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Rolling Moment Resistance of Particles on Surfaces

In the brief presentation attached, I am summarizing my lab's recent work in the field of adhesion and work-of-adhesion measurements, and hoping to see who else is working in the field.  Here is some intro to the topic (by no means, it is complete - maybe we can add some recent work to this list as discussions develop)

 Rolling resistance moment is a restoration moment that opposes the rotational motion of a particle adhered on a surface. Particle removal and strength/stability of particle networks depend on rolling resistance more than axial adhesion since the rolling forces are few orders of magnitude lower than the axial detachment forces.   Rolling resistance moment of an adhesion bond between a particle and flat substrate controls the motion of particles on surfaces, the strength/stability of network of adhered round objects in a diverse spectrum of applications (e.g. particles, powders, blood cells and nanotubes) on micro/nano-scale as in sintering and compaction. Also, it is essential in detachment and removal of micro/nano-particles from surfaces.  Many adhesion models and theories have been proposed and discussed to understand the axial (out-of-plane) stiffness and strengths of particle-surface bonds. In [1], a unifying framework for existing theories (namely, Hertz, JKR (Johnson-Kendall-Roberts), DMT (Derjaguin-Muller-Toporov), M-D (Maugis- Dugdale)) is proposed and transition between these theories and their applicability zones is established for ranges of external loads and an elasticity parameter. In one-dimensional (axial) adhesion models and theories the pressure field in the contact area is assumed symmetric. Studying particle rolling, however, requires a two-dimensional adhesion model and analysis where the stress at the bond interface is asymmetric during pre-rolling and rolling.  In [2] an expression for this rolling moment was derived by considering an external force applied at the centre of the spherical particle. This external force creating a moment with respect to the bond zone causes an asymmetric pressure distribution in the contact area, resulting in the pressure variations in contact area at the leading edge and at the trailing edge of the contact with the surface. The resulting asymmetric pressure field in the contact area creates a restoring moment in small rotational angles. Under external excitation, this restoring force along with the rotational inertia of the particle could result in free oscillatory vibrations of the particle with respect to its contact [3, 4]. In spite of the fact that extensive research has been dedicated for measuring the adhesion force between a particle and a substrate by detaching particles using AFM techniques, the rolling motion and resistance of a particle on a substrate has rarely been experimentally explored. The main disadvantage of axial detachment based-AFM techniques in such experiments is that the particle has to be fixed/glued to the tip of a probe; therefore it is essentially a destructive technique for the particle. Rolling resistance moment is particularly critical for various applications from biology to semiconductor manufacturing since it controls the stability of network of adhered round objects (e.g. particle, cells and nanotubes) on micro/nano-scale. While the rolling resistant moment can be estimated based on the adhesion model [2] and experimental method based on ultrasonic base excitation is reported in [3, 4].  Adhesion and frictional forces between spherical micron sized particles on the basis of rolling resistance moment and atomic force microscopy was studied in the past [5]. The rolling resistance moment and hence the adhesion force between a micro-particle on a substrate was determined in the past based on acoustic excitation and interferometric sensing [3, 4].  Many argue that this (detachment distance/the shift in contact area ξ) should be related to the lattice size and/or the molecular length of the particle and surface materials. However, there is no theoretical prediction for this critical value. 

Particle adhesion and force studies were performed with the aid of micromanipulators in the past [6, 7, 8]. For example, Saito et al analyzed the interaction forces between the microsphere, the substrate and the manipulation probe, and proposed a method to pickup and manipulate a microsphere [6]. They also suggested the existence of a maximum rolling resistance, i.e., an external moment has to be grater than a certain threshold to roll a particle.  Sitti performed pushing study on 500 nm Au-coated latex particles on a silicon substrate with atomic force microscope (AFM) probe [8]. The sliding, rolling and rotation motion of the particles were observed, and the particle-substrate frictional properties were estimated. No rolling resistance data was provided while its effect in the control loop was reported. However, the pushing process cannot be visually observed in situ in real-time because the pushing and imaging processes uses the same AFM cantilever probe.




[1] K.L. Johnson and J. A. Greenwood, J. Colloid Interface Sci. 192(2) 326 (1997).

[2] C. Dominik and A.G.G.M. Tielens, Phil. Mag. A 72(3) 783 (1995).

[3] M.D.M. Peri and C. Cetinkaya, Phil. Mag. 85(13) 1347 (2005).

[4] M.D.M. Peri and C. Cetinkaya, J. Colloid Interface Sci. 288 432 (2005).

[5] L. Heim and J. Blum, Phys. Rev. Lett. 83(16) 3328 (1999).   

[6] S. Saito, H.T. Miyazaki, T. Sato, K. Takahashi, J. Appl. Phys. 92(9) 5140 (2002).

[7] M. Sitti and H. Hashimoto, IEEE-ASME Trans. Mechatron. 5(2) 199 (2000).

[8] M. Sitti, IEEE-ASME Trans. Mechatron. 9(2) 343 (2004).

K.L. Johnson, K. Kendall, A.D. Roberts, Proc. Roy. Soc. London. Ser. A  324 301 (1971).

W. Ding, L. Calabri, K.M. Kohlhaas, X. Chen, D.A. Dikin, R.S. Ruoff, Exp. Mech. In press (2007).

J.E. Sader, I. Larson, P. Mulvaney, L.R. White, Rev. Sci. Inst. 66(7) 3789 (1995).  


Our recent/preliminary (with Prof. W. Ding) contact experiments suggests that the torsional stiffness of the adhesion bond (rolling resistance) is highly nonlinear - It appears that the bond weakens before detachment.

I was wondering if anyone else has made similar observations and/or predictions.

Liu's picture

Hi Cetin,

Your results are quite similar to our observations on the motion of a linear ball bearings. The curves for pushing force as a function of displacement are highly comparable with our results presented in Fig. 4c and Fig. 6a in the paper posted in my blog.

In the paper below, it seems the contact area remains symmetric even though the applied force acting on the cylinder has a horizontal component (parallel to the surface of the substrate):

S. Chen, T. Wang, General Solution to Two-Dimensional Nonslipping JKR Model with a Pulling Force in an Arbitrary Direction, J. of Collo. and Interface Science, 302, 2006.

Does anyone know any reference where the particle rotation is taken into consideration (by consindering non-symmetric pressure at the interface)? 


Rolling friction in adhesive powder flows is a dominant mechanism in determining the rheology of mixed and blended systems. It is amazing how simulation of these systems often shows insensitivity of the macroscopic behavior to a variety of physical parameters like modulus of elasticity; however, the mechanisms of energy dissipation (e.g., rolling friction, friction, and local plastic deformation) often control the system response. There are several researchers in adhesive powders that have looked at this problem both an experimental, numerical, and analytical perspective. Just as an introduction, you may consider looking at:

Tomas, J., Adhesion of ultrafine particles-a micromechanical
. Chemical Engineering Science,
62, 2007,  1997-2010.

There are also other papers that address this problem from a theoretical perspective; this paper by Tomas should provide a good set of citations to start you on your way. Also, the research group of Charles Cooney at MIT had been working on characterizing particle contact. A graduate student, Yu Pu, had been working on a contact model, and I imagine that it now includes consideration of rolling friction. You may also consider Otis Walton's considerable work on adhesion; several of his more difficult to find papers are at

In the figure I showed a mechanism, I want to make an analysis for that. consider the circles in the figure as cylenders which can be seen in the top view. these circles are regular cylenderical parts. I made the fig in paint thats why circle don't seem to be regular. I want to analyze the angle that at given angle, whether the rolling flow of these cylenders will be blocked or not. Please tell me some software to analyze in 2d Prefferably or 3d. Please help me. I'm in intense need.anaylis 2d

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