From experiment there are strong indications that the flux of particles $j(x,t)$, viz., the number of particles passing $x$ at a time $t$ is proportional to the gradient of $w(x,t)$. This proportionality is expressed mathematically through $$\begin{equation*} j(x,t) = -D\frac{\partial w(x,t)}{\partial x}, \end{equation*}$$ where $D$ is the so-called diffusion constant, with dimensionality length$^2$ per time.