Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- 1 Problem solving
- 2 Conservation of mass and theReynolds transport theorem
- 3 Steady and unsteadyBernoulli equation and momentum conservation
- 4 Viscous flow
- 5 Momentum boundary layers
- 6 Piping systems, frictionfactors, and drag coefficients
- 7 Problems involving surface tension
- 8 Non-Newtonian blood flow
- 9 Dimensional analysis
- 10 Statistical mechanics
- 11 Steady diffusion and conduction
- 12 Unsteady diffusion and conduction
- 13 Convection of mass and heat
- 14 Concentration and thermal boundarylayers
- 15 Mass and heat transfer coefficients
- 16 Osmotic pressure
- Appendix A Material properties of fluids
- Appendix B Transport equations
- Appendix C Charts
- References
- Permissions
12 - Unsteady diffusion and conduction
(21 unsteady diffusion; 3 unsteady conduction)
Published online by Cambridge University Press: 18 December 2013
- Frontmatter
- Dedication
- Contents
- Preface
- 1 Problem solving
- 2 Conservation of mass and theReynolds transport theorem
- 3 Steady and unsteadyBernoulli equation and momentum conservation
- 4 Viscous flow
- 5 Momentum boundary layers
- 6 Piping systems, frictionfactors, and drag coefficients
- 7 Problems involving surface tension
- 8 Non-Newtonian blood flow
- 9 Dimensional analysis
- 10 Statistical mechanics
- 11 Steady diffusion and conduction
- 12 Unsteady diffusion and conduction
- 13 Convection of mass and heat
- 14 Concentration and thermal boundarylayers
- 15 Mass and heat transfer coefficients
- 16 Osmotic pressure
- Appendix A Material properties of fluids
- Appendix B Transport equations
- Appendix C Charts
- References
- Permissions
Summary
We want to determine how fast the alveolar CO2 concentration can change in response to changes in blood CO2 concentration. Assume a spherically shaped alveolus (of radius 0.015 cm) with a spatially uniform internal gaseous composition at time t = 0. Calculate the time necessary to achieve 95% equilibration when the CO2 concentration in the alveolar wall is suddenly changed at t = 0. You may neglect any mass-transfer effects of the wall tissue and the liquid film in the alveolus. The diffusion coefficient of CO2 in air is 0.14 cm2/s.
Considering your answer, how important is the diffusion resistance to mass transport through the gas contained within the alveolus?
Fluorescein is a small fluorescent tracer molecule that is used in a wide variety of physiologic studies. In the eye, it is used in a technique known as fluorophotometry to characterize the transport characteristics of aqueous humor, the fluid that fills the anterior chamber behind the cornea.
A drop of fluorescein (50 μl of 0.005%, by mass, fluorescein in saline) is placed onto the cornea and spreads evenly over the corneal surface to create a thin film. It then diffuses through the cornea (D = 1 × 10–6 cm2/s) and enters the aqueous humor on the back side of the cornea. The thickness of the cornea is about 0.05 cm and its radius is 0.5 cm.
- Type
- Chapter
- Information
- Problems for Biomedical Fluid Mechanics and Transport Phenomena , pp. 103 - 118Publisher: Cambridge University PressPrint publication year: 2013