Particle Rolling on a Fibrillar Interface

Particle Rolling on a Fibrillar Interface
Uyiosa Abusomwan, Metin Sitti
Carnegie Mellon University
Pittsburgh, Pennsylvania, 15213, USA
sitti@cmu.edu
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.