= Irreversible capture of an advecting tracer
{title2=$C_t+UC_x=D_{\rm eff}C_{xx}-\lambda C,\quad S_t=\lambda C$}
A first-order irreversible transfer from fluid concentration $C$ to stored concentration $S$, measured per matching fluid storage volume, obeys the displayed balances. A sustained inlet can produce a stationary decaying fluid profile, but the stored amount then grows rather than becoming stationary. A finite pulse instead has $C\to0$ and a finite final deposit. Decay, desorption or finite adsorption capacity is additional physics, not a consequence of the linear capture term alone.
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