Chapter 5 Lecture

Biological PhysicsNelson

Updated 1st Edition

Slide 1-1

Life in the slow lane (part I):Low Reynolds number?

Slide 1-3

Announcement

• Midterm presentation for this Chapter (5)

– However, here are my slides for your

reference

• Remember a ten minute talk on one/two of the

subsections in this chapter

– Good Luck!

Slide 1-4

Chapter 4:- Summary

Slide 1-5

Chapter 4 Homework

• Read Section 4.6.5 and do “Your Turn 4G”

– Also “Your Turn 4F” on bacterium

• Solution of diffusion equation is a Gaussian

profile (Gaussians again)

– In 1D the solution is

– In 3D follow “Your Turn 4G” or do 1D case.

• Homework question 4.7:- “Vascular Design”

Slide 1-6

Outline ( part I)

• 5.1 Friction in fluids

– Bouyancy etc.

• 5.2 Low Reynolds number

– Time reversal symmetry

• 5.3 Biological applications (next week)

• 5.4 Excursion: Characteristics of physical laws

(extra reading)

Slide 1-7

• Remember vdrift = f/ζ but now consider the

amount of fluid displaced in order to move down

• Change in PEV is then

where the net force is

and we define mnet=m-Vρm

• From

this implies the sedimentation rate in equilibrium:

• If x*:=kBT/(mnetg) then x*~59m for Myoglobin then

for a 4 cm test tube c(x)=c(0)e-0.04/59~c(x)

5.1.1 Friction in fluids

Slide 1-8

Colloidal suspensions

• The particle don’t separate out and is is known

as a colloid. If mnetgh is big enough like e.g.,

sand it will settle out

• Try your turn 5A for milk

• Your turn 5B: Generalize Nernst like relation to

centripetal forces.

• This gives us Fick’s law for separation:

• Implying sedimentation rate in centrfuge:

Slide 1-9

5.1.2 Sedimentation rate?

• What about the time scale?

But Stoke’s formula and buoyancy

leads to:

• Assuming a polymer displaces water ~ mp then

s ~ mp-1 see Fig. 4.7 in book (next slide)

Slide 1-10

Polymer diffusion

Slide 1-11

5.1.3 It’s hard to mix a viscous fluid

• It’s very hard to mix the marked blob into the

bulk.

• The marked blob actually seems to take evasive

action when the stirring rod approaches.

• In the clockwise-counterclockwise experiment,

the blob will smear out in the first step. But if

you’re careful in the second step to retrace the

first step exactly, you’ll see the blob magically

reassemble itself into nearly its original position

and shape! That’s not what happens when you

stir cream into your coffee.

• Difference is Laminar or Turbulent Flow

Slide 1-12©1972, MIT Press. Used by permission.

Looks like magic?

No violation of 2nd Law! Diffusion time is just VERY slow

Slide 1-13

More details

Slide 1-14

5.2 .1 Critical force?

• A critical force demarcates the region between

laminar and turbulent flow (see Fig. 5.2b above):

• Constant of proportionality η is called the

viscosity and is dimensionful [η]= Pa・s-1

Slide 1-15

Viscous critical force

• Based on the dimensionality of η it turns out that

• Equivalently:

– a. There’s no dimensionless measure of

viscosity, and hence no intrinsic distinction

between “thick” and “thin” fluids, but. . .

– b. Still there is a situation-dependent

characterization of when a fluid’s motion will

be viscous, namely when the dimensionless

ratio f/fcrit is small.

Slide 1-16©1968. Used by permission of Elsevier Science.

5.2.2 Reynold’s number

Slide 1-17

Reynolds number

• Derivation on whiteboard (to be added later) ...

Slide 1-18

Homework

• Please

– Read 5.2.3 (time reversal asymmetry) &

Excursion 5.4:- “Physical Laws”

– Finish Your Turn 5e

– Do Problem 5.4

• Next week

– Section 5.3:- Biological applications

Slide 1-19

Next week: Part II (Bio applications)