Heat and Mass Lecture 1
Transcript of Heat and Mass Lecture 1
Heat and Mass Transfer II BE2-HHMT2
Winter Term 2010/11
Dr. Darryl R. Overby Lecturer, Dept. of Bioengineering
Office: RSM 4.33
Dr. Jennifer Siggers (Mass Transport) Dr. Danny O’Hare (Chemical Kinetics)
BE2-HHMT2, Heat&Mass Transfer II D.R. Overby, Revised Jan-17-11
Heat and Mass Transfer II (aka. Transport Phenomena)
BE2-HHMT2, Heat&Mass Transfer II D.R. Overby, Revised Jan-17-11
Heat and Mass Transfer II (aka. Transport Phenomena)
BE2-HHMT2, Heat&Mass Transfer II D.R. Overby, Revised Jan-17-11
BE2-HHMT2, Heat&Mass Transfer II D.R. Overby, Revised Jan-17-11
5-10 hrs
Heat and Mass Transfer II (aka. Transport Phenomena)
Heat and Mass Transfer II (aka. Transport Phenomena)
BE2-HHMT2, Heat&Mass Transfer II D.R. Overby, Revised Jan-17-11
BE2-HHMT2, Heat&Mass Transfer II D.R. Overby, Revised Jan-17-11
Schedule of Events:
Lectures: Mondays 11:00, RSM 2.28 Fridays 16:00, RSM 2.28
Tutorials: Mondays 09:00, RSM 3.21C, 3.03, 4.01 (starting Jan 24, 2011)
Office Hours: Wednesdays 12:00 – 14:00, RSM 4.33 or by appointment
Examination: TBA
Heat and Mass Transfer II (aka. Transport Phenomena)
Lecture 1: Introduction and Basic Definitions Lecture Objectives: 1. To define transport phenomena and give examples where
transport processes are important for the function of biological systems.
2. To describe the two fundamental processes of mass transport: convection and diffusion.
3. To describe the engineering definition of a fluid and its properties, the continuum assumption and the engineering concept of stress.
Reading: Truskey §1.1-1.3, 2.3.3 (1.4-1.8, extra)
BE2-HHMT2, Heat&Mass Transfer II D.R. Overby, Revised Dec-28-10
What is “Transport Phenomena”?
BE2-HHMT2, Heat&Mass Transfer II D.R. Overby, Revised Dec-28-10
• An engineering science that deals with the motion of mass, momentum and/or energy through a medium.
• Transport phenomena is often defined by sub-fields:
• momentum transport –how fluid flows in response to applied forces. (similar to fluid mechanics)
• mass transport – how chemical species move through a solid, liquid or gaseous medium.
• heat transport – how energy (including heat) moves through a solid, liquid or gaseous medium.
• There are links between the transport of heat, mass and momentum.
What are Transport Phenomena important for biology?
BE2-HHMT2, Heat&Mass Transfer II D.R. Overby, Revised Dec-28-10
- Homeostasis and normal physiological function requires substances to be in the right places in the body at the right concentrations.
- Knowledge of transport phenomena is essential for: - understanding physiology and mechanisms of disease - design and operation of medical devices - development of new therapies (e.g., drug delivery or molecular medicine)
- Let’s look at a few examples. (see Truskey §1.4-1.8).
Example 1: Calcium Transport Within the Cell
BE2-HHMT2, Heat&Mass Transfer II D.R. Overby, Revised Jan-16-11
Calcium is an important signalling molecule, and it’s concentration is tightly regulated in the cell.
Lodish et al., 2000 (fig 18-29).
Contraction in skeletal muscle cells
Alberts et al., 2002 (fig 16-69).
http://biology.kenyon.edu/courses/biol105/html/calcium2.jpg
Example 2: Low-Density Lipoprotein
BE2-HHMT2, Heat&Mass Transfer II D.R. Overby, Revised Dec-28-10
LDL is a large molecular complex that transports cholesterol from the liver to tissues throughout the body.
Rose and Afanasyeva, Nat Med, 2003
Hahn and Schwartz, Nature 2009 (Fig1)
Example 3: Gas Transport in the Lungs
BE2-HHMT2, Heat&Mass Transfer II D.R. Overby, Revised Dec-28-10
The primary job of the lungs is to exchange oxygen and carbon dioxide with the blood.
Weibel, 1984
Sapoval et al., 2002
Weibel, 1973
Fundamental Transport Processes
BE2-HHMT2, Heat&Mass Transfer II D.R. Overby, Revised Dec-28-10
There are 2 fundamental processes at play in transport phenomena
Diffusion – arises from random motion and collision between molecules.
Convection – transport due to bulk motion of a fluid medium.
Additional Definitions:
Solute – the species of interest that is being transported through the medium
Solvent – the medium itself, typically water for biological applications. Usually (but not always!) solvent molecules outnumber solute.
Solution – mixture of solute + solvent
Diffusion
BE2-HHMT2, Heat&Mass Transfer II D.R. Overby, Revised Dec-28-10
Hyperlinks: http://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/brownian/brownian.html
Generated using Lattice Random Walk in 3D in Mathematica by Stephen Wolfram
• Diffusion time:
€
td ∝L2
DL -- distance molecule diffuses [cm] D -- Diffusivity [cm2/sec]
http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/UVaBrownianDemo.mpg
• Attributed to Brownian motion (after Robert Brown, 1827)
• Arises from random collisions or “random walk”
• Efficient over very small distances (<~ 100 µm)
Typical Values of Diffusivity
BE2-HHMT2, Heat&Mass Transfer II D.R. Overby, Revised Dec-28-10
Diffusing Quantity Diffusion Coefficient* [cm2/sec] Gases in gases 0.1 – 0.5 Gases in liquids 1x10-7 – 7x10-5
Small molecules in liquids 1x10-5
Proteins in liquids 1x10-7 – 7x10-7
Proteins in tissues 1x10-7 – 7x10-10
Lipids in lipid membranes 1x10-9
Proteins in lipid membranes 1x10-10 – 1x10-12
Truskey, Table 1.1
* binary diffusion coefficient at room temperature
Convection
BE2-HHMT2, Heat&Mass Transfer II D.R. Overby, Revised Jan-17-11
• Arises from bulk flow of solvent.
• Solute is transported with same local velocity as solvent.
• Efficient over very large distances (>~ 100 µm).
• Convection time:
L -- distance molecule is convected [cm] V – local solvent velocity [cm/sec]
€
tc ∝LV
Quiz
BE2-HHMT2, Heat&Mass Transfer II D.R. Overby, Revised Dec-28-10
• Consider the transport of oxygen (O2) through the body by convection and diffusion.
• Calculate the time for O2 transport over a distance equal to one cell (10 µm) and over a distance equal to the thickness of tissue (1 mm).
• Make the following assumptions: • D = 2x10-5 cm2/sec for O2 • V = 100 µm/sec, corresponding to the capillary blood velocity
O2 Transport Time L = 10 µm L = 1 mm
Diffusion
Convection
Quiz
BE2-HHMT2, Heat&Mass Transfer II D.R. Overby, Revised Dec-28-10
• Consider the transport of oxygen (O2) through the body by convection and diffusion.
• Calculate the time for O2 transport over a distance equal to one cell (10 µm) and over a distance equal to the thickness of tissue (1 mm).
• Make the following assumptions: • D = 2x10-5 cm2/sec for O2 • V = 100 µm/sec, corresponding to the capillary blood velocity
O2 Transport Time L = 10 µm L = 1 mm
Diffusion 0.05 sec 500 sec
Convection 0.1 sec 10 sec
Diffusion Faster
Convection Faster
Peclet Number (Pe)
BE2-HHMT2, Heat&Mass Transfer II D.R. Overby, Revised Dec-28-10
• Used to weigh the relative contribution of convection to diffusion.
• Defined as a ratio of diffusion time to convection time.
• If Pe >> 1, convection is faster, and convection dominates transport. • If Pe << 1, diffusion is faster, and diffusion dominates transport. • If Pe ~ 1, diffusion and convection are both important.
• Pe is a dimensionless number, and like other dimensionless numbers (e.g., Reynold’s number) it weighs the relative importance of different physical phenomena (e.g., inertial vs. viscous forces).
€
diffusion timeconvection time
≡td
tc
=L2
DVL
=V LD
≡Pe
Fluid Properties: Stress
BE2-HHMT2, Heat&Mass Transfer II D.R. Overby, Revised Dec-28-10
€
σ =
σ xx σ xy σ xz
σ yx σ yy σ yz
σ zx σ zy σ zz
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
σyx
x
y
σyy
σxy
σxx
σxx
σyy
σxy
σyx
• Stress is force per unit area. Units: N/m2, Pa, dynes/cm2 • Depends on 2 vectors: force and surface orientation • Stress is a tensor of order 2.
- Often written as σij
i -- direction of orientation vector (x,y,z) j -- direction of force vector
i=j for a normal stress i≠j for a shear stress
Stress tensor is symmetric σij = σji
Fluid Properties: Definition of a Fluid
BE2-HHMT2, Heat&Mass Transfer II D.R. Overby, Revised Dec-28-10
• Any substance that deforms continually under shear stress. • Gasses and liquids are usually fluids. • Corollary: Shear stress must be zero in a fluid at rest.
• Some substances exhibit both fluid-like and solid-like behaviour (viscoelastic)
Upper plate moves, then stops. Upper plate continually moves.
Fluid Properties: Density, Viscosity
BE2-HHMT2, Heat&Mass Transfer II D.R. Overby, Revised Dec-28-10
Property Symbol Description Units
Density ρ Mass per unit volume g/cm3
Viscosity (Dynamic viscosity) µ Resistance to flow under shear g/(cm sec)
Kinematic viscosity ν = µ/ρ “Diffusivity” of momentum cm2/sec
Typical values of fluid parameters given in Truskey Table 1.2
The Continuum Concept
BE2-HHMT2, Heat&Mass Transfer II D.R. Overby, Revised Dec-28-10
€
ρ = limΔV→0
Δ massΔV
• Analysis requires that we define fluid properties at a point.
• As ∆V 0, eventually molecular variations dominate.
• Chose some δV that is much larger than molecules, but much smaller than dimensions of interest (L).
€
δV << L
For continuum assumption to hold,
Extensive vs. Intensive Properties
BE2-HHMT2, Heat&Mass Transfer II D.R. Overby, Revised Jan-17-11
Extensive property (or extrinsic property) • Depends on the size or amount of material contained in system • Cannot be defined at a point • Examples: mass, volume
Intensive property (or intrinsic property) • Independent of size or amount of material • Can be defined at each point • Examples: density, concentration
Integrating an intensive property over space translates an intensive property into an extensive property.
Note, defining intensive properties implicitly assumes that the continuum assumption is valid (otherwise, properties will fluctuate wildly!)
Lecture 1: Introduction and Basic Definitions Lecture Objectives: 1. To define transport phenomena and give examples where
transport processes are important for the function of biological systems.
2. To describe the two fundamental processes of mass transport: convection and diffusion.
3. To describe the engineering definition of a fluid and its properties, the continuum assumption and the engineering concept of stress.
Reading: Truskey §1.1-1.3, 2.3.3 (1.4-1.8, extra)
BE2-HHMT2, Heat&Mass Transfer II D.R. Overby, Revised Dec-28-10