Model number
0330

  

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

Description

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).

diff1 fig1

Equations

Partial Differential Equation

e0

Left Boundary Condition

e1

Right Boundary Condition

e2

Initial Condition

e3

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.

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Key terms
no flux
boundary condition
tutorial
Acknowledgements

Please cite https://www.imagwiki.nibib.nih.gov/physiome 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: 
Or send a copy to:
The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.

Model development and archiving support at https://www.imagwiki.nibib.nih.gov/physiome provided by the following grants: NIH U01HL122199 Analyzing the Cardiac Power Grid, 09/15/2015 - 05/31/2020, NIH/NIBIB BE08407 Software Integration, JSim and SBW 6/1/09-5/31/13; NIH/NHLBI T15 HL88516-01 Modeling for Heart, Lung and Blood: From Cell to Organ, 4/1/07-3/31/11; NSF BES-0506477 Adaptive Multi-Scale Model Simulation, 8/15/05-7/31/08; NIH/NHLBI R01 HL073598 Core 3: 3D Imaging and Computer Modeling of the Respiratory Tract, 9/1/04-8/31/09; as well as prior support from NIH/NCRR P41 RR01243 Simulation Resource in Circulatory Mass Transport and Exchange, 12/1/1980-11/30/01 and NIH/NIBIB R01 EB001973 JSim: A Simulation Analysis Platform, 3/1/02-2/28/07.