Mass Balance#

Big Ideas#

  • The law of conservation of mass gives rise to systems of differential equations which model the transfer of mass.

  • Constitutive laws such as the law of mass action for checmial reactions describe individual components of a mathematical model. Constitutive laws are themselves mathematical models!

  • The law of conservatin of mass is very general! It applies to any quantities that are flowing in and out of a system. Even a financial system where money is flowing in and out.

  • Any model of a real-world phenomenon will involve many parameters and the nondimensionalization procedure simplifies the model and determines what role the system parameters play.

  • Use SciPy to compute numerical solutions of differential equations. A computational approach to mathematical modelling allows us to easily simulate and visualize models.

Learning Goals#

  • Apply physical laws to construct mathematical models of mass transfer

  • Apply nondimensionalization process and interpret dimensionless parameters

  • Compute numerical solutions of systems of differential equations