An extension of the generalized energy-conserving dissipative
particle
dynamics method (GenDPDE) that allows mass transfer between mesoparticles
via a diffusion process is presented. By considering the concept of
the mesoparticles as property carriers, the complexity
and flexibility of the GenDPDE framework were enhanced to allow for
interparticle mass transfer under isoenergetic conditions, notated
here as GenDPDE-M. In the formulation, diffusion is described via
the theory of mesoscale irreversible processes based on linear relationships
between the fluxes and thermodynamic forces, where their fluctuations
are described by Langevin-like equations. The mass exchange between
mesoparticles is such that the mass of the mesoparticle remains unchanged
after the transfer process and requires additional considerations
regarding the coupling with other system properties such as the particle
internal energy. The proof-of-concept work presented in this article
is the first part of a two-part article series. In Part 1, the development
of the GenDPDE-M theoretical framework and the derivation of the algorithm
are presented in detail. Part 2 of this article series is targeted
for practitioners, where applications, demonstrations, and practical
considerations for implementing the GenDPDE-M method are presented
and discussed.