Thursday, January 22, 2015

Statistical Mechanics, Part 1

[This blog post is part of two series. The first series, titled Statistical Mechanics, is a series of lessons that I have developed to illustrate how curriculum and instruction can be designed to encourage vertical learning. We start by drilling down from our understanding of diffusion to develop a dynamic model of diffusion grounded in random particle motion using statistical mechanics. We then build on top of this foundation to construct deeper understandings of fluid flow, heat transfer, and electrical circuits. You can navigate through the lessons in this series using the links below. These lessons are then part of a larger series, Defining Vertical Learning.]

Part 1  |  Part 2  |  Part 3  |  Part 4  |  Part 5  |  Part 6  |  Part 7  |  Summary


If I take a drop of red food coloring and put it in a glass of water, what happens? The red food coloring begins spreading out until, eventually, the entire glass of water is a light pink color.

A drop of red food coloring in a glass of water

This process is known as diffusion. Diffusion is the flow of particles from regions of high concentration to regions of low concentration. What does this look like on a molecular scale?

An inaccurate and misleading visualization
of diffusion on a molecular scale

If the red dots represent particles of red dye, then we might think that diffusion looks something like this on a molecular scale. The red dye particles are moving away from each other, spreading out until they are evenly distributed. But how do the red dye particles know where to move? Can they detect regions of high concentration and low concentration? Even if particles could detect concentrations across distances, why would they want to move to a region where it is less crowded? Do particles have goals and desires?

For most of us, diffusion makes sense because we have lots of firsthand experience with it. We see diffusion happening in our everyday lives. It seems natural and intuitive. But few of us understand the local mechanisms that drive diffusion. We haven’t tried to drill down and ground our understanding in anything beyond the textbook definition of diffusion. This can result in misconceptions, such as the inaccurate and misleading visualization of diffusion on a molecular scale pictured above. Red dye particles don’t move away from each other; they move randomly. So how does diffusion happen? To figure that out, we will start with what we know.

Part 1  |  Part 2  |  Part 3  |  Part 4  |  Part 5  |  Part 6  |  Part 7  |  Summary


  1. I made a wikipedia animation + caption to try to illustrate this topic a few years ago -- see top of Fick's law article. It has room for improvement though. :-D

    1. Hi Steve. I included an animation in part two that was inspired by your animation. Hope you don’t mind!

  2. Hi Steve. Great animation! I like how you highlight how an individual solute molecule still moves randomly even though there is a steady net flow of molecules to the right. I’d be curious to hear what you think of this lesson as it unfolds.