Macrodynamics of Microparticles

Abstract

A primary goal of this paper is to describe the development of two, independent engineering models for the oblique mechanical impact dynamics of solid aerosol particles, treated as microspheres, in the presence of adhesion forces. One model is algebraic and is based on rigid body impact theory* using coefficients such as the coefficient of restitution and the impulse ratio. This model is augmented by an energy conservation expression. Being algebraic and based directly on Newton's laws, the model offers a rigor and simplicity that makes it ideal for analyzing, displaying and interpreting experimental data. Dealing with impulses, this model does not require a detailed knowledge of the forces to analyze energy loss. The second model takes the form of a simulation using the differential equations of planar motion of a sphere in contact with a flat barrier. It uses Hertzian theory for the normal restoring force, an idealized tensile line force around the periphery of the contact region to represent adhesion and Coulomb friction for the force tangent to the surface. Damping with a form of velocity-dependent hysteresis is used both for the material dissipation as well as the energy loss associated with adhesion. Original experimental data from normal and oblique impacts of poly-disperse aerosol particles are used to illustrate and compare both impact models. The rigid body model's segregation of dynamic material dissipation (or restitution) and adhesion dissipation allows the latter to be observed as a function of initial normal velocity. Results of this model follow the normally incident data trends quite well. The model also facilitates the interpretation of tangential motion, particularly the conditions of sliding and rolling at separation. Experimental data analyzed with this model indicate that initial angular velocities of microspheres of the order of magnitude of 10⁵ rad/s are common and significantly affect the rebound velocities for ordinary levels of friction. Physical constants, calculations and experimental data for silver coated glass spheres colliding with a stainless steel surface are used to estimate the parameter values of the simulation. With these parameters held fixed, the results of the simulation compare quite well to a broad range of experimental data including the transition region from rebound to attachment. The two models predict the impact dynamics almost identically but provide different estimates of the work of adhesion. Improvements of the models in this area are needed and are ongoing.

* In dynamics, a distinction is usually made between a point mass and a rigid body; for a rigid body, rotations and the extent of the mass are taken into account. The phrase rigid body impact theory in this paper implies the latter and does not imply an absence of deformation.

Notes

* In dynamics, a distinction is usually made between a point mass and a rigid body; for a rigid body, rotations and the extent of the mass are taken into account. The phrase rigid body impact theory in this paper implies the latter and does not imply an absence of deformation.