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:
1) An initial concentration C of value C=1000 (black) that will diffuse
over time as the chemical spreads. Using the insulated house example above,
this concentration definition would be equivalent to placing a hot rock in
an initially-cold room, and following over time how the room would be heated
as the rock cooled.
2) An initial concentration that is initialized with a value of C=1000
(blue) (or C=0 (green)) that will remain at that value throughout the
simulation. This is equivalent to a source of heat whose temperature is
maintained at its initial value. In the case of C=0, it is equivalent to a
"sink" where any concentration that diffuses into this area becomes zero. To
continue the insulated house example, this concentration type could be used
to create a constant temperature heater in one corner and a constant
temperature icebath in another.
3) An initial concentration of C=0 (red), but which increases by 10 at
each timestep of the simulation. This can represent a heating element that
adds heat at a fixed rate. Areas configured with this class of concentration
change according to the diffusion process. But at each step, an additional
concentration is added.
Suppose, there is a wall of high conductivity (diffusivity)(green), but
with an inner layer of low conductivity (red). And suppose one side of the
wall were maintained at a fixed high temperature C=1000 (blue) and the other
side of the wall were maintained at a fixed low temperature C=0 (green), and
one wants to discover how the temperature will adjust between these two
extremes within the wall. Such a problem would be set up as follows:
Concentration field:
 Diffusivity
field: 
How to run Diffusion Simulator
1) Click on "diffusivity" or "concentration" to configure that field.
2) Click on "rectangle" or "oval" to establish a shape; click on one of
the color options to establish a characteristic.
3) Move the mouse to the appropriate field, then click and drag to define
the position and size of that characteristic. When you release the mouse
button, a colored area will remain. (Note that an additional cursor appears
in the complementary field, so that a precise placement of initial
concentrations vis-a-vis diffusivity characteristics is possible.)
4) Repeat 2) and 3) until the field is properly configured.
5) Click on the button which defines the other field.
6) Repeat 2), 3), 4) until this second field is properly configured.
7) Click on "Ready to run"
8) Click on "Start/resume"
The simulation may be stopped at any time with "Stop", then restarted
with "Start/resume". When the simulation is stopped, any mouse position
within the concentration field will display the concentration at that
position. Also, when the simulation is stopped, clicking the mouse within
the vertical black stripe to the right of the concentration field will
produces a graph of the concentration distribution along the horizontal at
the mouse's vertical position.
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