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We present and discuss the derivation of a nonlinear non-localintegro-differential equation for the macroscopic time evolution of theconserved order parameter of a binary alloy undergoing phase segregation. Ourmodel is a d-dimensional lattice gas evolving via Kawasaki exchange dynamics,i.e. a (Poisson) nearest-neighbor exchange process, reversible with respect tothe Gibbs measure for a Hamiltonian which includes both short range (local) andlong range (nonlocal) interactions. A rigorous derivation is presented in thecase in which there is no local interaction. In a subsequent paper (part II),we discuss the phase segregation phenomena in the model. In particular we arguethat the phase boundary evolutions, arising as sharp interface limits of thefamily of equations derived in this paper, are the same as the ones obtainedfrom the corresponding limits for the Cahn-Hilliard equation.Comment: amstex with macros (included in the file), tex twice, 20 page

Phase segregation dynamics in particle systems with long range interactions. I. Macroscopic limits