Mass Transfer – Introduction, Brownian Diffusion 1-1

Chapter 1

Organization, Introduction, Brownian Diffusion

20.09.2017

Max Eggersdorfer

Mass Transfer

Two mandatory tests (30%)

Dr. Wegner Dr. Büchel

Davide Dr. Yoon Dr. Güntner Pascal Jan Nicolay Sebastian

Mass Transfer – Introduction, Brownian Diffusion 1-2

Literature:

E.L. Cussler, “Diffusion, Mass Transfer in Fluid Systems”

2nd edition, 1997, Cambridge University Press

3rd edition, 2009, Cambridge University Press

(2009) (1997)

2 TESTS of 45 min.

October 24

November 28

Mass Transfer – Introduction, Brownian Diffusion 1-3

What is mass transfer?Oxford Dictionary:

1. Introduction

Why does one substance move through or into another?

How large is the driving force?

How fast does it move?

How far does it move?

How much of a substance moves?

…

Why do we care?

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1. Introduction

The driving force for mass transfer is a difference in chemical

potential. A substance moves from high to low chemical potential,

for example:

Tea from a tea bag in hot water

travels from high concentration to low concentration.

The mass transfer process is a slow, rate limiting step that:

• Limits efficiency of commercial distillations.

• Limits rate of industrial reactions with catalysts.

• Influences corrosion of metals and marbles.

• Controls the growth of microorganisms.

Mass Transfer – Introduction, Brownian Diffusion 1-5

Combustion a reaction-diffusion process

Photos: El-Hamdi, Michael Gorman, University of Houston,

Texas (1994)

Cylindrical flame from above:

The temperature of the flame is lower

in the dark regions.

Oxygen and fuel (hydrocarbon)

diffuse with different speeds

Increasing gas feed rate forms

increasingly complex patterns

Mass Transfer – Introduction, Brownian Diffusion 1-6

Examples from nature with diffusion limitations

Recommended reading:

Philip Ball «Shapes: Nature’s Patterns»

Mineral dendrites of manganese in limestone

Computer simulations of

diffusion-limited agglomeration

Mass Transfer – Introduction, Brownian Diffusion 1-7

Naillon, Joseph, Prat, J. Crystal Growth (2017)

Crystallization Pharmaceuticals

Paracetamol

Mass Transfer – Introduction, Brownian Diffusion 1-8

Spray-drying

http://www.sakav.com

Vehring, Foss, Lechuga-Ballesteros, J. Aerosol Sci. (2007) 728-746

Particle diffusion > evaporation

Particle diffusion < evaporation

Mass Transfer – Introduction, Brownian Diffusion 1-9

Types of Mass Transfer:

1. Molecular diffusion (or just diffusion).

Mass is transferred by the random motion of molecules across

a concentration gradient. Sometimes, but not always, this is

similar to heat transfer by conduction.

2. Eddy diffusion (mixing or dispersion or agitation).

Mass is transferred by finite parcels of fluids as in momentum

and heat transfer.

Approximate rates of diffusion in:

Gases: 10 cm/min (a lady with a nice perfume).

Liquids: 0.05 cm/min (stir cream into the coffee).

Solids: 0.00001 cm/min (takes long to rust an iron axe)

Mass Transfer – Introduction, Brownian Diffusion 1-10

Relationship with Momentum and Heat Transfer

Mass transfer is similar to momentum and heat transfer but there

is nothing equivalent to radiation heat transfer.

Molecular diffusion easily gives rise to convection something that

was not so with conduction heat transfer. This is distinguished by

talking about diffusion at low and high concentrations.

Mass Transfer – Introduction, Brownian Diffusion 1-11

Description of Mass Transfer

1. Molecular model (Fick’s laws and diffusivity).

This is an elegant model based on first principles that

everyone dreams of having to work with especially in physics,

physical chemistry and biology.

2. Mass transfer coefficient model (Mass Transfer correlations)

This is a model typically employed by chemical and process

engineers when the complexity of the process leaves little

space for elegance.

The choice between models is a compromise between ambition and

resources.

Mass Transfer – Introduction, Brownian Diffusion 1-12

Example for Models

Imagine two large bulbs with equal volume connected by a long

thin capillary at constant temperature.

2

1

N2

CO2

area

Measure now the

CO2 concentration

inside the bulb

containing nitrogen.

Goal: To determine physical properties that determine the amount

of mass transferred.

Mass Transfer – Introduction, Brownian Diffusion 1-13

Define the flux: 2

amount of gas from 1 to 2CO flux

time area

This removes the influence of a particular apparatus.

2

1

N2

CO2

area

Model 2: Recognize that the CO2 flux is proportional to CO2

concentration difference between 1 and 2.

2 2CO flux k (CO concentration difference)

k is a mass transfer coefficient and this is the mass transfer coefficient model.

Model 1: Recognize that increasing the length of the capillary will

decrease the flux.

2

concentration differenceCO flux

capillary length D

D is the diffusion coefficient and this is the other model or Fick’s first law.

Mass Transfer – Introduction, Brownian Diffusion 1-14

This is similar to electric circuits, Ohm’s law:

current voltage1

or = × orresistance

area × flux of electrons potential difference

Thus the mass transfer coefficient k is analogous to the reciprocal

of the resistance.

An alternative form to Ohm’s law is:

current density1 potential difference

or = ×resistivity length

flux of electrons

The diffusion coefficient D is analogous to the reciprocal of resistivity.

Mass Transfer – Introduction, Brownian Diffusion 1-15

In heat transfer k is analogous to the heat transfer coefficient h,

while D is analogous to thermal conductivity l.

Neither the k-model nor the D-model are always successful as

they depend heavily on assumptions made in their development.

For example: The flux CO2 concentration difference if the capillary

is too thin or if the gases react.

Similarly Ohm’s law is not always valid at very high voltages.

However, both Fick’s and Ohm’s law work well in most practical uses.

Resistance or resistivity give a clue about the choice of the 2 models:

Using the resistance is good for practical applications & rough

measurements. In contrast, resistivity is a fundamental material

property.

We start with the fundamental description of the diffusion coefficient,

the D-model, following with the description of the k-model later on.