Definition of Flux Terms in Mass Transfer

Flux is defined as the amount of a quantity that is transported per unit time across a unit area that is perpendicular to the direction of transport. The molar flux of species i with units’ moles/m².s is represented as:

Where:

N_i-mol is the molar of species i

u_i is the velocity of i with respect to a fixed reference frame.

 

Similarly, the mass flux, N_i-mass, with units mass/m².s is represented as:

In some cases, it is convenient to interpret the total flux of species i with respect to an arbitrary reference frame rather than a fixed set of reference frame.

The molar flux of species i based on an arbitrary reference velocity u₀ is denoted by J_i-mol and is defined as:

Similarly mass flux of species i based on arbitrary reference velocity u₀ is denoted by J_i-mass which can be expressed as:

In a system a frame of moving reference must be chosen, since several molecular species move with different average velocities. The important moving references are mass average, molar average and volume average velocities.

Mass average velocity

This can be defined in terms of the mass concentration and the velocity of species i based on a fixed axis. It is expressed as:

Molar average velocity

This can be expressed by the expression analogous to the mass average velocity. It can be represented by replacing the mass concentration of species i, ρ_i with the molar concentration of species i, C_i:

Volume average velocity

This is important for experimental analysis in a fixed system of constant volume. The volume average velocity can be expressed by:

where v_i is the partial molar volume of species i.

Relation Between Fluxes

The molar flux of species i described previously can be obtained with respect to the molar average velocity as follows:

Substituting the molar flux of species i into the above equation and rearranging it results in:

Substituting the definition of molar average velocity into the above equation we get:

or: