Concentration profiles

A concentration profile is a sketch that indicates the magnitude of the concentration as a function of position.

This sketch is often superimposed on a process to indicate where these changes occur.

This is analogous to a velocity profile for fluid flow.

Exercise: Concentration profile

Based on the molecular distribution below, draw the concentration profile of species � as a function of �:

Exercise: Quick (iClicker) questions

1. Mass transfer occurs because of gradient in what quantity?
   1. temperature
   2. pressure
   3. fluid flow
   4. concentration
2. The two main types of mass transfer are
   1. diffusion and conduction
   2. convection and diffusion
   3. radiation and convection
   4. conduction and radiation
3. A tank contains a uniform concentration of a chemical. The fluid in the tank is pumped into another tank. In CBE, is this movement of fluid and mass considered to be a form of mass transfer?
   1. Yes
   2. No

Demonstrations

Simulations of particle diffusion

Follow a given molecule and see how far it goes over time. For the multiple species case, try to follow a molecule in all three species and track how far each goes over time.

• single species
• multiple species

Very roughly speaking, squaring the distance traveled and dividing by the time over which you followed the molecule gives a fundamental measure commonly used to quantify mass transfer. Of course, we need to consider a very large number of molecules and do some appropriate averaging and scaling depending on the number of dimensions.

�=⟨�2(�)⟩2��

where � is the diffusion coefficient, � is the mean displacement of the particle, � is time, and � is the number of dimensions.