Team:British Columbia/Modeling

From 2014.igem.org

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(a very first draft of the modeling section.)
 
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<p> Background:
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<p> <b>Background:</b>
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To aid the separation process in the bio-mining, bacteria will be used to attach to particles to float them to the top. However, bacteria do not attach to the particles instantaneously - thus it is desired to have a model for the bacteria attachment as a function of time.
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To aid the separation process in the bio-mining, bacteria will be used to attach to minerals to float the particles allowing them to be easily separated from other particles and debris. However, bacteria do not attach to the particles instantaneously - thus it is desired to have a model for the bacteria attachment as a function of time.
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</p>
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Analogous problems:
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<p> <b>Analogous problems:</b>
We find that our problem is analogous to that of surfactants adsorbing to a surface, where the surfactants are replaced by bacteria and the surface is the interface between the bulk and our particles. Thus the attachment can be reduced to a time dependent adsorption problem.
We find that our problem is analogous to that of surfactants adsorbing to a surface, where the surfactants are replaced by bacteria and the surface is the interface between the bulk and our particles. Thus the attachment can be reduced to a time dependent adsorption problem.
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</p>
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Adding time dependency:
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<p> <b>Extending to time dependent:</b>
To extend an adsorption model to be time dependent we must define at least three regions and consider the mass transfer through these regions. The three regions are the surface layer, the sub-surface layer (a small layer between the surface and the bulk) and the bulk - note that to create a more robust model we can add multiple subsurface layers, as this region will likely contain gradients, the more regions that we consider the more realistic our model becomes.
To extend an adsorption model to be time dependent we must define at least three regions and consider the mass transfer through these regions. The three regions are the surface layer, the sub-surface layer (a small layer between the surface and the bulk) and the bulk - note that to create a more robust model we can add multiple subsurface layers, as this region will likely contain gradients, the more regions that we consider the more realistic our model becomes.
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</p>
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<p>
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<b>Parameters to find: </b>
There are three rate determining constants, first the rate constant determining the rate at which the bacteria attach to the surface; second,the rate at which the bacteria are removed from the surface; and lastly the mass transfer diffusion coefficient of bacteria through the media.
There are three rate determining constants, first the rate constant determining the rate at which the bacteria attach to the surface; second,the rate at which the bacteria are removed from the surface; and lastly the mass transfer diffusion coefficient of bacteria through the media.
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Once latex updated to our webpage, we will be able to throw some equations on.
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<p>
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Once we have latex updated to our wiki, we will be able to throw on some good looking equations. Figures, model validation and more modeling to come soon as well!
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For now sit tight with this:
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\frac{d\Gamma}{dt}
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</p>
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</p>
</p>

Latest revision as of 21:10, 5 August 2014



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Modeling

Background: To aid the separation process in the bio-mining, bacteria will be used to attach to minerals to float the particles allowing them to be easily separated from other particles and debris. However, bacteria do not attach to the particles instantaneously - thus it is desired to have a model for the bacteria attachment as a function of time.

Analogous problems: We find that our problem is analogous to that of surfactants adsorbing to a surface, where the surfactants are replaced by bacteria and the surface is the interface between the bulk and our particles. Thus the attachment can be reduced to a time dependent adsorption problem.

Extending to time dependent: To extend an adsorption model to be time dependent we must define at least three regions and consider the mass transfer through these regions. The three regions are the surface layer, the sub-surface layer (a small layer between the surface and the bulk) and the bulk - note that to create a more robust model we can add multiple subsurface layers, as this region will likely contain gradients, the more regions that we consider the more realistic our model becomes.

Parameters to find: There are three rate determining constants, first the rate constant determining the rate at which the bacteria attach to the surface; second,the rate at which the bacteria are removed from the surface; and lastly the mass transfer diffusion coefficient of bacteria through the media.

Once we have latex updated to our wiki, we will be able to throw on some good looking equations. Figures, model validation and more modeling to come soon as well! For now sit tight with this: \frac{d\Gamma}{dt}

If you choose to create a model during your project, please write about it here. Modeling is not an essential part of iGEM, but we encourage any and all teams to model some aspect of their project. See previous "Best Model" awards for more information.

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