Adsorptions

Model for Caulobactor Attachment to Chalcopyrite

The mechanism for caulobactor (~1um diameter) attachment to particles of chalcopyrite (~100um) share many similarities with a standard adsorption problem. The Langmuir isotherm has been adopted for modelling caulobactor to chalcopyrite. The model defined 3 distinct regions, the surface, subsurface and bulk. The surface is the interface between chalcopyrite and the medium, with the medium being the suspension fluid holding both the caulobactor and chalcopyrite. The surface consist of a finite number of sites for caulobactor attachment. The subsurface is an arbitrary volume around the surface where we allow the concentration of caulobactor to fluctuate. The bulk is everything else, it differs from the subsurface as we assume the concentration of caulobactor is relatively constant. This model hence assumes the total number of caulobactor in the system is much greater than the totally number of attachment sites on chalcopyrite.

The total number of free sites can be estimated given the surface area of chalcopyrite particles and foot print of caulobactor. A matlab code was written to randomly place circles (simulating the caulobactor) of 1 unit diameter around a square. The x,y coordinates of the circles were generated with a uniform random distribution, each time coordinate was generated it was checked against other circles that have already been placed to see if they collide before placing onto the square. The script stops when 1000 consecutive attempted placements fail. The script was run for a surface 100 squared unit 5 times and verified against a surface of 1000 squared units run twice.

As the results for 100 and 1000 unit area surface both give reasonably close values for circles per unit area it is safe to assume there are about 0.6 sites for caulobactor attachment per square um of chalcopyrite.