mage:ic:kinetics1 - Diffusion in 1D and 3D

By Michael L. Falk

Johns Hopkins University

Download (PDF)

Licensed according to this deed.

Published on


This module guides students through two analyses of diffusion problems using the COMSOL finite element software. Students are then asked to use what they have learned to guide the design of a drug delivery device.

Disciplinary Goals: Understand mass transport in 1D and 3D, effects of boundary conditions
Computational Goals: Correctly parameterize and set boundary conditions for a finite element model, analyze and interpret results, be aware of numerical error and the potential for inaccuracies in numerical results.

Learning Objectives
1.A well-posed mass transport problem requires specifying the diffusivity of the species, the intial value of the concentrations of the species and the boundary conditions.
2.Mass conservation requires that the time rate of change of a species in the absence of local sources and sinks is given by the difference between the flux into the region and the flux out of the region.
3.The geometry of a mass transport problem has an influence on the way one expresses the gradient in the problem. This has an effect on the rate of mass transport.


Michael Falk is a Professor in the departments of Materials Science and Engineering (MSE), Mechanical Engineering and Physics and Astronomy at Johns Hopkins University where he devises atomic scale computational methods for understanding non-equilibrium processes that govern deformation, failure, phase transitions and friction within and between materials. His education research focuses on integrating computation into the MSE undergraduate core curriculum. This has involved pioneering a flipped-classroom project-based intro computing course fully contextualized within the MSE discipline. In addition this work resulted in the integration of 12 computational modules into the 6 core lecture classes for MSE majors. Falk also serves as PI for STEM Achievement in Baltimore Elementary Schools (SABES) an NSF funded Community Enterprise for STEM Learning partnership between JHU and the Baltimore City Public Schools. He currently serves as advisor to JHU oSTEM (Out in Science, Technology, Engineering and Mathematics) and the JHU Diverse Sexuality and Gender Alliance.


created by Michael L. Falk

Sponsored by

These materials were developed in part with funding from the National Science Foundation under Grant No. EEC-1137006.


Research associated with this module can be found at: A.J. Magana, M.L. Falk, M. Reese, " Undergraduate Materials Science and Engineering Students' Experiences with Modeling and Simulation," Journal of Research in Science Teaching, (2014) under review. Additional research products are forthcoming.

Cite this work

Researchers should cite this work as follows:

  • Michael L. Falk (2014), "mage:ic:kinetics1 - Diffusion in 1D and 3D,"

    BibTex | EndNote


  1. diffusion
  2. kinetics of materials
  3. computational materials science
  4. finite element modeling