6. Diffusive Mass Transfer

Mass transfer is the movement of mass due to the concentration gradients of species in a mixture. For this to be possible: 

• • You need more than one species in the medium

  • There needs to be a concentration gradient within the mixture of species in the medium

The movement of mass which makes up mass transfer is caused by the random movement of species in the direction of decreasing concentration. Eventually, uniform concentrations are achieved throughout the substance. This is called the dynamic equilibrium and is where species are still moving but uniform concentration remains.

Mass transfer by diffusion is analogous to heat transfer by conduction when the medium involved in mass transfer is stationary. Instead of Fourier’s Law, Fick’s Law (shown below) is used to find the molar and mass fluxes of species A during to diffusion in the mixture of A and B.

where  is the mass concentration of species A within the mixture. 

In order to aid understanding of the equations to come, the following table shows what each character stands for.

    Molar flux - the rate at which the species being looked at in the mixture moves through the mixture            relative to a molar average velocity of the mixture

• • By definition , and when combined with the knowledge of the definition of molar flux and   we can say:   

• •  

  • Then with the definition of absolute molar flux and the molar flux from Fick's Law 

    Absolute mass flux - the rate at which the species being looked at in the mixture moves through the         mixture relative to a fixed reference frame

• • By definition , and when combined with the knowledge of the definition of mass flux and   we can say:  

• •  

  • Then with the definition of absolute mass flux and the mass flux from Fick's Law 

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SPECIAL CASE: A Stationary Medium in Steady State Conduction

At stationary the medium has no molar average velocity or molar velocity. Then when applied to the absolute molar and mass fluxes it gives the absolute molar flux equal to the molar flux, and the absolute mass flux equal to the mass flux.

As the medium is stationary it allows for the principal of conservation of mass to be applied to the species in a control volume

 where st=stationary and g=generated.

This idea can be used to create a Mass Diffusion Equation that is analogous to the Heat Transfer Equation. This is done for a differential control volume within the stationary medium with constant

or C or .

With a Mass Basis:

With a Molar Basis:

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Boundary Conditions

There are different boundary conditions:

When these boundary conditions are applied to a stationary medium the condition  is held as the boundary of the control volume is essentially impermeable.

The boundary conditions for mass transfer are more complex than those for heat transfer. This is due to temperature generally being continuous at a boundary whereas mass is generally discontinuous. Therefore, a relationship between the different concentrations of mass on either side of the boundary is required. This can be found in a variety of ways based on the scenario, including using Raoults Law and Henrys Law.