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In this paper, we present a brief review of the application of boundary integral methods in two dimensions to multi-component fluid flows and multi-phase problems in materials science. We focus on the recent development and outcome of methods which accurately and efficiently include surface tension. In fluid flows, we examine the effects of surface tension on the Kelvin-Helmholtz and Rayleigh-Taylor instabilities in inviscid fluids, the generation of capillary waves on the free surface, anddoi:10.1006/jcph.2000.6626 fatcat:nnd7nesam5amjhfzfennikc3fu