# DCVGCMDwithNanotube:Background:DCVGCMD with Nanotube Diffusion

 Introduction Background Basic Layout Examples Problems Problems 1 Run Simulation Assessment Credits Etomica Modules

Diffusion is the movement of a component through space under the influence of a physical stimulus. The most common cause of diffusion is a concentration gradient, which tends to adjust the component concentration until it reaches equilibrium. In short, diffusion is the physical flow of material.

There are four related concepts used in the diffusion theory. One, velocities are needed to describe the movements for the total phase and the individual component. Two, the concentration, molar density, or mole fraction is used to define the number of molecules of interest within a defined volume. Third, the concentration gradient will show the shifts in concentration as time increases. Forth, the molar flux of a component is proportional to the concentration gradient and the diffusivity of that component. The equation that describes the molar flux is Fick's first law

${\displaystyle J=-D{\frac {dc}{dx}}}$

also,

${\displaystyle J=c\left(U_{1}-u_{0}\right)}$

where

• J is the flux
• D is the diffusivity constant of proportionality
• ${\displaystyle {\frac {dc}{dx}}}$ is the concentration gradient in the x-direction
• c is the concentration
• u1 is the velocity relative to a stationary plane
• u0 is the bulk fluid velocity

This equation is the basic equation for mass transfer in a nonturbulent fluid phase. It accounts for the amount of the component carried by the bulk flow of the fluid and the amount of the component being transferred by diffusion.

Simluation techniques are explained in the next section.