MIT OpenCourseWare

Browse materialsMIT 20.430J · Fall 2015

Fields, Forces, and Flows in Biological Systems

Subjects: Biology · Engineering · Mechanical Engineering

Art: PSM V09 D115 Pasteur apparatus for germ studies, 1876 · Public domain

Instructors: Prof. Mark Bathe, Prof. Alan Grodzinsky
Term: Fall 2015
Level: Graduate
What's inside: 8 problem sets · 1 solution · 1 reading · 24 other files · 5 web pages
Materials open: MIT OCW

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About this course

Source: MIT OpenCourseWare 20.430J Fields, Forces, and Flows in Biological Systems, Fall 2015, Prof. Mark Bathe, Prof. Alan Grodzinsky — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.

Materials are grouped the way MIT organized them. A verified, course-wide order has not been established here.

Before you start

Prerequisites are not listed here. Check MIT's own syllabus for this course.

How this course was organized

What's here, and what isn't

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MIT's page format for this item wasn't recognized clearly enough to place it safely. (8 items)
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Materials by section

Grouped by section, as MIT organized them. Not sequenced or ordered.

Lecture Slides

25 files

Assignments

8 problem sets

MIT OpenCourseWare, Prof. Mark Bathe, Prof. Alan Grodzinsky, 20.430J Fields, Forces, and Flows in Biological Systems, Fall 2015.

License: CC BY-NC-SA 4.0 · Edition: Fall 2015 · Open the original course on OCW ↗

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Fields, Forces, and Flows in Biological Systems

Before you start

What's here, and what isn't

Not included here

Materials by section

Lecture Slides

Assignments

Lecture 1: Course introduction, overview, and objectives (PDF - 2.5MB)

Lecture 2: Introduction to random processes; Boltzmann distribution and statistical thermodynamics (PDF - 1.3MB)

Lecture 3: Diffusion as a random walk; Stokes-Einstein relation for diffusion coefficient (PDF - 1.5MB)

Lecture 4: Constitutive equations for diffusion (Fick’s Laws); Conservation of mass for a control volume; Differential form; Steady diffusion (1D); Boundary conditions (PDF)

Lecture 5: Diffusion and reaction; Reaction rates, order, molecularity and mechanisms; Scaling and the Damköhler number; Solution procedures (Lecture slides are not available)

Lecture 6: Examples of diffusion-reaction: Diffusion of a ligand through tissue with cell receptor-ligand interactions; Diffusion-reaction kinetics (PDF)

Lecture 7: Case study: IGF-1 diffusion-reaction within tissues and cell seeded scaffolds; binding to IGF binding proteins & cell surface receptors; experimental methods (PDF - 1.9MB)

Lecture 8: E-fields and transport; Maxwell’s equations (PDF - 1.2MB)

Lecture 9: Define electrical potential; conservation of charge; Electro-quasistatics (PDF - 6.5MB)

Lecture 10: Laplacian solutions via Separation of Variables; Electric field boundary conditions; Ohmic transport; Charge Relaxation; Electrical migration vs. chemical diffusive fluxes (PDF - 2.2MB)

Lecture 11: Electrochemical coupling; Electrical double layers; Poisson–Boltzmann Equation (PDF - 2.5MB)

Lecture 12: Donnan equilibrium in tissues, gels, polyelectrolyte networks (PDF - 2.0MB)

Lecture 13: Charge group ionization & electro-diffusion-reaction in molecular networks (PDF - 1.7MB)

Lecture 14: Case study: Charged protein transport in charged tissues & gels; Donnan partitioning, diffusion-reaction in extracellular matrix; experimental methods (PDF - 2.2MB)

Lecture 15: Conservation of mass and momentum in fluids; convective solute transfer (PDF - 2.7MB)

Lecture 16: Viscous stress-strain rate relations; Navier–Stokes equations (PDF - 1.5MB)

Lecture 17: Low Reynolds number flows; Stokes equation; Scaling and dimensional analysis (PDF - 1.3MB)

Lecture 18: Newtonian, fully developed low Reynolds number flows (PDF)

Lecture 19: Diffusion and convection; The Peclet number; Convection-diffusion-reaction and boundary layers (PDF - 2.6MB)

Lecture 20: Concentration boundary layers: Fully-developed flow and transport (PDF)

Lecture 21: Capillary electroosmosis: Theory and experiments (PDF - 1.8MB)

Lecture 22: MEMs, microfluidics + electrokinetics, cells and hydrogels; (with guest lecture) (PDF - 1.5MB)

Lecture 23: Electrophoresis, chromatography and extracellular matrix biochemistry (PDF - 2.6MB)

Lecture 24: DLVO theory: Double layer repulsion and molecular interactions (proteins, DNA, GAGs) (PDF - 1.3MB)

Lecture 25: Porous media flows: Extracellular and intracellular (PDF - 2.1MB)

Lecture 26: Cell / molecular electrokinetics; review of term paper project (PDF - 2.3MB)