- Rolling friction of adhesive microspheres
- Journal of physics. D, Applied physics
- Volume | Issue number
- 47 | 17
- Number of pages
- Document type
- Faculty of Science (FNWI)
- Anton Pannekoek Institute for Astronomy (API)
The rolling friction of adhesive microspheres is an important quantity as it determines the strength and stability of larger aggregates. Current models predict rolling forces that are 1 to 2 orders of magnitude smaller than observed experimentally. Starting from the well-known Johnson-Kendall-Roberts (JKR) contact description, we derive an analytical theory for the rolling friction based on the concept of adhesion hysteresis, e.g. a difference in apparent surface energies for opening/closing cracks. We show how adhesion hysteresis causes the pressure distribution within the contact to become asymmetrical, leading to an opposing torque. Analytical expressions are derived relating the size of the hysteresis, the rolling torque, and the rolling displacement, ξ. We confirm the existence of a critical rolling displacement for the onset of rolling, the size of which is set by the amount of adhesion hysteresis and the size of the contact area. We demonstrate how the developed theory is able to explain the large rolling forces and particle-size dependence observed experimentally. Good agreement with experimental results is achieved for adhesion hysteresis values of (Δγ/γ) sime 3 for polystyrene, and (Δγ/γ) sime 0.5 for silicates, at crack propagation rates of 0.1 µm s−1 and 1-10 µm s−1, respectively.
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