361Lec31 Fri, 28oct16 Sedimentation (of an object of mass ...
Transcript of 361Lec31 Fri, 28oct16 Sedimentation (of an object of mass ...
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 )
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
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
E = electric field in volts/metere = elementary chargeZ = charge in units of e
= 0, +1, -1, +2, -2, etc. 11