Fick's first law describes the relationship governing the movement of atoms, ions, or molecules through a medium by diffusion, and it is directly applicable to steady-state conditions in which the concentration of the diffusing species (atoms, molecules, ions, or other particles) at any given point within the material remains constant over time. This law underpins analyses of long-term durability in structures, such as the migration of chloride ions through concrete cover to embedded reinforcement steel or the transport of contaminants through soil barriers where engineers must predict constant rates of mass transfer without time-dependent accumulation or depletion. The negative sign ensures that net flow occurs from regions of higher concentration to lower concentration, consistent with the second law of thermodynamics.
Fick's First Law Formula |
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| \( J \;=\; - D \cdot \dfrac{ dC }{ dx} \) (Fick's First Law) | ||
| Symbol | English | Metric |
| \( J \) = Diffusive Flux | \(lbm \;/\;ft^2-sec\) | \(kg \;/\;m^2-s\) |
| \( D \) = Diffusion Coefficient | \(ft^2 \;/\;sec\) | \(m^2 \;/\;s\) |
| \( C \) = Concentration of the Diffusing Species (atoms, molecules, ions, or other particles) | \(lbm \;/\;ft^3\) | \(kg \;/\;m^3\) |
| \( x \) = Position Coordinate | \(ft\) | \(m\) |
| \( dfrac{ dC }{ dx} \) = Concentration Gradient | ||
Under steady-state diffusion specifically, the concentration profile does not vary with time at any location, which means the divergence of the flux is zero everywhere according to the continuity equation.
