Sedimentation (of an object of mass m)terminal velocity =

u forcefrictional coef

Ff

mafterm= = =

.

a, the acceleration may be from any source such asgravity or centrifugal, and is controlled by the

experimenter.

but m and f are molecular propertiesuterm = (m/f) a = s a where s = sedimentation coefficent

s has the units of time i.e., seconds 1

361Lec31Fri, 28oct16

dividing by a, gives uterm/a = m/f = sTypical macromolecule has m = 10-19 g and f = 10-6 g/sso that s is often about 10-13 seconds = 1 Svedberg = 1 S

Buoyancy must be considered if the object is in solution;both the object and solvent feel the acceleration. If the

object is more dense than the solvent it displaces, it willsink and the solvent will rise. Force = (mobj – mass of fluid displaced by object) a

= (mobj – volume of object x density of fluid ) a

.in fluid theofdensity theis and

,lin object theof is vwhere

) v- (1m ] ))(v(m - [m F

fluid

obj

fluidobjfluidobjobjobj

fluidfluid

objobj

/mlg

/gm

ρ

ρρ

volumespecific partialthe

aa obj==

2

(∆G = ∆U is negative if the more dense object sinks )

3

4

.in fluid theofdensity theis and

,in object theof theis

but , terminalis where

279 p. (8.31) )1(m

A

B

3fluidfluid

obj3obj

/mlg

/gml

ρ

ρ

volumespecific partial

velocity

B

t

ABrott

v

vf

vav −=

Some Notation clarifications

5

Archimedes’ Principle in thermodynamics language

∆G = ∆H - T∆S = ∆U + ∆pV - T∆SBut ∆pV and T∆S are negligible for here, so

∆G = ∆U = ∆mgh = mfluid g ∆ hfluid + mfluid g ∆ hobject∆G is negative for spontaneous falling mass

The center of mass of the system will fall if it can in a gravitational field.

IF the object is more dense than fluid it will fall—which means the fluid will RISE.

IF the fluid is more dense than object it will fall—which means the object will RISE.

6

. viscosityis and,in fluid theofdensity theis and

,in object theof volumespecific partial theis where

281 p. (8.34) )1(

)1(s s

A

,20

,20w20,

ηρ

ρρ

ηη

3fluidfluid

obj3obj

/cmg

/gcmB

AB

wAB

w

v

vv−

−

=

s20,w means sedimentation coefficient at 20o C in pure waterD20,w means diffusion coefficient at 20o C in pure waterη20,w means viscosity at 20o C in pure water

1-

1211

1-1-2-213

B

B

mol kg 4003 )m1052.1)(0.161.01()(293K)K mol sm kg s)(8.3145106.82(M

D)1(M

=

××−×

=

−=

−−

−

s

vRTs

ABρ

Example 8.7 s20,w = 82.6 S; D20,w=1.52x10-11 m2s-1; vB=0.61 mL g-1

7

Molecular Weight by combining sedimentation and diffusion coefficients

D)1(M

.in fluid theofdensity theis and

,in object theof volumespecific partial theis

kg/mol,in Wt.Molecular theis M where

D)1(MD)1(m )1(m

B

A

B

BBB

AB

B

ABB

ABAB

vRTs

v

RTv

Tkvv

fs

ρ

ρ

ρρρ

−=

−=−=−=

3fluidfluid

obj3obj

/cmg

/gcm

8

9

1 poise = 1g x10-3 kg/g x (1 cm x 1x10-2 m/cm)-1s-1

= 0.1 kg m-1 s-1

fFuF

dA ==

η

In other words,the frictional coef.is viscosity xarea / distance

10

E = electric field in volts/metere = elementary chargeZ = charge in units of e

= 0, +1, -1, +2, -2, etc. 11

12

Previous Lecture: sedimentation s= terminal velocity/accelerations = uterm/a = mass/frictional coef.

=m/f = sedimentation coefficient

Today: electrophoresis µ= terminal velocity/electric fieldµ = uterm/E = charge/frictional coef.

=ze/f mobility