Mass flux
In physics and engineering, mass flux is the rate of mass flow per unit area, perfectly overlapping with the momentum density, the momentum per unit volume. The common symbols are j, J, q, Q, φ, or Φ (Greek lower or capital Phi), sometimes with subscript m to indicate mass is the flowing quantity. Its SI units are kg s−1 m−2. Mass flux can also refer to an alternate form of flux in Fick's law that includes the molecular mass, or in Darcy's law that includes the mass density.
Unfortunately, sometimes the defining equation for mass flux in this article is used interchangeably with the defining equation in mass flow rate. For example, Fluid Mechanics, Schaum's et al uses the definition of mass flux as the equation in the mass flow rate article.
Mathematically, mass flux is defined as the limit:
where:
is the mass current (flow of mass m per unit time t) and A is the area through which the mass flows through.
For mass flux as a vector jm, the surface integral it over a surface S, followed by an integral over the time duration t1 to t2, gives the total amount of mass flowing through the surface in that time (t2 − t1):
The area required to calculate the flux is real or imaginary, flat or curved, either as a cross-sectional area or a surface.
For example, for substances passing through a filter or a membrane, the real surface is the (generally curved) surface area of the filter, macroscopically - ignoring the area spanned by the holes in the filter/membrane. The spaces would be cross-sectional areas. For liquids passing through a pipe, the area is the cross-section of the pipe, at the section considered.
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