Various Separation Processes Have Certain Basic Principles That Can Be Classified into 3 Fundamental Transport Processes

Assignment

Food Engineering

Submitted To-

Submitted By-

• Aakash Sharma (114001)
• Aashna Sharma (114002)
• Aastha Sahotra (114003)
• Abhinav Jain      (114004)
• Abhishek Dangi(114005)
• Akash Kathuria (114006)

INTRODUCTION

Various separation processes have certain basic principles that can be classified into 3 fundamental transport processes:

• Momentum transfer
• Heat transfer
• Mass transfer

Momentum transfer occurs in operations such as – fluid flow, mixing, sedimentation and filtration. Heat transfer occurs in conductive and convective transfer of heat, evaporation, distillation and drying. Mass transfer occurs in distillation, absorption, drying, liquid -liquid extraction, adsorption, ion exchange, crystallization and membrane separation processes.

When mass is being transferred from one distinct phase to another or through a single phase, the basic mechanisms are the same whether the phase is a gas, liquid or solid.

FICK’S LAW FOR MOLECULAR DIFFUSION

Fick's law relates the diffusive flux to the concentration under the assumption of steady state. It postulates that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient (spatial derivative), or in simplistic terms the concept that a solute will move from a region of high concentration to a region of low concentration across a concentration gradient. In one (spatial) dimension, the law is:

 = -  [pic 1][pic 2][pic 3]

Where,

•  Is the "diffusion flux," of which the dimension is amount of substance per unit area per unit time, so it is expressed in such units as mol m−2 s−1. It measures the amount of substance that will flow through a unit area during a unit time interval.[pic 4]
• Is the diffusion coefficient or diffusivity. Its dimension is area per unit time, so typical units for expressing it would be m2/s.[pic 5]
•   (For ideal mixtures) is the concentration, of which the dimension is amount of substance per unit volume. It might be expressed in units of mol/m3.[pic 6]
•  Is position, the dimension of which is length. It might thus be expressed in the unit m.[pic 7]

The general Fick’s law equation can be written as follows for the binary mixture A and B:

[pic 8]

If c is constant then x :    c         [pic 9][pic 10][pic 11]

Thus, substituting, we get :  = -  [pic 12][pic 13][pic 14]

In terms of partial pressure it can be written as:             [pic 15][pic 16]

Diffusion through solids

In many processes such as drying, adsorption and membrane separations require the contact of gases or liquids with solids. The diffusion rate in solids tends to be very slow in comparison to liquids and gases. Yet, Mass transfer is quiet important in chemical and biological processes. Diffusion occurs in these cases in the solid phase and the diffusion mechanism is not as simple as in the case of gases or liquids. Diffusion through solids can be broadly classified into two categories –

• Diffusion in nonporous dense solids ( not depending on actual structure of solids) – following Fick’s law.
• Diffusion in porous solids (depending on the structure and void channels in solids) – not following Fick’s law  

The latter one is possible to be described by the Fick’s law used in the case of fluids.

1. Diffusions in solids following Fick’s law

This diffusion occurs when the fluid or solute diffusing is actually dissolved in the solid to form a more or less homogeneous solution. If the diffusivity is independent of concentration and there is no bulk flow, the steady state molar flux (NA) in the Z direction is given by Fick’s law as follows:[pic 17]

Where, DA is the diffusivity of A through the solid.

Integration of the above Equation gives diffusion through a flat slab of thickness z:[pic 18]

Where, CA1 and CA2 are the concentrations at two opposite sides of the slab. This is similar expression for diffusion obtained for fluids under identical situation.

For other solid shapes the general Equation for rate of diffusion (w) is-

[pic 19]

The diffusion coefficient DA in the solids as stated above is not dependent upon the pressure of the gas or liquid on the outside of the solid. However, the solubility of the solute in the solid is directly proportional to pA.

The solubility of a solute gas (A) in a solid is usually expressed as S in m3 solute (at STP of 0 degree Celsius and 1 atm pressure) per m3 solid per atm partial pressure of A.

To convert this to CA concentration in the solid in kg mol A/m3 using SI units,

[pic 20]

Permeability Equation for diffusion in solids

In many cases the experimental data for diffusion of gases in solids are not given as diffusivities and solubilities but as permeabilities, PM, in m3 of solute gas A at STP diffusing per m2 cross sectional area through a solid 1 meter thick solid under a pressure difference of 1 atm pressure. This can be related to Fick’s equation as-

From the above stated equations-[pic 21]

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