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
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).,
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:
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.
Time to try Diffusion Simulator.