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--- notebooks:peclet_number [2025/02/13 18:15] – rishabhstein
+++ notebooks:peclet_number [Unknown date] (current) – external edit (Unknown date) 127.0.0.1
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+Peclet number
+Peclet number $(\text{Pe})$, named after [Jean Claude Eugene Peclet](jeanPeclet) (1793-1857), is a dimensionless number which is very useful in studying different transport phenomena. It is defined as the ratio of diffusive time scale $(\tau_D)$ to advective time scale ($\tau_A$). In a porous medium, diffusive time scale can be written as ($\tau_D = l_0^2/D$) where $D$ is the diffusion constant of the reactive fluid. Then, $\text{Pe}$ can be written as following:
+\begin{equation}\label{eq:defPe}
+\text{Pe} = \frac{\tau_D}{\tau_A} = \frac{v_0 l_0}{D}
+\end{equation}
+For larger length scales ($\text{Pe} \gg 1$), flow in the system is naturally advection-dominated, while for smaller $l_0$,  $\text{Pe}$ is $\ll1$; therefore, diffusion dominates the transport phenomenon.