Concentration gradient ($\nabla c$)

A concentration gradient is the spatial gradient $\nabla c$ of a scalar concentration field. It points toward the greatest local increase of $c$; its components are spatial partial derivatives, so its units are those of concentration divided by length.

For a one-dimensional profile $c(x)=c_0+ax$, the concentration gradient is the constant $a\hat{\mathbf{x}}$. Fick's first law gives a diffusive flux proportional to $-\nabla c$ when that constitutive model applies: the minus sign describes transport toward lower concentration. A fluid velocity can simultaneously advect the constituent in another direction, so a concentration gradient alone does not determine its total flux.