Introduction to Biofluiddynamics (Math 222)



Instructors: Professor Angela Cheer


Credits: 3 units


Meeting Schedule: Twice a week


Prerequisites: Math. Methods in Population Biology (PBG/ECL 231) and Computing Modelling in Neurobiology and Cell Physiology (NPB 245) or consent of the instructor.


Course Description


The course aims to establish a foundation for discussion and working relationships in the area of biofluiddynamics among the graduate students. The first half of the course is intented to illustrate that adaptation to fluid flow underlies much biological design and basic principles of fluid dynamics will be introduced by describing various phenomena which have been studied from a biofluids perspective. We hope to provide some intuition on the nature of the physical phenomena, discuss what has been done, and present what can be done. In this part of the course, there will be no derivation of equations. The second half of the course will be more rigorous where the equations of motion will be introduced. The ideas, fluid quantities and phenomena discussed in the first half of the quarter will, in the second half, be associated with algebraic and differential equations. The relationship between the equations and the physics discussed in the first half of the quarter will be emphasized.



Lecture Outline


Week 1
(a) Introduction, Dimension.
(b) Fundamental Concepts: Velocity Field, Stress Field, Viscosity.
(c) The Principle of Continuity, Streamlines, Pathlines and Streaklines.


Week 2
(a) Bernoulli's Principle.
(b) Drag, Scale and Reynolds number.
(c) The Biology of Drag, Shape of Drag, Drag in the Forest and Drag at the Seashore.
(d) Streamlining and Drag Coefficients, Shape and Drag of a Small insect.


Week 3
(a) The Boundary Layer on a Flat Surface, The Earth's Boundary Layer.
(b) Forces at and near Surfaces.
(c) Diffusion through Boundary Layers, The Mass of the Boundary Layer. (?) Movies?
(d) Tour of Professor's White's Laboratory.


Week 4
(a) Basic Rules for Laminar Flow, Basic Rules for Turbulent Flow.
(b) Manipulating the Velocity Profile.
(c) The Flow of Blood and Other Body Fluids.


Week 5
(a) The Origin of Lift, Biological Airfoils, Gliding, Soaring, Flapping and Thrust.
(b) Non steady effects.


End of the first half.


Week 6     Fluid Kinematics
(a) The Velocity Field: Eulerian and Lagrangian description, One-, Two- and Three- Dimensional Flow, Steady and Unsteady Flows, Streamlines, Streaklines and Pathlines.
(b) The Acceleration Field: The Material Derivative, Unsteady Effects, and Convective Effects.
(c) Tour of Professor J. Cech's laboratory.


Week 7
(a) Conservation of Mass - The Continuity Equations.
(b) Newton's Second Law.
(c) More Movies?



Week 8     Inviscid Flow
(a) Euler's Equation of Motion.
(b) Bernoulli's.
(c) Irrotational Flow.
(d) Velocity Potential.
(e) Guess Lectures: Computational Fluid Dynamics (Dwyer and Brown).
(f) Guess Lecture: Mogilner (Topic to be announced).


Week 9     Viscous Flow
(a) Stress-Deformation Relationships.
(b) Navier-Stokes Equations.


Week 10     Viscous Incompressible Flow
(a) Steady, laminar flow between fixed parallel planes.
(b) Couette Flow.
(c) Steady, Axial, Laminar Flow in Circular Tubes.
(d) Project Presentations.

References

(1) Life in Moving Fluids: the physical biology of flow (1989), S. Vogel, Princeton University Press.
(2) Life's Devices (1988), S. Vogel, Princeton University Press.
(3) Swimming and Flying in Nature (1975), Wu, Brokaw and Brennen, Plenum Press, New York.

(1) Munson, Young, and Okiishi. Fundamentals of Fluid Mechanics (1994). 2nd edition, Wiley.
(2) Allen and Ditsworth. Fluid Mechanics.
(3) Potter and Foss. Fluid Mechanics.
(4) White. Fluid Mechanics.
(5) Shames. Fluid Mechanics.


Syllabus updated 22 October 2001.