Fick's second law is the governing equation for non-steady-state diffusion, provides a mathematical description of how the concentration of diffusing species changes with time in a medium when the system has not yet reached equilibrium. It arises directly from the combination of Fick's First Law, which relates the diffusive flux to the negative gradient of concentration via the diffusion coefficient, and the continuity equation that enforces mass conservation in a small volume element.
Fick's Second Law Formula |
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| \( \dfrac{ \partial C }{ \partial t } \;=\; D \cdot \dfrac{ \partial^2 C }{ \partial x^2 } \) (Fick's Second Law) | ||
| Symbol | English | Metric |
| \( C \) = Concentration of the Diffusing Species (atoms, molecules, ions, or other particles) | \(lbm \;/\;ft^3\) | \(kg \;/\;m^3\) |
| \( t \) = Time | \(sec\) | \(s\) |
| \( D \) = Diffusion Coefficient | \(ft^2 \;/\;sec\) | \(m^2 \;/\;s\) |
| \( x \) = Position Coordinate | \(ft\) | \(m\) |
Physically, the law states that the rate at which concentration accumulates or depletes at any given point (the left-hand side, representing the time derivative) is proportional to the curvature of the concentration profile (the second spatial derivative on the right-hand side).
