This page will look better in a graphical browser that supports web standards, but is accessible to any browser or internet device.

Served by Samwise.

# Diffusion1DpdeConsumption

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

Model number: 0364

 Run Model: Help running a JSim model.
Java runtime required. Web browser must support Java Applets.
(JSim model applet may take 10-20 seconds to load.)

## 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

$\large \frac{\partial C_p}{\partial t} = D_p \cdot \frac{\partial^2 C_p}{\partial x^2} -G(x) \cdot C_p$

#### Left Boundary Condition

$\large {\it {\frac {\partial }{\partial x}}C_p=0$ .

#### Right Boundary Condition

$\large {\it {\frac {\partial }{\partial x}}C_p=0$

#### Initial Condition

$\large C_p=C_p0(x)$ .

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.

## References





## Key Terms

1d, 1-d, 1D, 1-D, one dimension, diffusion, PDE, consumption, function generator, optimize, no flux, boundary condition, tutorial

## Model History

Get Model history in CVS.

Posted by: Name

## Acknowledgements

Please cite www.physiome.org in any publication for which this software is used and send an email with the citation and, if possible, a PDF file of the paper to: staff@physiome.org.
Or send a copy to:
The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.