= Taylor dispersion in a linear porous-layer velocity profile
{c}
{title2=$D_{\rm eff}=D_L+U^2H^2/(30D_T)$}
For pore velocity $u(y)=2Uy/H$ on $0<y<H$, with reflecting transverse boundaries, solve $D_T\chi''=u-U$, $\chi'(0)=\chi'(H)=0$, $\overline\chi=0$. The <Taylor dispersion> enhancement is $D_T\overline{(\chi')^2}=U^2H^2/(30D_T)$. Here $U$ is the mean advective pore velocity, not the <Darcy velocity>, and $D_L$ is the original longitudinal dispersion. The averaged equation applies after transverse equilibration and on suitably long longitudinal scales.
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