= Thin-film mass flux
The <thin-film mass flux> is the <mass> transported along a thin layer per unit width and per unit time. For constant <density> $\rho$, thickness $h$ and depth-averaged streamwise <velocity> $\overline u$,
$$
j_m=\int_0^h\rho u\,dz=\rho h\overline u.
$$
The quantity $q=h\overline u$ is instead the <volume flux> per unit width. Their units differ by density: $j_m$ has units $\mathrm{kg\,m^{-1}\,s^{-1}}$, whereas $q$ has units $\mathrm{m^2\,s^{-1}}$.
For a constant-density incompressible film with no sources, <mass conservation> becomes $h_t+q_x=0$. In a steady region, $q$ is constant; in a profile moving at speed $c$, the conserved relative flux is $q-ch$. Thus a slowly varying or moving transition does not automatically have constant laboratory-frame flux. Keeping the density factor and the reference frame explicit prevents confusing a geometric thickness balance with the transported mass.
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