References

Andrews J.P. Experiments on impact. Proceedings of the Physical Society. 1930;43:8–17.

Barnocky G, Davis R.H. Elastohydrodynamic collision and rebound of spheres: experimental verification. Physics of Fluids. 1988;31:1324–1329.

Bergström L. Hamaker constants of inorganic materials. Advances in Colloid and Interface Science. 1997;70:125–169.

Bitter J.G.A. A study of erosion phenomena, part I. Wear. 1963;6:5–21.

Brach R.M. Impact dynamics with applications to solid particle erosion. International Journal of Impact Engineering. 1988;7:37–53.

Bridges F.G, Hatzes A, Lin D.N.C. Structure, stability and evolution of Saturn's rings. Nature. 1984;309:333–335.

Bryant M.D, Keer L.M. Rough contact between elastically and geometrically identical curved bodies. Transactions of the American Society of Mechanical Engineers, and Journal of Applied Mechanics. 1982;49:345–352.

Cappella B, Dietler G. Force-distance curves by atomic force microscopy. Surface Science Reports. 1999;34(1–3):1–104.

Davis R.H, Rager D.A, Good B.T. Elastohydrodynamic rebound of spheres from coated surfaces. Journal of Fluid Mechanics. 2002;468:107–119.

Derjaguin B.V, Muller V.M, Toporov YuP. Effect of contact deformations on the adhesion of particles. Journal of Colloid and Interface Science. 1975;53:314.

Fisher R.A. On the capillary forces in an ideal soil, correction of formulae given by W.B. Haines. Journal of Agricultural Science. 1926;16:492–505.

Goldsmith W, Lyman P.T. The penetration of hard-steel spheres into plane metal surfaces. Transactions of the American Society of Mechanical Engineers, and Journal of Applied Mechanics. 1960;27:717–725.

Gorham D.A, Kharaz A.H. Measurement of particle rebound characteristics. Powder Technology. 2000;112:193–202.

Hamaker H.C. The London – van der Waals attraction between spherical particles. Physica. 1937;4(10):1058–1072.

Hamilton G.M, Goodman L.E. The stress field created by a circular sliding contact. Transactions of the American Society of Mechanical Engineers, and Journal of Applied Mechanics. 1966;33:371–376.

Hertz H. In: Jones, Schott, eds. Miscellaneous Papers. London: Macmillan and Co; 1896.

Hill R. The Mathematical Theory of Plasticity. London: Oxford Univ. Press; 1950.

Hutchings I.M. Energy absorbed by elastic waves during plastic impact. Journal of Physics D: Applied Physics. 1979;12:1819–1824.

Israelachvili J.N. Intermolecular and Surface Forces. London: Elsevier; 1991.

Johnson K.L. Adhesion at the contact of solids. In: Koiter, ed. Theoretical and Applied Mechanics, Proc. 4th IUTAM Congress. Amsterdam: North Holland; 1976:133.

Johnson K.L. The bounce of ‘superball’. International Journal of Mechanical Engineering Education. 1983;111:57–63.

Johnson K.L. Contact Mechanics. Cambridge University Press; 1985.

Johnson K.L, Jefferis J.A. Plastic flow and residual stresses in rolling and sliding contact. In: Proc. I. Mech. E. Symp. On Rolling Contact Fatigue. London: Institute of Mechanical Engineers; 1963:54–65.

Johnson K.L, Kendall K, Roberts A.D. Surface energy and the contact of elastic solids. Proceedings of the Royal Society of London. 1971;A324:30.

Kantak A.A, Davis R.H. Oblique collisions and rebound of spheres from a wetted surface. Journal of Fluid Mechanics. 2004;509:63–81.

Kantak A.A, Davis R.H. Elastohydrodynamic theory for wet oblique collisions. Powder Technology. 2006;168(1):42–52.

Kharaz A.H, Gorham D.A, Salman A.D. An experimental study of the elastic rebound of spheres. Powder Technology. 2001;120:281–291.

Labous L, Rosato A.D, Dave R.N. Measurements of collisional properties of spheres using high-speed video analysis. Physical Review. E. 1997;56:5717–5725.

Lian G. Computer Simulation of Moist Agglomerate Collisions (Ph.D. thesis). University of Aston; 1994.

Lian G, Adams M.J, Thornton C. Elastohydrodynamic collisions of solid spheres. Journal of Fluid Mechanics. 1996;311:141–152.

Lian G, Thornton C, Adams M.J. A theoretical study of the liquid bridge forces between two rigid spherical bodies. Journal of Colloid and Interface Science. 1993;161:138–147.

Love A.E.H. A Treatise on the Mathematical Theory of Elasticity. fourth ed. Cambridge: Cambridge University Press; 1952.

Maw N, Barber J.R, Fawcett J.N. The oblique impact of elastic spheres. Wear. 1976;38:101–114.

Maw N, Barber J.R, Fawcett J.N. The role of elastic tangential compliance in oblique impact. Transactions of the American Society of Mechanical Engineers, and Journal of Lubrication Technology. 1981;103:74–80.

Mesarovic S.D, Johnson K.L. Adhesive contact of elastic-plastic spheres. Journal of the Mechanics and Physics of Solids. 2000;48:2009–2033.

Mindlin R.D. Compliance of elastic bodies in contact. Transactions of the American Society of Mechanical Engineers, and Journal of Applied Mechanics. 1949;16:259–268.

Mindlin R.D, Deresiewicz H. Elastic spheres in contact under varying oblique force. Transactions of the American Society of Mechanical Engineers, and Journal of Applied Mechanics. 1953;20:327–344.

Muller V.M, Yuschenko V.S, Derjaguin B.V. On the influence of molecular forces on the deformation of an elastic sphere and its sticking to a rigid plane. Journal of Colloid and Interface Science. 1980;77:91.

Muller V.M, Yushchenko V.S, Derjaguin B.V. General theoretical consideration of the influence of surface forces on contact deformation. Journal of Colloid and Interface Science. 1983;92:92.

Pietsch W.B. Tensile strength of granular materials. Nature (London). 1968;217:736.

Savkoor A.R, Briggs G.A.D. Effect of tangential force on the contact of elastic solids in adhesion. Proceedings of the Royal Society of London A. 1977;356:103–114.

Seville J.P.K, Tüzün U, Clift R. Processing of Particulate Solids. London: Blackie Academic & Professional; 1997.

Tabor D. A simple theory of static and dynamic hardness. Proceedings of the Royal Society of London. 1948;A192:247–274.

Tabor D. Hardness of Metals. Oxford: Oxford University Press; 1951.

Tabor D. Surface forces and surface interactions. Journal of Colloid and Interface Science. 1977;58:2.

Thornton C. Coefficient of restitution for collinear collisions of elastic-perfectly plastic spheres. Transactions of the American Society of Mechanical Engineers, and Journal of Applied Mechanics. 1997;64:383–386.

Thornton C, Ning Z. A theoretical model for the stick/bounce behaviour of adhesive, elastic-plastic spheres. Powder Technology. 1998;99:154–162.

Thornton C, Ning Z, Wu C.-Y, Nasrullah M, Li L.-Y. Contact mechanics and coefficients of restitution. In: Poschel T, et al., ed. Granular Gases. Springer; 2001:56–66.

Timoshenko S, Goodier J.N. Theory of Elasicity. third ed. New York: McGraw-Hill; 1951.

Walton O.R. Numerical simulation of inelastic, frictional particle–particle interactions. In: Roco M.C, ed. Particulate Two-phase Flow, Ch. 25. Boston: Butterworth-Heinemann; 1992.

Walton O.R, Braun R.L. Viscosity, granular-temperature, and stress calculations for shearing assemblies of inelastic, frictional disks. Journal of Rheology. 1986;30:949–980.

Whittaker E.T. A Treatise on the Analytical Dynamics of Particles and Rigid Bodies. London: Cambridge University Press; 1904.

Willett C.D, Adams M.J, Johnson S.A, Seville J.P.K. Capillary bridges between two spherical bodies. Langmuir. 2000;16(24):9396–9405.

Wu C.Y. Finite Element Analysis of Particle Impact Problems (Ph.D. thesis). University of Aston; 2002.

Wu C.Y, Li L.Y, Thornton C. Rebound behaviour of spheres for plastic impacts. International Journal of Impact Engineering. 2003;28(9):929–946.

Wu C.Y, Li L.Y, Thornton C. Energy dissipation during normal impact of elastic-plastic spheres. International Journal of Impact Engineering. 2005;32(1–4):593–604.

Wu C.Y, Thornton C, Li L.Y. A semi-analytical model for oblique impacts of elastoplastic spheres. Proceedings of the Royal Society of London A. 2009;465:937–960.


1 Closer consideration of the geometry shows that the bridge cannot be truly toroidal since according to the Laplace equation (Eq 8.136) 1/r1 - 1/r2 = a constant, since the pressure is the same everywhere in the bridge. It is apparent that r1 depends on where on the bridge it is evaluated, being smallest at the neck, so r2 cannot be a constant and the shape of the bridge is not an arc in the plane of the figure. Nevertheless, the toroidal approximation is satisfactory for many applications especially if the liquid loading is small.

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