What is Mass transfer? Fick's law of diffusion.

Mass transfer is the transfer of mass from a region of higher concentration to lower concentration. It is a unit operation(physical changes). So we can not see any chemical change. Mass transfer plays an important role in industrial process.
Examples: ln petroleum refinery, distillation of crude oil converts into many fraction like LPG, petrol, kerosene, diesel, lubricating oil, etc.

CLASSIFICATION OF MASS TRANSFER

OPERATION: We can classify the mass transfer operation into six phase contact.
1. Gas-Gas
2. Gas-Liquid
3.Gas-Solid
4. Liquid-Liquid
5. Liquid-Solid
6. Solid-Solid

1. Gas-Liquid: we talk about gas liquid mass transfer operation we can say that transfer can be from gas to liquid or liquid to gas.we study;

(a). Distillation it is a  separating  process.in distillation we created the gas phase from liquid by application of heat; or created the liquid  from the gas by removal of heat.
Ex. Solution of acetic acid and water is partially vaporized  by heating, and after some time acetic acid will separate from water.we condense the newly created vapor phase.it is not proper way to separating process, So we can use fractional distillation instead of distillation.

(b). Gas Absorption: Gas Absorption refer to an operation in which the transfer of material from a gas to liquid with the help of liquid solvent like water.
Example if ammonia air mixture is contacted with water then a large amount of ammonia dissolve in liquid but air does not dissolve, from this process we can separate air from ammonia-air mixture.

(C). stripping or desorption: lt is a reverse process of gas absorption.It ia an operation when we separate the gas solute from liquid solvent.
Example: if air is brought into contact with an ammonia- water mixture, ammonia leaves the water and enters into gas phase is called stripping.

(d). Humidification or de-humidification: if we contact the dry air with liquid water result in evaporation some amount of water enter into air this process called humidification.and de-humidification is a reverse process of humidification.

2. Gas-solid: it is an another mass transfer operation.we study in gas-solid :-

(a). Sublimation: solid to gas phase transitions without first becoming liquid is called sublimation.
Example: solid carbon dioxide is known as  dry ice and sublimates at room temperature.and freeze drying is an another example of sublimation.

(b). Deposition: when gas changes directly into solid without first becoming liquid is called deposition.it occurs when temperature fall down.

(C). Drying: Drying is defined as the removal of water or other liquid from solids by heat and other process is called drying.

Example: Removal of moisture from a wet filter cake by exposure to dry air, dry laundry by exposure to air, etc.

3. Liquid-Liquid: in this mass transfer operation we talk about liquid extraction operation.
Example : acetone water solution  is shaken in separating funnel with carbon tetrachloride and liquids allowed to settle down a large portion  of acetone will be found in the carbon tetrachloride  and this way it separate from water.means we use one liquid solvent for separating the other liquid mixtures.

4.Liquid-solid: in this operation we study about crystallisation, leaching.

(a).Crystallisation is a process of formation  of solid from liquid solution  based on difference in solute conectartion and it's solubility.

(b). Leaching: separating of liquid from a solid by a liquid solvent is called leaching.
Example: leaching of gold from its ores by cyanide solution.

Flux; Rates of Mass Transfer describe in terms of flux(Molar flux or mass flux). Flux of mass transfer caused by the existence of difference in velocity and concentration.
It is defined as the amount of component either in mass or in molar, which crosses a given area per unit time is called flux. In gas phase, the concentration are usually expressed as the partial pressure.
According to ideal gas law;
Pa.V =nRT
Molar concentration of component A is defined as the number of moles of A per unit volume.

Ca=na/V =pa/RT
Ca = Concentration of component  A in the term of moles/litre.
na = number of moles of
V = Total volume of mixture.
Pa = partial pressure of component A.
R is gas constant and T is temperature in K.
Mass fraction = It is defined as the ratio of mass concentration of A to the total mass density of mixture. or ratio of mass of component A to total mass of mixture. Mole fraction is defined as the ratio of concentration of A to concentration of mixture.it is different for gas and liquid.o r the ratio of number of moles of A to total number of moles in mixture.
For gas ya = Pa/P
Fir liquid xa = ca/C
ya and xa are molar fraction of component A for gas and liquid respectively.
Above all terms are important in mass transfer for calculation or understand the formula's.

Fick's law of diffusion:-
For understanding a fick's law of diffusion we see a example. Consider a chamber containing a mixture of two different gases(A and B), at the same temparature, pressure initially separated by a partition. The left chamber has high concentration of A and the right has more concentration of B. As the partition wall us removed, the driving force comes into play. The molecules of A and B start diffusing into one another So as to undergo the concentration difference.  The diffusion will take place in the direction of decreasing concentration or higher to lower concentration.Hence there is a net movement of A to the right and B to the left.the process of diffusion continuous till the equilibrium is attained in other words when concentration of A and B are uniform in both the chamber and the concentration gradient to exist.The rate of diffusion of constituents is expressed in the term of flux by fick's law, which relates the flux of diffusing substance to the concentration gradient which responsible for the transfer. Ja is directly proportional to concentration gradient.
Ja = -Dab.dCa/dx
Ja is Molar flux in z direction relative to the molar average velocity, moles/square meter.second.
dCa/dx is a concentration gradient in decreasing concentration or x direction.
Dab is proportionality constant, called diffusion coefficient or mass diffusivity of component A through B in square meter/second.

Important notes about fick's law;

1. Negative sign indicates that the transfer in the direction of decreasing concentration.

2. Flux equation is valid only when the diffusion occurs due to concentration gradient and fail wgen diffusion occurs due to temperature, pressure or external force.

3. Flux is relative to average molar velocity of all the constituents the equation are invalid if the flux is taken relative to a fixed point in space (Na).

4. Fick's law ia based on experimental evidence not derived from first principle.

5. It is valid for all the states( gas, liquid and solid).

6. D is depend upon temperature, pressure and nature of material or substance. However for ideal gas and dilute substances, it can be assumed to remains practically constant for a given range of temperature and pressure.
unit of Dab is
Dab = -Ja/dCa/dx.  = square meter/second.
The unit of diffusion coefficient is similar to units of thermal diffusivity alpha in heat transfer and momentum diffusivity or kinetic viscosity v in fluid flow. Using kinetic theory of gases it is possible to predict the diffusion coefficient Dab for a binary mixture of gases.
D is directly proportional to 3/2 power of temperature/ total pressure.
So,.  D1/D2 =. (T1/T2) power 3/2 ×P2/P1.