Mass flux

In physics and engineering, mass flux is the rate of mass flow. Its SI units are kg m−2 s−1. 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. 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. 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. For mass flux as a vector jm, the surface integral of 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. The vector area is a combination of the magnitude of the area through which the mass passes through, A, and a unit vector normal to the area, . The relation is . If the mass flux jm passes through the area at an angle θ to the area normal , then where · is the dot product of the unit vectors. That is, the component of mass flux passing through the surface (i.e. normal to it) is jm cos θ, while the component of mass flux passing tangential to the area is jm sin θ, but there is no mass flux actually passing through the area in the tangential direction.