Diffusion in one dimension with asymmetrical consumption is modeled using a partial differential equation.

Description

This model illustrates using function generators to
generator an initial condition and a parameter that
are spatial functions in x. It also generates a
comparison function, Ctest, which shows that the
solution in the presence of consumption evolves into
a profile which is approximately Gaussian although the
mean has been shifted downstream.

The diffusion of a substance in one dimension over a finite
length is modeled. The solution is plotted as 
(1) Contours in the x-t plane,
(2) As functions of distance at specific times, and
(3) As functions of time and specific locations.

The initial values are given as
C(x) = 5,  0.049<=x<=0.051, 
C(x) = 0,  x<0.049 or x>0.051.

The boundary conditions are the zero-flux condition
(boundaries are reflective).

The consumption in the model is controlled by the area of a Gaussian curve
centered at 1/4 the length from the entrance of the capillary. Set the
area to 1e-8 to remove the effect.

Equations

Partial Differential Equation

Left Boundary Condition

Right Boundary Condition

Initial Condition

The equations for this model may be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.