= Solution
For a <binary fluid mixture>, the scalar <compositional order parameter> $\phi(\mathbf r)$ may be taken as the local concentration difference between its two molecular species. Its spatial integral is fixed by their separately fixed total amounts:
$$
\int_V\phi(\mathbf r)\,d\mathbf r=V\bar\phi.
$$
Locally, $\phi$ can change only through transport and therefore obeys a <continuity equation>. By contrast, $\mathbf p$ is the local <polar order parameter> measuring the mean tail-to-head orientation of the <surfactant> molecules. Individual molecules can rotate in place, so the integral of $\mathbf p$ need not be conserved.
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