## Course Meeting Times

Lectures: 3 sessions / week, 1 hour / session

Tutorials (optional): 1 session / week, 1 hour / session

This page includes a course calendar.

## Course Objectives

This course develops and applies scaling laws and the methods of continuum mechanics to biomechanical phenomena over a range of length scales, from molecular to cellular to tissue or organ level. It is intended for undergraduate students who have taken a course in differential equations (18.03), an introductory course in molecular biology, and a course in transport, fluid mechanics, or electrical phenomena in cells (e.g. 6.021, 2.005, or 20.320).

## Topic Outline

### Part I: Mechanical Driving Forces

- Conservation of momentum
- Inviscid and viscous flows
- Convective transport
- Dimensional analysis

### Part II: Electrical Driving Forces

- Maxwell's equations
- Ion transport
- E and B field in biological systems
- Electroquasistatics
- Poisson's and Laplace's equation

### Part III: Chemical Driving Forces

- Conservation of mass
- Diffusion
- Steady and unsteady diffusion
- Diffusion with chemical reactions

### Part IV: Electrokinetics

- Debye layer
- Zeta potential
- Electroosmosis
- Electrophoresis
- Application of electrokinetics
- Dielectrophoresis
- Debye layer repulsion forces

## Textbooks and Reference Materials

### Required Text (to purchase)

Truskey, G. A., F. Yuan, and D. F. Katz. *Transport Phenomena in Biological Systems*. East Rutherford, NJ: Prentice Hall, 2003. ISBN: 9780130422040.

### Additional Texts with Assigned Readings (not required to purchase)

Haus, H. A., and J. R. Melcher. *Electromagnetic Fields and Energy*. Upper Saddle River, NJ: Prentice Hall, 1989. ISBN: 9780132490207. (A free online textbook.)

Probstein, R. F. *Physicochemical Hydrodynamics: An Introduction*. New York, NY: Wiley-Interscience, 2003. ISBN: 9780471458302.

Jones, T. B. *Electromechanics of Particles*. 2nd ed. New York, NY: Cambridge University Press, 2005. ISBN: 9780521019101.

### Other Useful References

Bird, R. B., E. N. Lightfoot, and W. E. Stewart. *Transport Phenomena*. New York, NY: Wiley, 2006. ISBN: 9780470115398.

Weiss, T. F. *Cellular Biophysics - Volume 1: Transport*. Cambridge, MA: MIT Press, 1996. ISBN: 9780262231831.

Morgan, H., and H. Green. *AC Electrokinetics: Colloids and Nanoparticles*. Baldock, UK: Research Studies Press, 2002. ISBN: 9780863802553.

Hiemenz, P. C., and R. Rajagopalan. *Principles of Colloid and Surface Chemistry*. New York, NY: Marcel Dekker, 1997. ISBN: 9780824793975.

Dill, K., and S. Bromberg. *Molecular Driving Forces*. New York: Garland Press, 2002. ISBN: 9780815320517.

## Class Structure

20.330/2.793/6.023 will be taught in lecture format (3 hours/week), but with liberal use of class examples to link the course material with various biological issues. Readings will be drawn from a variety of primary and text sources as indicated in the lecture schedule.

Optional tutorials will also be scheduled to review mathematical concepts and other tools (Comsol FEMLAB) needed in this course.

Weekly homework problem sets will be assigned each week to be handed in and graded.

Office hours by the TA will be scheduled to help you in exams and homeworks.

There will be two in-class midterm quizzes (1 hour long), and a comprehensive final exam (3 hours long) at the end of the term.

## Term Grade

The term grade will be a weighted average of exams, term paper and homework grades. The weighting distribution will be:

ACTIVITIES | PERCENTAGES |
---|---|

Two quizzes (20% each) | 40% |

A comprehensive final exam | 30% |

Homeworks | 30% |

## Homework

Homework is intended to show you how well you are progressing in learning the course material. You are encouraged to seek advice from TAs and collaborate with other students to work through homework problems. However, the work that is turned in must be your own. It is a good practice to note the collaborator in your work if there has been any.

Homework is due at the end of the lecture (11 am), on the stated due date. Solutions will be provided on-line after the due date and time.

We will not accept late homework for any reason. Instead, we will not use 2 lowest homework grades (out of 9 total) for the calculation of the term homework grade (30%). Students are encouraged to use this to their benefit, to accommodate special situations such as interview travel/illness.

## Midterm Quizzes and Final Exam

There are two in-class (1 hour) closed-book midterm quizzes scheduled for the term. Please note the schedule for the exam dates. There will also be a closed-book, three-hour-long, comprehensive final exam during the finals week. The final exam will cover the whole course content.

Exam problems will be similar (in terms of difficulty) to homework problems, and if one can work all the homework problems without looking at notes one should be able to solve the exam problems as well.

Make-up exams will only be allowed for excused absence (by Dean's office) and if arranged at least 2 weeks in advance. Students must sign an honor statement to take a make-up exam. Exams missed due to an excused illness and other reasons excusable by Dean's office will be dropped and the term grade will be calculated based on the remaining exams and homework.

## Calendar

The table below provides information on the course's lecture (L) and tutorials (T) sessions.

SES # | TOPICS | DETAILS |
---|---|---|

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

L1 |
Introduction to the course Fluid 1: Introduction to fluid flow |
Logistics Introduction to the course Importance of being "multilingual" Complexity of fluid properties |

T1 | Curl and divergence | |

L2 | Fluid 2: Drag forces and viscosity |
Fluid drag Coefficient of viscosity Newton's law of viscosity Molecular basis for viscosity Fluid rheology |

L3 | Fluid 3: Conservation of momentum |
Fluid kinematics Acceleration of a fluid particle Constitutive laws (mass and momentum conservation) |

L4 | Fluid 4: Conservation of momentum (example) |
Acceleration of a fluid particle Forces on a fluid particle Force balances |

L5 | Fluid 5: Navier-Stokes equation |
Inertial effects The Navier-Stokes equation |

L6 | Fluid 6: Flows with viscous and inertial effects |
Flow regimes The Reynolds number, scaling analysis |

L7 | Fluid 7: Viscous-dominated flows, internal flows |
Unidirectional flow Pressure driven flow (Poiseuille) |

L8 | Fluid 8: External viscous flows |
Bernoulli's equation Stream function |

L9 | Fluid 9: Porous media, poroelasticity |
Viscous flow Stoke's equation |

L10 | Fluid 10: Cellular fluid mechanics (guest lecture by Prof. Roger Kamm) | How cells sense fluid flow |

Part 2: Fields (Instructor: Prof. Jongyoon Han) |
||

L11 | Field 1: Introduction to EM theory |
Why is it important? Electric and magnetic fields for biological systems (examples) EM field for biomedical systems (examples) |

L12 | Field 2: Maxwell's equations |
Integral form of Maxwell's equations Differential form of Maxwell's equations Lorentz force law Governing equations |

L13 | Quiz 1 | |

L14 | Field 3: EM field for biosystems |
Quasi-electrostatic approximation Order of magnitude of B field Justification of EQS approximation Quasielectrostatics Poisson's equation |

L15 | Field 4: EM field in aqueous media |
Dielectric constant Magnetic permeability Ion transport (Nernst-Planck equations) Charge relaxation in aqueous media |

L16 | Field 5: Debye layer |
Solving 1D Poisson's equation Derivation of Debye length Significance of Debye length Electroneutrality and charge relaxation |

T2 | FEMLAB Demo | |

L17 | Field 6: Quasielectrostatics 2 |
Poisson's and Laplace's equations Potential function Potential field of monopoles and dipoles Poisson-Boltzmann equation |

L18 | Field 7: Laplace's equation 1 |
Laplace's equation Uniqueness of the solution Laplace's equation in rectangular coordinate (electrophoresis example) will rely on separation of variables |

L19 | Field 8: Laplace's equation 2 | Laplace's equation in other coordinates (solving examples using MATLAB®) |

L20 | Field 9: Laplace's equation 3 | Laplace's equation in spherical coordinate (example 7.9.3) |

Part 3: Transport (Instructor: Prof. Scott Manalis) |
||

L21 | Transport 1 |
Diffusion Stokes-Einstein equation |

L22 | Transport 2 | Diffusion based analysis of DNA binding proteins |

L23 | Transport 3 |
Diffusional flux Fourier, Fick and Newton Steady-state diffusion Concentration gradients |

L24 | Transport 4 |
Steady-state diffusion (cont.) Diffusion-limited reactions Binding assays Receptor ligand models Unsteady diffusion equation |

L25 | Transport 5 |
Unsteady diffusion in 1D Equilibration times Diffusion lengths Use of similarity variables |

L26 | Transport 6 | Electrical analogy to understanding cell surface binding |

L27 | Quiz 2 | |

L28 | Transport 7 |
Convection-diffusion equation Relative importance of convection and diffusion The Peclet number Solute/solvent transport Generalization to 3D |

L29 | Transport 8 |
Guest lecture: Prof. Kamm Transendothelial exchange |

L30 | Transport 9 |
Solving the convection-diffusion equation in flow channels Measuring rate constants |

Part 4: Electrokinetics (Instructor: Prof. Jongyoon Han) |
||

L31 | EK1: Electrokinetic phenomena |
Debye layer (revisit) Zeta potential Electrokinetic phenomena |

L32 | EK2: Electroosmosis 1 |
Electroosmotic flow Electroosmotic mobility (derivation) |

L33 | EK3: Electroosmosis 2 |
Characteristics of electroosmotic flow Applications of electroosmotic flow |

L34 | EK4: Electrophoresis 1 |
Electrophoretic mobility Theory of electrophoresis |

L35 | EK5: Electrophoresis 2 |
Electrophoretic mobility of various biomolecules Molecular sieving |

L36 | EK6: Dielectrophoresis |
Induced dipole (from part 2) C-M factor Dielectrophoretic manipulation of cells |

L37 | EK7: DLVO |
Problem of colloid stability Inter-Debye-layer interaction |

L38 | EK8: Forces |
Van der Waals forces Colloid stability theory |

L39 | EK9: Forces | Summary of the course/evaluation |

3 hour final exam (comprehensive of the course) during the finals week |