A General Equation for Fitting Contact Area and Friction vs Load Measurements

The variation of contact area with load between adhesive elastic spheres depends upon the effective range of attractive surface forces. Relatively simple forms to describe limiting cases exist, but the general intermediate case requires a more complex analysis. Maugis, using a Dugdale model [D. Maugis, J. Colloid. Interf. Sci. 150, 243 (1992)], provides an analytic solution, but the resulting equations are cumbersome if one wishes to compare with experimental data such as atomic force microscope measurements. In this paper we present a simpler general equation that approximates Maugis' solution extremely closely. The general equation is amenable to conventional curve fitting software routines and provides a rapid method of determining the value of the "transition parameter" which describes the range of surface forces. Copyright 1999 Academic Press.