Modeling Project: Lithium ion batteries

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• The modeling project is optional and to take it you must register. Register by sending me an email to Dag. Either register a full (or partially full) group, or individually, and I will put you in a group.
• The project part of the course will count 25% of the final grade. If the project grade makes your final grade worse than the exam grade, the final exam counts 100% for your final grade.
• In the project you will work on a modeling problem in a group of 4-5 students over a period of 3 weeks.
• The project description will published here in week 43. This year's topic is modelling Lithium ion batteries.

You will find the project groups here. Please notify me if something is wrong. If you enter the Blackboard site for this course, you will find e-mail addresses for all students there.

Mathematical modeling of Lithium battery

• 29/10 : projet description is posted
• 30/10 : fixes in terminology (positive versus negative electrode in first part)
• 2/11 :
  • new question in section 1 (Chemical equilibrium and Gibbs free energy)
  • Fixed governing equation for concentration evolution in section 2 (Kinetics of chemical reactions in solutions)
  • more details and precise expressions in the questions in section 3 (Effect of the electrical state of the reaction kinetics)
  • fixed asymptotic expansion in section 7 (Modeling equations for the whole battery)
• 3/11 : fix notation for total number of reactants and products in the general form of a chemical reaction (section 1 and 2)
• 4/11 :
  • Fix in equation (7)-(8) in section 2.
  • Fixed definition of $\eta$ in question 6 in section 3 (it should be the same as given previously)
  • Added definition of current in question 6 in section 3
• 8/11 :
  • Fixed typo in equation for $r$ at the end of section 2 (Kinetics of chemical reactions in solutions)
  • Fixed typo in the definition of $i_0$ and of the current $i$ at the end of section 3 (Effect of the electrical state of the reaction kinetics)
  • Fixed expression for the value of the resistance at the end of section 4 (charge conservation equation)
  • Clarified question in section 5 (activation phase) and added choice of $\beta = \frac12$ in question in section
  • Added unit for mobility in section 6 (Ion transport in the electrolyte)
• 22/11 :
  • Fixed typo in equation (15b) for the conservation equation of $PF_6^-$

1. A written report 5-10 pages long.
   • The report can be either English or Norwegian.

• Manage your time:
  • Expected total time per person: About 3x12=36 hours.
  • Try to plan, focus, and limit the work so that you get some results in the expected time without using many extra hours.
  • Imagine you work in a company and the group is given 3 weeks and 36 hours per member to finish the project (some results, report, presentation). Do your best with these constraints.
• Focus - at least to begin with. You are not expected to work on all the questions/projects.
• You can present partial results.
• Try and fail is ok as long as you do not cover up.
• You may discuss across the groups, but reports and presentations must be made independently.
• You may use any literature you find, but you must give references to the source!
• Do not copy from any source without understanding the material first!

• Do not use too much time during your presentation.
• Language: Norwegian or English
• Vote for best presentation: Anonymous, one vote per group, can not vote for your own group.