Question

Summarise the Mass Transfer module for Chemical Engineering, list all the main equations, and basic definitions.

(Mass transport/ diffusion/ steady states / flux/ficks laws 1st/2nd, laminar turbulent, volume flow rate, dispersion, pore diffusion, film theory, absorption, distillation,)

Answer 1

Summarising all main equations & definations

• Mass transport

It is the net movement of molecules of one component from one location or phase to other .This phenomenon is known as mass transfer it takes place due to difference in concentration of component at different location .i.e. concentration gradient is the driving force .

• Diffusion

The mass transfer of the species from region of higher concentration to region of lower concentration is accomplished by actual migration of molecules. This phenomenon is called as molecular diffusion .

that means mass transfer takes place via molecular diffusion .

• Steady states

System can be said at steady state if behaviour of system remain unchange with respect to time .If we take energy or mass balance over such systems accumalation term is set to zero . as there is no accumlation in steady state processes .

• Ficks First law

The Diffusivity ,D_AB , of component A is is in solution with B which is a measure of diffusive mobility is defined as the ratio of its flux J_A to the concentration gradient

where J_AZ is molar flux of A in Z - direction relative to the molar average velocity .

= conc. gradient of A in Z direction

= mole fraction gradient of A in Z direction

• Fick's Second Law

Unsteady state processes have three variables - concentration, time & position .Therefore the diffusion process must be described by partial differential equations.

where,

C_A = concentration of A

t = time

D = the diffusion coefficient

x = the position

• Laminar & turbulant

The laminar flow is more systematic flow fluid particals follows smooth path & no particals interfere with one another

while turbulent flow is irregular flow in case of turbulant flow there is vigorous mixing & eddy diffusition comes in picture .it doesnt follow smooth path . molecules inerfere in others path . & flow characters are related by Reynold no.

• Volume flow rate

It is defined as volume of fluid passes per unit time .Usually represented by symbol Q

& SI unit is m³/s

Q = V.A

V = flow velocity

A = cross sectional area of flow

• Dispersion

Dispersion is spreading of mass from highly concentrated area to low concentration area . it is analogous to diffusion & it can describe using ficks first law

where

U is fluid velocity & is some characteristic length scale .

• Pore diffusion

diffusion within pore of adsorbent is relatively important rate determining step of adsorption process also known as Knudson diffusion which occur on scale length

R = gas constant

M_A= molecular mass

D_KA= knudson diffusivity

pore diffusion

where l is length of pore .

• film theory

in case of one dimentional mass transfer the concentration is linear . The coefficient of MT in this case is proportional to diffusiion coeffiecient & inversely proportional to the film . this phenomenon is commonly known as Film theory .

this theory is based on some assumptions

a) Mass transfer occur through molecular diffusion through a fluid layer at phase boundary ,> beyond film concentration is homogeneous.

b) Mass transfer through the film occurs at steady state.

c) flux is low & MT occurs at low concentration.

• Absorption

it is separation process used to separate a specific solute from gas mixture using liquid solvent in which solute get soluble & then solute is recovered by stripping .

• Distillation

distillation is also separation process used to seaparated liquids from mixture .It work on pribnciple of relative volatility . It generally used to get more pure products .