Slides for the eLearning course Separation and purification processes in biorefineries (https://open-learn.xamk.fi) in IMPRESS project (https://www.spire2030.eu/impress). Section: Mass transfer processes Subject: 2.1 Overview

1. This project has received funding from the European Union’s Horizon 2020
research and innovation programme under grant agreement No 869993.
Overview of the
mechanisms of
mass transfer
processes

2. Mechanisms of mass transfer processes
• Mechanisms of mass transfer are divided into three groups:
• Molecular mass transfer
• Convective mass transfer
• Interphase mass transfer
• They often occur simultaneously, but one of them is usually dominant.
• Molecular and convective mass transfer consider the diffusion of
substances within a single phase.
• Calculations of molecular and convective mass transfer are based on the
rate of diffusion and total mass transfer.
• In interphase mass transfer, two insoluble phases are brought into
contact. Calculations are based on equilibrium data.

3. Comparison of mechanisms
Molecular
mass transfer
Molecular diffusion
Fick’s law
Diffusion coefficients
Example: dissolving
sugar in coffee
without stirring
Convective
mass transfer
Mass transfer in
bulk motion
Mass transfer
coefficients
Example: dissolving
sugar in coffee and
stirring at the same
time
Interphase
mass transfer
Equilibrium between
two phases
Equilibrium data
Example: distillation
of ethanol from
water-ethanol
mixture

4. Velocities and fluxes
• Knowledge about velocities and fluxes are needed in diffusion calculations.
• SI unit for velocity is m/s and the common symbols are v and u.
• In mass transfer operations, velocity can mean both the molecular velocity in
microscopic scale and the bulk motion.
• Various components of the solution move with different velocities.
• The term flux means the amount (mass or molar) of species passing through
the unit area in unit time. The unit area is normal to the direction of diffusion.
• Flux is a vector quantity. SI unit for mass flux is kg/(m2∙s) and for molar
flux mol/(m2∙s).
• Common symbols for mass fluxes are ni and ji and for molar fluxes Ni and Ji.
• The fluxes can be determined in relative to a stationary observer or to an
observer moving with the average velocity.

5. Mass-average and molar-average velocities
• Mass-average velocity v
[v] = m/s
• Molar-average velocity V
• If the molecular weight of
all species are equal, v = V.
• In dilute solutions, the
average velocity becomes
virtually equal to the
velocity of the solvent.
𝑣 =
𝑖=1
𝑛
𝜌𝑖𝑣𝑖
𝑖=1
𝑛
𝜌𝑖
=
𝑖=1
𝑛
𝜌𝑖𝑣𝑖
𝜌
=
1
𝜌
𝑖=1
𝑛
𝜌𝑖𝑣𝑖 =
𝑖=1
𝑛
𝜔𝑖𝑣𝑖
𝑉 =
𝑖=1
𝑛
𝑐𝑖𝑣𝑖
𝑖=1
𝑛
𝑐𝑖
=
𝑖=1
𝑛
𝑐𝑖𝑣𝑖
𝑐
=
1
𝑐
𝑖=1
𝑛
𝑐𝑖𝑣𝑖 =
𝑖=1
𝑛
𝑥𝑖𝑣𝑖
𝜌𝑖 = mass concentration of 𝑖
kg
m3
𝜔𝑖 = mass fraction of 𝑖
kg
kg
𝑐𝑖 = molar concentration of 𝑖
mol
m3
𝑥𝑖 = mole fraction of 𝑖
mol
mol

6. Example: Average velocities
• A gas mixture is flowing through a pipe (⌀ 25 mm).
Composition of the mixture and velocities of each
component are shown in the table. Calculate the
mass-average and molar-average velocities of the
mixture. Total pressure is 4 atm.
Molar-average velocity:
𝑉 =
𝑖=1
𝑛
𝑦𝑖𝑣𝑖 = 0.65 0.03 + 0.08 0.03 + 0.24 0.035 + 0.03 0.02 = 0.0309 m/s
% Velocity
NH3 65 % 0.03 m/s
N2 8 % 0.03 m/s
H2 24 % 0.035 m/s
Ar 3 % 0.02 m/s
For mass-average velocity, you need the molecular weights of each component.
The correct answer is 0.029 m/s. Try to solve the exercise by yourself. You can
find the explanation from the bonus materials.

7. Mass flux and molar flux
• Fluxes are commonly used to describe the diffusion rates.
• There are three ways to define the flux:
1. With respect to coordinates that are fixed (stationary oserver)
2. With respect to the mass-average velocity (moving observer)
3. With respect to the molar-average velocity (moving observer)
Mass fluxes
kg/(m2∙s)
Molar fluxes
mol/(m2∙s)
1. Stationary obsever ni = ρivi Ni = civi
2. Observer moving with
mass-average velocity
ii = ρi(vi – v) Ii = ci(vi – v)
2. Observer moving with
molar-average velocity
ji = ρi(vi – V) Ji = ci(vi – V)
ρi = mass concentration of i
vi = linear velocity of i
v = mass-average velocity
V = molar-average velocity
ci = molar concentration of i

8. This project has received funding from the European Union’s Horizon 2020
research and innovation programme under grant agreement No 869993.
References
Benitez, J. 2016. Principles and Modern Applications of Mass Transfer Operations. Wiley,
pp. 1-13.
Dutta, B. K. 2007. Principles of mass transfer and separation processes. New Delhi:
Prentice-Hall, pp. 7-10, 74-76, 102-103.
Treybal, R. E. 1980. Mass-transfer operations. 3rd ed. Auckland: McGraw-Hill, pp. 19-22,
104-105.
Videos:
• Convection versus diffusion: https://youtu.be/EG4ZoVTSA5I
• Mass average and molar average velocities: https://youtu.be/w89NSgug5v8
• Convection and diffusion: https://youtu.be/HA3RrWW8uGQ