20.330J | Spring 2007 | Undergraduate

Fields, Forces and Flows in Biological Systems

Lecture Notes

The following table presents slides for selected lectures in Parts 2 and 4, plus an introductory lecture in Part 1. Table entries for Parts 1 and 3 are retained, even though no lecture notes are available, to present the overall flow of topics during the term.

Part 1: Fluids (Instructor: Prof. Scott Manalis)

Introduction to the course

Fluid 1: Introduction to fluid flow (PDF)


Introduction to the course

Importance of being “multilingual”

Complexity of fluid properties

2 Fluid 2: Drag forces and viscosity

Fluid drag

Coefficient of viscosity

Newton’s law of viscosity

Molecular basis for viscosity

Fluid rheology

3 Fluid 3: Conservation of momentum

Fluid kinematics

Acceleration of a fluid particle

Constitutive laws (mass and momentum conservation)

4 Fluid 4: Conservation of momentum (example)

Acceleration of a fluid particle

Forces on a fluid particle

Force balances

5 Fluid 5: Navier-Stokes equation

Inertial effects

The Navier-Stokes equation

6 Fluid 6: Flows with viscous and inertial effects

Flow regimes

The Reynolds number, scaling analysis

7 Fluid 7: Viscous-dominated flows, internal flows

Unidirectional flow

Pressure driven flow (Poiseuille)

8 Fluid 8: External viscous flows

Bernoulli’s equation

Stream function

9 Fluid 9: Porous media, poroelasticity

Viscous flow

Stoke’s equation

10 Fluid 10: Cellular fluid mechanics (guest lecture by Prof. Roger Kamm) How cells sense fluid flow
Part 2: Fields (Instructor: Prof. Jongyoon Han)
11 Field 1: Introduction to EM theory (PDF)

Why is it important?

Electric and magnetic fields for biological systems (examples)

EM field for biomedical systems (examples)

12 Field 2: Maxwell’s equations (PDF)

Integral form of Maxwell’s equations

Differential form of Maxwell’s equations

Lorentz force law

Governing equations

13 Quiz 1  
14 Field 3: EM field for biosystems (PDF)

Quasi-electrostatic approximation

Order of magnitude of B field

Justification of EQS approximation


Poisson’s equation

15 Field 4: EM field in aqueous media (PDF)

Dielectric constant

Magnetic permeability

Ion transport (Nernst-Planck equations)

Charge relaxation in aqueous media

16 Field 5: Debye layer (PDF)

Solving 1D Poisson’s equation

Derivation of Debye length

Significance of Debye length

Electroneutrality and charge relaxation

17 Field 6: Quasielectrostatics 2 (PDF)

Poisson’s and Laplace’s equations

Potential function

Potential field of monopoles and dipoles

Poisson-Boltzmann equation

18 Field 7: Laplace’s equation 1 (PDF)

Laplace’s equation

Uniqueness of the solution

Laplace’s equation in rectangular coordinate (electrophoresis example) will rely on separation of variables

19 Field 8: Laplace’s equation 2 (PDF) Laplace’s equation in other coordinates (solving examples using MATLAB®)
20 Field 9: Laplace’s equation 3 (PDF) Laplace’s equation in spherical coordinate (example 7.9.3)
Part 3: Transport (Instructor: Prof. Scott Manalis)
21 Transport 1


Stokes-Einstein equation

22 Transport 2 Diffusion based analysis of DNA binding proteins
23 Transport 3

Diffusional flux

Fourier, Fick and Newton

Steady-state diffusion

Concentration gradients

24 Transport 4

Steady-state diffusion (cont.)

Diffusion-limited reactions

Binding assays

Receptor ligand models

Unsteady diffusion equation

25 Transport 5

Unsteady diffusion in 1D

Equilibration times

Diffusion lengths

Use of similarity variables

26 Transport 6 Electrical analogy to understanding cell surface binding
27 Quiz 2  
28 Transport 7

Convection-diffusion equation

Relative importance of convection and diffusion

The Peclet number

Solute/solvent transport

Generalization to 3D

29 Transport 8

Guest lecture: Prof. Kamm

Transendothelial exchange

30 Transport 9

Solving the convection-diffusion equation in flow channels

Measuring rate constants

Part 4: Electrokinetics (Instructor: Prof. Jongyoon Han)
31 EK1: Electrokinetic phenomena

Debye layer (revisit)

Zeta potential

Electrokinetic phenomena

32 EK2: Electroosmosis 1 (PDF)

Electroosmotic flow

Electroosmotic mobility (derivation)

33 EK3: Electroosmosis 2 (PDF)

Characteristics of electroosmotic flow

Applications of electroosmotic flow

34 EK4: Electrophoresis 1

Electrophoretic mobility

Theory of electrophoresis

35 EK5: Electrophoresis 2 (PDF)

Electrophoretic mobility of various biomolecules

Molecular sieving

36 EK6: Dielectrophoresis (PDF)

Induced dipole (from part 2)

C-M factor

Dielectrophoretic manipulation of cells

37 EK7: DLVO (PDF)

Problem of colloid stability

Inter-Debye-layer interaction

38 EK8: Forces

Van der Waals forces

Colloid stability theory

39 EK9: Forces Summary of the course/evaluation