Diffusion Processes

Basic idea:

In its simplest form, diffusion is the transport of a material or chemical by molecular motion. If molecules of a chemical are present in an apparently motionless fluid, they will exhibit microscopic erratic motions due to being randomly struck by other molecules in the fluid. Individual particles or molecules will follow paths sometimes known as "random walks."

In such processes, a chemical initially concentrated in one area will disperse. That is, there will be a net transport of that chemical from regions of high concentration to regions of low concentration.

An analogous form of diffusion is called conduction. In this case, heat is the "chemical" that is transported by molecular motion. As in chemical diffusion, heat migrates from regions of high heat to regions of low heat. The mathematics describing both conduction and diffusion are the same.

What this lab is about:

In this laboratory, students will explore two-dimensional diffusion phenomena by configuring and running a program called Diffusion Simulator (DS). Given an initial concentration of a chemical (heat), DS calculates and displays how a chemical diffuses over time. Results are visual, but quantitative data may be obtained from the display.

DS operates within a rectangular area. For every point in this area, two things must be specified: 1) the diffusivity--which characterizes the rate at which a chemical will diffuse, and 2) the initial concentration of a chemical (heat). Since there are two variables which must be specified over the field, it is best to imagine that there are actually two fields, a "diffusivity field" and a "concentration field". To prepare a problem for simulation, students must configure both of these rectangular fields before a problem can be run.

In DS, each of these fields is configured by creating colored areas that represent different diffusivities or different types of initial chemical concentrations. Colored areas are produced with a primitive "painting" tool consisting of a drawing shape--rectangle or oval--and a color. Both elements--shape and color--must be chosen before the painting tool can be used. These choices exist as buttons within a menu and are specific to each field.

The diffusivity field begins as an area having uniformly high diffusivity (green). Subareas may be created with high (green), low (red), or zero (white) diffusivity. By the careful positioning of rectangles and ovals with different diffusivities, this field can be configured to represent many physical systems. For example, a well-insulated room with a not-well-insulated window can be represented as an inner rectangle of high diffusivity (the room) which is framed by a rectangular region of zero diffusivity (the walls) with a segment of this frame defined as low diffusivity (the window)., i.e.,

Diffusivity field:        

The concentration field begins with zero chemical concentration. It must be configured with initial concentrations, before DS can be run. When DS is started, the initial concentrations will begin to diffuse. At each point, the concentration will change at a rate determined by the corresponding point on the diffusivity field. Again, by adding colored rectangles and ovals to this field, an initial field of chemical (heat) concentration can be created. Three classes of concentration are available: