A mathematical analysis of the transport of heat or mass through eccentric spherical closed fluid shells at large Peclet numbers is presented. The bispherical coordinates system is utilized to solve the flow of heat or mass between the two spherical boundaries. The analysis also includes an approximate solution for the motion, if exists, of the inner sphere within the external one. These solutions are then employed in analysing the problem of the evaporation of three-phase liquid drop. The general analysis presented here might prove useful also in the general case of "soap bubble" (as in foam) or in liquid-liquid systems.