Breakthrough Curves for Adsorption with Longitudinal Diffusion Assuming Linear Equilibrium

An important unit operation in biotechnology and chemical engineering is fixed-bed adsorption.
Species to be separated, called separands, are either in the mobile phase or adsorbed by the stationary phase. The separands are subject to convection, mechanical dispersion, and molecular diffusion.
A mass balance, obtained by considering a disk of cross-sectional area equal to that of the column, gives:
where and are the concentrations of the separand in the mobile and stationary phases, respectively, is the void fraction of the column, is the mobile phase superficial velocity, is the effective dispersivity of the separand in the column, is the longitudinal position in the column, and finally is time.
Since linear equilibrium is assumed: . Also consider that mass transfer resistances are negligible (i.e.,
The breakthrough curve, the separand concentration versus time at the exit of the column, can be determined experimentally or computed numerically. In the present Demonstration, breakthrough curves are computed for a variety of values of the relevant parameters.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+