In order to interpret measured intensity autocorrelation functions obtained in evanescent wave scattering, their initial decay rates have been analyzed recently [P. Holmqvist, J. K. G. Dhont, and P. R. Lang, Phys. Rev. E74, 021402 (2006) https://doi.org/10.1103/PhysRevE.74.021402; B. Cichocki, E. Wajnryb, J. Blawzdziewicz, J. K. G. Dhont, and P. R. Lang, J. Chem. Phys.132, 074704 (2010) https://doi.org/10.1063/1.3305328; J. W. Swan and J. F. Brady, J. Chem. Phys.135, 014701 (2011)] https://doi.org/10.1063/1.3604530. A theoretical analysis of the longer time dependence of evanescent wave autocorrelation functions, beyond the initial decay, is still lacking. In this paper we present such an analysis for very dilute suspensions of spherical colloids. We present simulation results, a comparison to cumulant expansions, and experiments. An efficient simulation method is developed which takes advantage of the particular mathematical structure of the time-evolution equation of the probability density function of the position coordinate of the colloidal sphere. The computer simulation results are compared with analytic, first and second order cumulant expansions. The only available analytical result for the full time dependence of evanescent wave autocorrelation functions [K. H. Lan, N. Ostrowsky, and D. Sornette, Phys. Rev. Lett.57, 17 (1986)] https://doi.org/10.1103/PhysRevLett.57.17, that neglects hydrodynamic interactions between the colloidal spheres and the wall, is shown to be quite inaccurate. Experimental results are presented and compared to the simulations and cumulant expansions.

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