20.430J | Fall 2015 | Graduate
Fields, Forces, and Flows in Biological Systems

Lecture Slides

Lecturer Key

AG = Alan Grodzinsky
MB = Mark Bathe

1 Course introduction, overview, and objectives (PDF - 2.5MB) AG
I. Chemical Subsystem
2 Introduction to random processes; Boltzmann distribution and statistical thermodynamics (PDF - 1.3MB) MB
3 Diffusion as a random walk; Stokes-Einstein relation for diffusion coefficient (PDF - 1.5MB) MB
4 Constitutive equations for diffusion (Fick’s Laws); Conservation of mass for a control volume; Differential form; Steady diffusion (1D); Boundary conditions (PDF) MB
5 Diffusion and reaction; Reaction rates, order, molecularity and mechanisms; Scaling and the Damköhler number; Solution procedures (Lecture slides are not available) MB
6 Examples of diffusion-reaction: Diffusion of a ligand through tissue with cell receptor-ligand interactions; Diffusion-reaction kinetics (PDF) MB
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) AG
II. Electrical Subsystem
8 E-fields and transport; Maxwell’s equations (PDF - 1.2MB) AG
9 Define electrical potential; conservation of charge; Electro-quasistatics (PDF - 6.5MB) AG
10 Laplacian solutions via Separation of Variables; Electric field boundary conditions; Ohmic transport; Charge Relaxation; Electrical migration vs. chemical diffusive fluxes (PDF - 2.2MB) AG
11 Electrochemical coupling; Electrical double layers; Poisson–Boltzmann Equation (PDF - 2.5MB) AG
12 Donnan equilibrium in tissues, gels, polyelectrolyte networks (PDF - 2.0MB) AG
13 Charge group ionization & electro-diffusion-reaction in molecular networks (PDF - 1.7MB) AG
14 Case study: Charged protein transport in charged tissues & gels; Donnan partitioning, diffusion-reaction in extracellular matrix; experimental methods (PDF - 2.2MB) AG
III. Mechanical Subsystem
15 Conservation of mass and momentum in fluids; convective solute transfer (PDF - 2.7MB) MB
16 Viscous stress-strain rate relations; Navier–Stokes equations (PDF - 1.5MB) MB
17 Low Reynolds number flows; Stokes equation; Scaling and dimensional analysis (PDF - 1.3MB) MB
18 Newtonian, fully developed low Reynolds number flows (PDF) MB
19 Diffusion and convection; The Peclet number; Convection-diffusion-reaction and boundary layers (PDF - 2.6MB) MB
20 Concentration boundary layers: Fully-developed flow and transport (PDF) MB
IV. Integrative Case Studies: Physicochemical, Mechanical, & Electrical Interactions
21 Capillary electroosmosis: Theory and experiments (PDF - 1.8MB) AG
22 MEMs, microfluidics + electrokinetics, cells and hydrogels; (with guest lecture) (PDF - 1.5MB) AG
23 Electrophoresis, chromatography and extracellular matrix biochemistry (PDF - 2.6MB) AG
24 DLVO theory: Double layer repulsion and molecular interactions (proteins, DNA, GAGs) (PDF - 1.3MB) MB
25 Porous media flows: Extracellular and intracellular (PDF - 2.1MB) MB
26 Cell / molecular electrokinetics; review of term paper project (PDF - 2.3MB) AG