Module 7. Mass transfer

Lesson 30

MASS TRANSFER, DIFFUSION PROCESS, FICK’S LAW, CONECEPT OF PERMEABILITY, DIFFUSION COEFFICIENT

30.1  Introduction

The study of mass transfer carries special importance in energy transfer because all heat transfer processes within one fluid or within different fluids which are mixing with each other are associated with mass transfer. There are enough examples of industrial importance where mass transfer is keynote for energy transfer as in the case of humidification of air in cooling tower, evaporation of liquid NH3 in the atmosphere of H2 in Electro flux refrigerator and neutron diffusion within nuclear reactors. Many of our day-to-day experiences involve mass transfer. Smoke leaving tall chimneys diffuses into the surrounding atmosphere. A lump of sugar added to a cup of coffee eventually dissolves and then spreads uniformly throughout the coffee. Water retained in newly cut timber or a wet cloth diffuses initially through the wood to its surface and then evaporates into the atmosphere.

When a system contains one or more components whose concentration vary from point to point, there is a natural tendency for mass to be transferred, minimizing the concentration differences within the system. The transport of one concentration is called mass transfer. The mechanism of mass transfer can be understood by drawing an analogy to heat transfer as follows:

1.      Heat is transferred toward the lower temperature decreasing the temperature gradient, mass is transferred towards the lower concentration decreasing the concentration gradient.

2.      Heat transfer ceases when there is no longer a temperature difference, mass transfer ceases when concentration gradient is reduced to zero.

3.      The rates of both heat and mass transfer depend on a deriving potential and resistance.

The general subject of mass transfer encompasses both mass diffusion on a molecular scale and the bulk mass transport which may result from convection process. These two distinct modes of transport, molecular mass transfer and convective heat transfer. In this chapter only the first mode of mass transfer will be discussed.

30.2  Fick’s Law of Diffusion

Consider the system shown in Fig. 30.1. A partition separates the two gases C and B. when the partition is removed, the two gases diffuse through one another until the equilibrium is established throughout the system.

The diffusion rate is given by Fick’s law of diffusion which states that the mass flux of an element per unit area is proportional to the concentration gradient.

Fig. 30.1

 

                                                                                                                                                                                                             ………(a)

Where

                         = mass flow per unit time per unit area kg/hr/m2

                         F = Area through which mass is flowing

                         D = Diffusion coefficient m2/hr

                         Cb = Mass Concentration of components B in kg/m3

The Fourier equation for conduction and Newton’s equation for shear are written as follows

                                                                                                                                                                                                                                                                      ………(b)

And

                                                                                                                                                                                                                       ………(c)
Comparing equation (a), (b) and (c), the heat conduction equation describes the transport of energy, the shear equation describes the transport of momentum and diffusion law describes the transport of mass.

Fick’s law may be expressed conveniently in term of partial pressures by making use of the perfect gas equation.

            p =ρRT

where the density ρ represents the mass concentration to be used in Fick’s law.

The gas constant for a particular gas is given by the equation

Where

               G = Universal Gas constant = 848

              Mb = Molecular weight of the gas.

                                                                                                                                                                                                       ………(d)

Substituting the value of ρb into the equation (a), Fick’s law of diffusion for component B into the component C can be written as follows:

                                                                                                                                                                                                        ……….(e)

Similarly, diffusion of component C into the component B is given by:

                                                                                                                                                                                                         ……….(f)

The above equation hold good only for isothermal diffusion.