= Cell conservation in a swimming suspension
= Cell conservation equation
{synonym}
If $C$ is the cell number density, $\mathbf u$ the fluid <velocity>, $V_s\langle\mathbf p\rangle$ the mean swimming <velocity>, and $D$ an isotropic translational <diffusion> coefficient, conservation is $\partial_tC+\nabla\cdot[C(\mathbf u+V_s\langle\mathbf p\rangle)-D\nabla C]=0$. Impermeable boundaries have zero normal total cell flux. For constant cell volume $v$, the volume fraction is $vC$ and obeys the same equation, but its buoyancy coefficient has no additional factor $v$.
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