Background
Modeling diffusion from the systems dynamics perspective involves the following steps:
- Dividing the region containing the diffusing elements into compartments
- Developing mathematical formulas to describe the movement of particles between compartments
- Defining the starting amounts in each compartment
- Calculating the amounts in each compartment at regular time intervals through the total duration being simulated.
Vensim PLE is a free modeling tool with an intuitive graphical user interface that allows us to build such a model by drawing a system diagram, inserting formulas and parameter values, and then carrying out the calculations to simulate the behavior of the system through time.
A simple model of diffusion that is used to demonstrate this process in a variety of modeling environments is a case in which particles all start within one quadrant of a rectangular area, and then diffuse across all four quadrants, eventually reaching some equilibrium distribution. The Vensim diagram of such a model is shown below. The tutorial that can be downloaded from this page describes the construction and simulation of this model, along with some variations on this model that can help us to understand how to make this model better represent different aspects of diffusion.
Model Source Files
Zip archive containing four models of diffusion in Vensim PLE. The four-compartment model pictured, two- and nine-compartment models, and a model in which the compartments are coupled to represent diffusion coupled along a linear chamber.model.zip
Size: 8081 bytes