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Cardiac Physiome Society workshop: November 6-9, 2017 , Toronto

Diffusion1Dpde

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

Model number: 0330

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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).



Equations

Partial Differential Equation

$\large \frac{\partial C_p}{\partial t} = D_p \cdot \frac{\partial^2 C_p}{\partial x^2}$

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

no flux, boundary condition, tutorial

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Posted by: RCJ

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.