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1. Module 5
MASS TRANSFER
Dr. CIJIL B. JOHN
Asst. Professor
Dept. of Mechanical Engineering
Jyothi Engineering College
2. MODULE 5 – Syllabus
• Introduction to mass transfer- Molecular diffusion in fluids- Steady state molecular diffusion
in fluids under stagnant and laminar flow conditions - Fick’s law of diffusion- Types of solid
diffusion- mass transfer coefficients in laminar and turbulent flows- Introduction to mass
transfer coefficient, Equimolar counter-diffusion- Correlation for convective mass transfer
coefficient- Correlation of mass transfer coefficients for single cylinder- Theories of mass
transfer- Overall mass transfer coefficients
46. TYPES OF SOLID DIFFUSION
Diffusion in solids can occur by two different mechanisms:
a) Interstitial diffusion
b) Substitutional diffusion
Examples: If we write on the blackboard and leave it uncleaned for a longer time we will observe that it
is difficult to clean the blackboard afterwards. This is because of the diffusion of chalk particles into the
blackboard.
If two metals blocks are bound together tightly and kept undisturbed for a few years, then the particles
of one metal are found to have diffused into the other metal.
Gold and lead can diffuse into each other by contacting.
47. 1. Substitutional diffusion
• Substitutional diffusion occurs by the movement of atoms from one atomic site to another.
• In a perfect lattice, this would require the atoms to “swap places” within the lattice.
• A straight-forward swapping of atoms would require a great deal of energy, as the
swapping atoms would need to physically push other atoms out of the way in order to
swap places.
• In practice, therefore, this is not the mechanism by which substitutional diffusion occurs.
49. • Substitutional diffusion occurs only if there is a vacancy (missing atom) in the lattice.
• If a vacancy is present, one of the adjacent atoms can move into the vacancy, creating a vacancy on the site
that the atom has just left.
• In the same way that there is an equal probability of an atom moving into any adjacent atomic site, there is
an equal probability that any of the adjacent atoms will move into the vacancy.
• It is often useful to think of this mechanism as the diffusion of vacancies, rather than the diffusion of
atoms.
50. • The diffusion of an atom is therefore dependent upon the presence of a vacancy on an
adjacent site.
• The rate of diffusion is dependent upon two factors: how easily vacancies can form
in the lattice, and how easy it is for an atom to move into a vacancy.
• The dependence upon the presence of vacancies makes substitutional diffusion slower
than interstitial diffusion
• Another theoretical substitution mechanism is ring substitution. This involves several
atoms in the lattice simultaneously changing places with each other.
• Like the direct swap method, ring substitution is not observed in practice. The
movement of the atoms required is too improbable.
51. 2. Interstitial diffusion
• In this case, the diffusing atom is not on a lattice site but on an interstice. The diffusing atom
is free to move to any adjacent interstice, unless it is already occupied.
• The rate of diffusion is therefore controlled only by the ease with which a diffusing atom can
move into an interstice.
• Theoretically, at very high impurity concentrations movement may be restricted by the
presence of atoms in the adjacent interstices. In practice, however, it is very likely that a new
phase would be formed before this had an effect.
59. MASS TRANSFER COEFFICIENT (kc) - Wikipedia
• The mass transfer coefficient is a diffusion rate constant that relates the mass
transfer rate, mass transfer area, and concentration change as driving force:
Mass transfer coefficient is defined as the rate of mass transfer per unit area per unit concentration
difference.
60.
61.
62. MASS TRANSFER COEFFICIENT [Contd…]
• This can be used to quantify the mass transfer between phases, immiscible and
partially miscible fluid mixtures (or between a fluid and a porous solid). Quantifying
mass transfer allows for design and manufacture of separation process equipment that
can meet specified requirements, estimate what will happen in real life situations etc.
• Mass transfer coefficients can be estimated from many different
theoretical equations, correlations, and analogies that are functions of material
properties, intensive properties and flow regime (laminar or turbulent flow)
63. CONVECTIVE MASS TRANSFER
• Molecular diffusion M.T is analogous to conduction H.T (In molecular diffusion, the bulk
velocities are insignificant, only the diffusion velocities are considered).
• Convective M.T is analogous to Convective H.T
• M.T by convection takes place in cases where the bulk velocity is appreciable or when both the
species, in a binary mixture, are moving with significant velocities.
• Like heat convection, mass convection may occur under free or forced conditions.
• The buoyancy force causing circulation in free convection M.T results from the differences in
density of the vapor-air mixtures of varying compositions.
64. The evaporation of alcohol is an example of free convection M.T, whereas the evaporation of water
from an ocean when air blows over it is a case of forced convection M.T
70. Reynold’s & Colburn Analogies for Mass Transfer-
Combined Heat & Mass Transfer
71.
72.
73. THEORIES OF MASS TRANSFER
1. Two-film theory
This is the oldest theory for gas-liquid mass transfer developed by Lewis and Whitman in 1924.
• The theory postulates the existence of a film of a thickness (δ) in both the gas and liquid phases
separated by an interface.
It is based on the following assumptions:
a) the mass transfer occurs by molecular diffusion through the film, beyond which the
concentration (CAb) is homogeneous;
b) the mass transfer through the film occurs under steady state conditions; and
c) the flux is small and the mass transfer occurs at low concentration.
74. • Accordingly, for convective mass transfer, the concentration profile is linear as shown in the figure and
the liquid-side mass transfer coefficient is expressed by equation:
𝑲𝑳 =
𝑫𝑨𝑩
δ𝑳
“Even when 2 phases are in turbulent motion, still
a crucial amount of M.T occurs by diffusion”
75. • Most of the industrial processes of mass transfer are unsteady processes.
• In such cases, the contact time between the phases is too short to achieve a stationary state / steady
state.
• This non stationary phenomenon is not generally taken into account by the film model.
• In the absorption of gases from bubbles, the mass transfer surface is formed instantaneously &
transient diffusion of the material takes place.
• This phenomenon is explained by the Higbie’s penetration model.
THEORIES OF MASS TRANSFER
76. THEORIES OF MASS TRANSFER
2. Penetration theory
The “penetration theory” or “Higbie’s model” assumes that each liquid element at the gas-liquid
interface is exposed to the gas for a short time, as schematically shown in the figure.
The basic assumptions of the theory are:
a) mass transfer from the gas into a liquid element occurs under unsteady-state conditions once they
are in contact;
b) each of the liquid elements stays in contact with the gas for same time period; and
c) equilibrium exists at the gas-liquid interface.
This theory was considered an improvement from the two-film theory since mass transfer occurs under
unsteady-state conditions in many industrial processes.
77. • The penetration theory expresses the liquid-side mass transfer coefficient in terms of the contact
time (θ) and the molecular diffusivity of the gas in the liquid according to the equation:
“The mass transfer coefficient is proportional
To the square root of the diffusivity”
78. THEORIES OF MASS TRANSFER
• For the M.T in liquid phase, Danckwert (1951) modified the Higbie’s penetration
theory.
• He stated that a portion of the mass transfer surface is replaced with a new surface by
the motion of eddies near the surface.
79. THEORIES OF MASS TRANSFER
3. Surface renewal theory
The surface renewal theory, developed by Danckwerts, applies mathematics of the penetration
theory to a more plausible situation, where the liquid is pictured as two regions, a large well mixed
bulk region and an interfacial region, which is renewed so fast that it behaves as a thick film as
shown in the figure (next slide).
The basic assumptions of the theory are
(1) liquid elements at the interface are being randomly swapped by fresh elements from the bulk;
(2) at any moment, each of the liquid elements at the interface has the same probability of being
substituted by a fresh element; and
(3) mass transfer from the gas into the liquid element during its stay at the interface takes place
under unsteady-state conditions.
80. • Thus, instead of using a constant contact time (θ), the differential liquid volume at the gas-liquid interface
is renewed due to the turbulence around the interface, referred to as the surface renewal frequency (s)
• The surface renewal theory expresses the liquid-side mass transfer coefficient in terms of the surface
renewal frequency (s) and the molecular diffusivity of the gas in the liquid according to equation:
81. THEORIES OF MASS TRANSFER
4. Boundary layer theory
M.T often take place in a thin boundary layer near the surface where the fluid is in laminar flow.
• The mass transfer coefficient (K) depends on 2/3 power of diffusivity and decreases with
increasing distance along the surface in the direction of flow.
• Boundary layer theory can be used to estimate K for some situations, but exact prediction cannot
be made when the boundary layer becomes turbulent.
