Fick's Second Law

For diffusion in a continuum with concentration‑dependent or constant diffusion coefficient D under isothermal conditions and negligible bulk motion, the time evolution of the local concentration c_i(r,t) obeys the diffusion equation derived from mass conservation and Fick’s first law: ∂c_i/∂t = ∇·(D·∇c_i). For constant D this reduces to ∂c_i/∂t = D·∇^2 c_i.