A new algorithm to enable the implementation of dual control volume grand canonical molecular dynamics (DCV-GCMD) on massively parallel (MP) architectures is presented. DCVGCMD can be thought of as hybridization of molecular dynamics (MD) and grand canonical Monte Carlo (GCMC) and was developed recently to make possible the simulation of gradient-driven diffusion. The method has broad application to such problems as membrane separations, drug delivery systems, diffusion in polymers and zeolites, etc. The massively parallel algorithm for the DCV-GCMD method has been implemented in a code named LADERA which employs the short range Lennard-Jones potential for pure fluids and multicomponent mixtures including bulk and confined (single pore as well as amorphous solid materials) systems. Like DCV-GCMD, LADERA's MP algorithm can be thought of as a hybridization of two different algorithms, spatial MD and spatial GCMC. The DCV-GCMD method is described fully followed by the DCV-GCMD parallel algorithm employed in LADERA. The scaling characteristics of the new MP algorithm are presented together with the results of the application of LADERA to ternary and quaternary Lennard-Jones mixtures.