Multiscale Simulations

The computational research in Professor Alkire's laboratory is comprised of efforts aimed at developing flexible simulations that can be applied to a wide array of applications with varying spatial and temporal domains. The codes that are being developed range from simulations of discrete surface phenomena occurring on electrode surfaces, in areas such as electrochemical copper deposition, to simulations focused on the behavior of local chemistry in the electrolyte solution adjacent to the electrode surface. Monte Carlo simulations are used for the surface models, while continuum transport models of electrochemical systems are developed for the electrolyte phase.

The Monte Carlo (MC) model is a 3-D model in which deposit growth occurs. Species in the Monte Carlo domain can participate in many different kinds of actions, such as reaction, adsorption, desorption, bulk diffusion, surface diffusion, and incorporation in the deposit. Fluxes of particles into the Monte Carlo domain from the "continuum" region is obtained by coupling the Monte Carlo code with a continuum code that describes advection, diffusion, and migration (drift).

The continuum transport codes are based on governing partial differential equations describing both transient and steady state transport of chemical species in an electrolyte. The transport of species is dominated by three processes: diffusion due to a concentration gradient; migration due to a potential field in solution; and convection as a result of bulk fluid motion. All three of these processes are important in electrochemical deposition and corrosion applications. In addition, equilibration of chemical species in solution as a result of hydrolysis and equilibrium reactions must be incorporated to accurately describe the solution chemistry. A final constraint on the system is the condition of electroneutrality. The physical model described leads to a set of tightly coupled non-linear partial differential equations and algebriac constraints. Two solution techniques are implemented to solve these equations. The first is a global solution technique of the coupled non-linear equations implemented in a research level finite difference using PETSc. The second is a segregated solution technique using a modified version of the commerical CFD software FIDAP.