Biomechanics of Continuum Media II (fluids)

Biomechanics of continuum media II (fluids) (257 - 15544)
Study: Bachelor in Biomedical Engineering
Semester 2/Spring Semester
2nd Year Course/Lower Division

*Please note that although this course is considered to be "Lower Division" (since it is a second-year course), it is extremely important to understand the course's prerequisites.

Students Are Expected to Have Completed:

Calculus I and II
Linear algebra
Differential equations
Biomechanics of continuum media I (solid mechanics)

Compentences and Skills that will be Acquired and Learning Results:

- The students must become familiar with the basic concepts of Fluid Mechanics: conservation laws, dimensional analysis, simplification of the general equations, etc.
- The students must become fluent in the usage of the mathematical tools commonly used in fluid mechanics: partial differential equations, usage of different coordinate systems, surface and volume integrals, complex variable, etc.

Description of Contents: Course Description

1.- Introduction to fluid mechanics
1.1. Solids, liquids and gases
1.2. The continuum hypothesis
1.3. Density, velocity and internal energy
1.4. Local thermodynamic equilibrium. Equations of state.
2.- Kinematics of the fluid flow
2.1. Eulerian and Lagrangian descriptions
2.2. Uniform flow. Steady flow. Stagnation points.
2.3. Trajectories. Paths. Streamlines.
2.4. Substantial derivative. Acceleration.
2.5. Circulation and vorticity. Irrotational flow. Velocity potential.
2.6. Stream function
2.7. Strain-rate tensor
2.8. Convective flux. Reynolds transport theorem.
3.- Conservation laws in fluid mechanics
3.1. Continuity equation in integral form
3.2. Volume and surface forces
3.3. Stress tensor. Navier-Poisson law
3.4. Forces and moments on submerged bodies.
3.5. Momentum equation in integral form. Angular momentum equation.
3.6. Heat conduction vector. Energy equation in integral form.
4.- The Navier-Stokes equations
4.1. Navier-Stokes equations.
4.2. Initial and boundary conditions.
4.3. Bernoulli¿s equation
5.- Dimensional analysis
5.1. Dimensional analysis. The Pi theorem.
5.2. Applications
5.3. Nondimensionalization of the Navier-Stokes equations
5.4. Dimensionless numbers in fluid mechanics
6.- Flow in ducts with biomedical applications: circulatory flow, flow in airways
6.1. Unidirectional flows
6.2. The Stoke's problem
6.3. Quasi-one-directional flow
6.4. Applications to flows of interest in biology

Learning Activities and Methodology:

Lectures: the main concepts of fluid mechanics are derived rigorously using physical and mathematical tools.
Seminars: the concepts derived in the lectures are used to solve problems. Also, new concepts are introduced through examples.
Homework: two homework covering different areas of Fluid Mechanics are given to the students.
Lab sessions: the students will become familiar with the usage of numerical (computational) and experimental tools to investigate a canonical flow of biomedical interest.

Assessment System:

1) Mid-term exam. It will cover approximately half the programme. If the grade is >= 5.0, the students do not need to take the exam on this part in the final (40% of the total grade)
2) Final exam. It will cover the second half of the programme. Additionally, the students will have another opportunity to pass the exam of the first half. A minimum grade of 5.0 in the final is required to pass the course (40% of the total grade)
3) Homework (10%). There are two homework that the students are expected to complete.
4) LAB SESSION (4): Semi-analytical/Numerical simulation of the flow in an artery. Experimental characterization of the flow using Particle Image Velocimetry (PIV). The lab report will be 10% of the final grade.

Basic Bibliography:

G.I. Barenblatt. Scaling. Cambridge University Press. 2003
G.K. Batchelor. An Introduction to Fluid Dynamics. Cambridge University Press. 2000
Landau L.D., Lifshitz E.M.. Fluid Mechanics. Pergamon Press. 1989
Y.C. Fung. Biomechanics: Mechanical Properties of Living Tissues, Second Edition. Springer; 2nd edition. 1993
Y.C. Fung. Biomechanics: Circulation. Springer; 2nd edition. 1996
Y.C. Fung. Biomechanics: Motion, Flow, Stress, and Growth. Springer. 1998