bar represents the mean and standard deviation respectively, of the steady state shear force measured during each experiment. Figure 3. Shear force measured for a 500 μm radius particle rolling between a glass substrate and a flat polyurethane elastomer surface at various normal loads. Each point in the graph represents data from a single rolling experiment. The solid line is obtained from fitting the experimental data to Eq. 4 with ξpf = 0.2 nm + 0.0028Fz.