Drying of oil paint on a humid day
Edward Green
longer to dry on a humid day, all else being equal.
Is this so, and if so, why?
It certainly isn't predicted from a simplest level of theory: as ideal
gasses, the partial pressure of water and organic solvents in the air
should be entirely independent, hence the chemical potential
difference driving the evaporation of organic solvents should be
independent of humidity.
Do interactions in the gas phase modify the chemical potential of
other constituents of wet air? Does the presence of water vapor
modify the kinetics of evaporation (it has been suggested that an
evaporation impeding film form on the paint surface in humid air)? Is
the effect illusory, maybe based on the confounding effect of
temperature (wet days cooler), or on the softening adsorption of the
drying paint film by the adsorption of water?
Frank Martin
Maybe water vapour is a negative catalyst (this can also suppress
preignition in auto engines).
Maybe the solvent evaporates faster in wet air due to the azeotropic effect,
so stiffening the paint film prematurely.
"Edward Green" <null...@aol.com> wrote in message
news:2a0cceff.03072...@posting.google.com...
keith stein
I don't know the answers to any of these questions Mr. Green, and if
neither you nor i know the answers it's a fair bet no one else on
sci.physics knows for sure either eh!. Scope for some research here then.
Shouldn't be difficult to get someone to undertake this, after all WHAT
COULD BE MORE INTERESTING - than watching paint dry eh! :-)
keith stein
Magnus Nyborg
> longer to dry on a humid day, all else being equal.
>
> Is this so, and if so, why?
Possibly, the humid air tends to give off water to the liquid spirit which
complicates and slows down the evaporation of the spirit. At least this
makes sence...
Clear Skies,
Magnus
Ed Keane III
> longer to dry on a humid day, all else being equal.
>
> Is this so, and if so, why?
>
> It certainly isn't predicted from a simplest level
of theory:
Experience, intuition, and the simplest level of
theory? Oh my!
Here's another toughie: How does paint stick
after it dries? Both experience and intuition
would suggest that paint is no longer sticky
after it dries.
Steve Turner
>Experience and intuition suggest that even spirits based paint takes
>longer to dry on a humid day, all else being equal.
>
>Is this so, and if so, why?
I think the first question to answer would be whether this is indeed
true. My intuition agrees with yours, but intuition is often wrong.
If the RH is very near 100%, the evaporation of solvent from the paint
layer may cool it below the dew point, which would cause condensation
onto the layer. This would act to retard further evaporation by
reducing the available surface area.
Steve Turner
Real address contains worldnet instead of spamnet
Ken Muldrew
>Experience and intuition suggest that even spirits based paint takes
>longer to dry on a humid day, all else being equal.
>
>Is this so, and if so, why?
The "drying" of oil-based paint is mostly oxidation and cross-linking,
hastened by mettalic dryers added as a catalyst. Dissolved water
probably interferes with oxidation on a humid day.
Ken Muldrew
kmul...@ucalgary.ca
Edward Green
I was wondering whether there was a distinction between "oil" based
paint and paint relying on the evaporation of organic solvents
("spirit" based paint?).
I hedged the issue. I was familiar with the oxidation thing in
artists' paints, but OTOH I know that so-called oil based enamel give
off substantial quantities of solvent on drying.
John Spevacek
If you are painting wood, the paint will penetrate the pores of the
wood making it very difficult to remove the dried polymer film. Other
nonporous materials have paint adhere by van der Waals forces. You're
definitely not talking pressure-sensitive adhesives here.
John
Ed Keane III
John Spevacek <jspe...@msn.com> wrote in message
news:38c9b55b.03072...@posting.google.com...
> "Ed Keane III" <ke...@westelcom.com> wrote in message
news:<3f1fed88$0$39740$38ce...@news.newshosting.com>...
> > after it dries? Both experience and intuition
> > would suggest that paint is no longer sticky
> > after it dries.
>
> If you are painting wood, the paint will penetrate the pores of the
> wood making it very difficult to remove the dried polymer film. Other
> nonporous materials have paint adhere by van der Waals forces. You're
> definitely not talking pressure-sensitive adhesives here.
>
> John
Thankyou John.
I was beginning to think that I was posting to *sci.todumbtogetit*
David Lloyd-Jones
John Spevacek wrote:
>
> If you are painting wood, the paint will penetrate the pores of the
> wood making it very difficult to remove the dried polymer film. Other
> nonporous materials have paint adhere by van der Waals forces. You're
> definitely not talking pressure-sensitive adhesives here.
And the way pressure sensitive adhesives stick is...?
-dlj.
Ed Keane III
Paint, latex or oil based, does not harden, or cure, by drying. It hardens
by reacting with oxygen and polymerizing. It takes a lot longer for paint to
cure than it takes to dry. I know from experience that paint takes longer to
dry when it is humid. Are you sure that it takes longer to cure? If so you
are looking at different effects.
Ken Muldrew
Shellac and nitrocellulose lacquer are two finishes that merely
dissolve in their solvent and leave a solid finish when the solvent
evaporates. I'm not sure how humidity affects the drying of these
finishes (I use shellac a lot but it rarely gets humid here). I guess
I made the mistake of thinking that "spirit" meant "mineral spirits"
(usually called "paint thinner" around here). Oil based paint or
"stain" that uses mineral spirits usually contains linseed oil as a
binder. The mineral spirits evaporate but the paint isn't dry until a
significant amount of oxidation and cross-linking occurs in the
remaining oil. Again, we don't get very high humidity, so my
experience has always been that the mineral spirits evaporate long
before the oil loses its tack.
Ken Muldrew
kmul...@ucalgary.ca
Steve Turner
>Shellac and nitrocellulose lacquer are two finishes that merely
>dissolve in their solvent and leave a solid finish when the solvent
>evaporates. I'm not sure how humidity affects the drying of these
>finishes (I use shellac a lot but it rarely gets humid here). I guess
>I made the mistake of thinking that "spirit" meant "mineral spirits"
>(usually called "paint thinner" around here).
No, and that could be a key point. Shellac vehicle is mostly ethanol,
and ethanol is quite hygroscopic. It would not surprise me at all if
a shellac layer absorbed enough moisture in humid weather to
appreciably retard drying. Same comments for NC lacquer (typically
containing ketones as the vehicle), though to a lesser degree.
Edward Green
> null...@aol.com (Edward Green) wrote:
>
> >kmul...@ucalgary.ca (Ken Muldrew) wrote in message news:<3f201f54...@news.ucalgary.ca>...
> >> null...@aol.com (Edward Green) wrote:
> >>
> >> >Experience and intuition suggest that even spirits based paint takes
> >> >longer to dry on a humid day, all else being equal.
> >> >
> >> >Is this so, and if so, why?
> >>
> >> The "drying" of oil-based paint is mostly oxidation and cross-linking,
> >> hastened by mettalic dryers added as a catalyst. Dissolved water
> >> probably interferes with oxidation on a humid day.
> >
> >I was wondering whether there was a distinction between "oil" based
> >paint and paint relying on the evaporation of organic solvents
> >("spirit" based paint?).
> >
> >I hedged the issue. I was familiar with the oxidation thing in
> >artists' paints, but OTOH I know that so-called oil based enamel give
> >off substantial quantities of solvent on drying.
>
> Shellac and nitrocellulose lacquer are two finishes that merely
> dissolve in their solvent and leave a solid finish when the solvent
> evaporates. I'm not sure how humidity affects the drying of these
> finishes (I use shellac a lot but it rarely gets humid here). I guess
> I made the mistake of thinking that "spirit" meant "mineral spirits"
> (usually called "paint thinner" around here).
That's exactly what I meant. It's listed on the label as such.
> Oil based paint or
> "stain" that uses mineral spirits usually contains linseed oil as a
> binder. The mineral spirits evaporate but the paint isn't dry until a
> significant amount of oxidation and cross-linking occurs in the
> remaining oil. Again, we don't get very high humidity, so my
> experience has always been that the mineral spirits evaporate long
> before the oil loses its tack.
OK ... I thought that just described artist's paint. Are you saying
your garden variety oil based paint of commerce, which one might use
to paint the chair in the garden, has a similar chemistry? I guess
you are.
Since you mention lacquers and shellacs, I mention as an aside that I
once received a refinished piano bench, in some kind of such finish,
which _never_ dried completely. After six monthes, it was still
slightly tacky, and the cloth of your pants seat left a distinct
impression on it. IIRC, the store eventually took that one back and
gave me a new one.
Anyway, my premise may be wrong: it could be that I simply noticed
that the paint hadn't lost its tack after a certain time when the
whether was wet, when it wouldn't have lost its tack in a similar time
if the whether was dry. But I put that hedge in my first post, so I
am indemnified. ;-)
I haven't learned the answer to my question, but I've seen enough
plausible mechanisms suggested that at least my bemusement about the
impossibility of explaining this effect -- if there is one -- in terms
of partial pressures has evaporated. There's plenty of fudge room at
the inn.
Baseball anecdote: the person who used linseed oil instead of glove
oil.
David Lloyd-Jones
Edward Green wrote:
>
> Since you mention lacquers and shellacs, I mention as an aside that I
> once received a refinished piano bench, in some kind of such finish,
> which _never_ dried completely. After six monthes, it was still
> slightly tacky, and the cloth of your pants seat left a distinct
> impression on it. IIRC, the store eventually took that one back and
> gave me a new one.
This sometimes happens with cricket bats, on which one is using
linseed oil. My *impression* is that this is a matter of laying it
on too thick, which would suggest that permeablity to air is
important there. Maybe.
I report the datum with confidence, but have nothing to say about
the possible mechanisms.
-dlj.
Edward Green
No I'm not sure. Thanks for pointing out the distinction.
Note that even taking longer to dry vs. longer to cure raises the same
question: what role does water vapor play in the kinetics of
evaporation of organic solvents? But I've received enough fodder to
BS about these questions for months. And thanks for admitting that
you too have "experience": your first kind of sniffy reaction to mine
suggested you didn't value the stuff much. :-)
> If so you
> are looking at different effects.
Right.
As I said, for some reason I associated the curing process only with
artist's oils. I still think I am right that the solvent
concentration in the "oil based enamel" you buy in the hardware store
is much higher than in artist's paints -- therefore that evaporative
drying plays a greater role in the overall process after the paint is
exposed to air.
The Ghost In The Machine
<ke...@westelcom.com>
wrote
on Fri, 25 Jul 2003 13:15:29 -0400
<3f216810$0$39649$38ce...@news.newshosting.com>:
Does the polymerization involve removal of a water molecular,
as in the formation of starch from sugar? If so, humidity
would affect the removal of the resultant water molecule.
Otherwise, probably not. (Not that I actually know this
for sure, and there has to be a paint chemist out there
somewhere that does... :-) )
--
#191, ewi...@earthlink.net
It's still legal to go .sigless.
David Lloyd-Jones
Edward Green wrote:
>
> Since you mention lacquers and shellacs, I mention as an aside that I
> once received a refinished piano bench, in some kind of such finish,
> which _never_ dried completely. After six monthes, it was still
> slightly tacky, and the cloth of your pants seat left a distinct
> impression on it. IIRC, the store eventually took that one back and
> gave me a new one.
This sometimes happens with cricket bats, on which one is using
Ed Keane III
> "Ed Keane III" <ke...@westelcom.com> wrote in message
news:<3f216810$0$39649$38ce...@news.newshosting.com>...
>
> question: what role does water vapor play in the kinetics of
> evaporation of organic solvents? But I've received enough fodder to
> BS about these questions for months. And thanks for admitting that
> you too have "experience": your first kind of sniffy reaction to mine
> suggested you didn't value the stuff much. :-)
>
I apologize. Years ago there was a recurring thread along
the lines of, "Does paint dry in outer space?". I thought that
you and some of the other posters were fooling around. Do
people at sci.chem know about chemistry? And I sometimes
make a living as a contractor and will paint for money if I have to.
> > If so you
> > are looking at different effects.
>
> Right.
>
> As I said, for some reason I associated the curing process only with
> artist's oils. I still think I am right that the solvent
> concentration in the "oil based enamel" you buy in the hardware store
> is much higher than in artist's paints -- therefore that evaporative
> drying plays a greater role in the overall process after the paint is
> exposed to air.
As I understand it there are two stages. First the
liquid that is used to thin the paint to the point that
is the desired consistency for spreading (sometimes
adjusted by the painter) evaporates. At this point
the paint is tacky or sticky to the touch. Then
molecules in the paint react with oxygen and begin
to form long chains called polymers. A common
example of this is dried egg yolk. These fist form a
skin on the surface. At this point the paint is dry to
a light touch but still soft. When the paint has hardened
enough that a paint brush won't make marks you can
put on a second coat. It takes about a week for the
paint to *dry* completely. The solvent evaporates
in four to twelve hours. That's speaking as a painter,
not as someone who knows anything about chemistry.
I imagine that air can only be saturated by a certain
amount of vapor and that humid air will not absorb
as much solvent as dry air. I do not think that humid
air that is above the dew point temperature is going
to cause any kind of film that would impede oxygen
but I would have to call my guy at the paint store to
find out if humidity effects curing time.
-Edmund Keane
Edward Green
Except that bit about permeability to air. ;-)
Bruce Hamilton
>Experience and intuition suggest that even spirits based paint takes
>longer to dry on a humid day, all else being equal.
I was beginning to wonder which was more exciting - reading the
spurned lover posts on sci.chem, or watching paint dry ( there are
"watching paint dry" webcams for those unable to apply paint... ).
For those curious, an MRI study of paint drying is at
http://www.europhysicsnews.com/full/14/article3/article3.html
Paint drying rate will be controlled by several factors ( aside from
formulation ) including film thickness, surface temperature, air
temperature, wind, humidity, etc etc. Paint products are formulated to
ensure that several essential requirements are fulfilled during
drying, including:
- removal of solvents ( including water),
- sufficient time for the paint to develop the initial durable film (
which can depend on the substrate - wood requires great flexibility
and higher water and gas permeability than steel ),
- final hardening into a robust polymeric coating suitable for the
substrate and environment ( metals usually don't expand and contract
as much as wood does, because the wood is sensitive to humidity and
temperature ).
It's long been known that most paints lose solvents ( including water
) faster in low humidity, and in some extreme cases, form a white
bloom as the solvent evaporation causes cooling and some condensation
of moisture ( from the air, or separation of water formulated into the
paint ). Higher temperatures can also cause the same effect. Paints
that lose all solvents too fast may not have time to develop the
durable film, but become a powder film instead.
If the other solvents are removed, but the water removal rate is too
slow ( possibly due to high humidity ), the hardening starts to occur
and then the paint later shrinks and cracks. Obviously an ideal paint
would utilitize all the solvents to inhibit hardening ( oxidation,
cross-linking etc. ), so that when the water has all disappeared, the
other solvents have also disappeared, and the hardening reactions
begin in earnest to create the durable film
The hardening rate is also strongly affected by factors outside the
control of the formulators, such as moisture, waxes, oils, resins and
gums in wood and other substrates, previously applied paints, film
thickness, temperature, humidity, etc. Anybody who has painted bare
wood knows that some timbers are known to cause really slow hardening
of some paints due to natural resins and gums, and special undercoats
are used on them.
For those that want more information, I'm sure the technical sections
of any major paint company would provide data relevant to their
products.
The USDA offers some helpful comments to painters at:-
http://www.fpl.fs.fed.us/documnts/finlines/knaeb95a.pdf
[ Followups set to sci.chem only ]
Bruce Hamilton
John Spevacek
They certainly stick with better clarity than my answer!
The last sentence was regarding the implication of the poster that
tackiness is needed for paint to stick. They point I was making is
that tackiness is not necessary. Tacky or not, van der Waals forces
are important for film adhesion, which is the point you were making.
Ken Muldrew
>Since you mention lacquers and shellacs, I mention as an aside that I
>once received a refinished piano bench, in some kind of such finish,
>which _never_ dried completely. After six monthes, it was still
>slightly tacky, and the cloth of your pants seat left a distinct
>impression on it. IIRC, the store eventually took that one back and
>gave me a new one.
This can happen with shellac that is left too long in solvent. An
esterification occurs in the resin and it never hardens. This is the
kind of thing that can happen to a hobbyist who leaves their shellac
for months between finishing projects but it's surprising that this
would happen in a pro shop. You would think that they would go through
the stuff pretty quickly. BTW, the storage time for dry shellac flakes
is essentially indefinite.
Ken Muldrew
kmul...@ucalgary.ca
David Lloyd-Jones
John Spevacek wrote:
> David Lloyd-Jones <da...@rogers.com> wrote
>
>>John Spevacek wrote:
>>
>>>If you are painting wood, the paint will penetrate the pores of the
>>>wood making it very difficult to remove the dried polymer film. Other
>>>nonporous materials have paint adhere by van der Waals forces. You're
>>>definitely not talking pressure-sensitive adhesives here.
>>
>>And the way pressure sensitive adhesives stick is...?
>
> They certainly stick with better clarity than my answer!
>
> The last sentence was regarding the implication of the poster that
> tackiness is needed for paint to stick. They point I was making is
> that tackiness is not necessary. Tacky or not, van der Waals forces
> are important for film adhesion, which is the point you were making.
John,
Yup, though I wasn't sure. So thank you.
-dlj.
Gregory L. Hansen
A friend of mine tried working with shellac. He was surprised to find a
bag full of shellac bugs that had to be soaked and strained.
--
"A good plan executed right now is far better than a perfect plan
executed next week."
-Gen. George S. Patton
Ken Muldrew
>A friend of mine tried working with shellac. He was surprised to find a
>bag full of shellac bugs that had to be soaked and strained.
That's pretty common with seedlac. You can get more refined grades if
you don't want to strain it yourself. You can also get dewaxed shellac
without having to pay too dearly. Nothing compares to a rubbed-out
shellac finish; you just have to reach out and touch it.
Ken Muldrew
kmul...@ucalgary.ca
Edward Green
> null...@aol.com (Edward Green) wrote:
>
> > ... I mention as an aside that I
> >once received a refinished piano bench, in some kind of such finish,
> >which _never_ dried completely. After six monthes, it was still
> >slightly tacky, and the cloth of your pants seat left a distinct
> >impression on it. IIRC, the store eventually took that one back and
> >gave me a new one.
>
> This can happen with shellac that is left too long in solvent. An
> esterification occurs in the resin and it never hardens. This is the
> kind of thing that can happen to a hobbyist who leaves their shellac
> for months between finishing projects but it's surprising that this
> would happen in a pro shop. You would think that they would go through
> the stuff pretty quickly. BTW, the storage time for dry shellac flakes
> is essentially indefinite.
Well, their business was really refinishing pianos, not piano benchs;
so I figured this project had been left to an apprentice: not that
that readily explains how he got his hands on out-of-date shellac!
B.Ham...@irl.cri.nz (Bruce Hamilton) wrote in message news:<3f22ec9b....@newshost.comnet.co.nz>...
Obviously. I don't see why you even mention it. :-)
> The hardening rate is also strongly affected by factors outside the
> control of the formulators, such as moisture, waxes, oils, resins and
> gums in wood and other substrates, previously applied paints, film
> thickness, temperature, humidity, etc. Anybody who has painted bare
> wood knows that some timbers are known to cause really slow hardening
> of some paints due to natural resins and gums, and special undercoats
> are used on them.
>
> For those that want more information, I'm sure the technical sections
> of any major paint company would provide data relevant to their
> products.
>
> The USDA offers some helpful comments to painters at:-
> http://www.fpl.fs.fed.us/documnts/finlines/knaeb95a.pdf
I thank you for the definitive paint-drying answer. Just to close the
loop on my original question though: although by now we have learned
that paint drying is a complicated process involving some tandem
progress in solvent evaporation and film forming and hardening, you do
seem to confirm my initial speculation that even non-aqueous solvents
evaporate more slowly in high humidity.
Would you care to speculate on the dominant mechanism for this effect?
jmfb...@aol.com
null...@aol.com (Edward Green) wrote:
>kmul...@ucalgary.ca (Ken Muldrew) wrote in message
>news:<3f258450....@news.ucalgary.ca>...
>> The USDA offers some helpful comments to painters at:-
>> http://www.fpl.fs.fed.us/documnts/finlines/knaeb95a.pdf
>
>I thank you for the definitive paint-drying answer. Just to close the
>loop on my original question though: although by now we have learned
>that paint drying is a complicated process involving some tandem
>progress in solvent evaporation and film forming and hardening, you do
>seem to confirm my initial speculation that even non-aqueous solvents
>evaporate more slowly in high humidity.
>
>Would you care to speculate on the dominant mechanism for this effect?
Speculation: No wind. On humid days, if I have the fan blowing
on my dishes, they will dry "quicker".
/BAH
Subtract a hundred and four for e-mail.
The Ghost In The Machine
<jmfb...@aol.com>
wrote
on Tue, 29 Jul 03 10:23:43 GMT
<bg5lir$3h1$4...@bob.news.rcn.net>:
Even on non-humid days they should. :-) I'll admit I'm not
entirely certain why, though; the average velocity of an air
molecule is about 478 m/s, which suggests that once the
water molecule leaps into the vapor it's long gone before
you can breathe on or fan your eating utensils. :-)
Admittedly there may be Brownian motion issues, though; the
mean free path is about 3.34 * 10^-9 m. This means that on
average a molecule can travel 6.99 * 10^-12 seconds before
it hits something. If the average distance varies as the
cube root of time [*], this suggests that the water molecule
will only get to, on average, about 3.34 * 10^-9 * (1/(6.99 * 10^-12))^(1/3) =
1.75 * 10^-5 m after 1 second. (There is also a probability
distribution, mentioned below.)
http://www.rwc.uc.edu/koehler/biophys/8a.html
So maybe that fan is useful after all. :-) A fan moving the air
1.75 * 10^-5 m / s would be a very slow fan indeed.
>
> /BAH
>
>
> Subtract a hundred and four for e-mail.
[*] For whatever reason, mathematical random walks vary as the
square root of time on 2-D, but I'm not entirely clear on
the 3-D variant. The aforementioned webpage isn't all that
clear, either. :-)
jmfb...@aol.com
GAWD you keep putting science in your posts...and with numbers
and equations and stuff :-).
I don't enough to do what you just did. I was thinking more about
saturation and concentration...oh...that's what you were talking
about w.r.t. Brownian motion...no..that's not it. On a humid day,
with no wind, the "concentration" of the stuff evaporing out of
the paint is concentrated low to the ground; thus, the new stuff
has no place to go. Ed was talking about this with his store
at customer capacity.
>[*] For whatever reason, mathematical random walks vary as the
> square root of time on 2-D, but I'm not entirely clear on
> the 3-D variant. The aforementioned webpage isn't all that
> clear, either. :-)
2-D gives you two choices each time. 3-D should give you three.
John Spevacek
Chemical engineers are taught (although very few actually learn it!)
that forced convective transport always exceeds natural convective
transport. Heat, mass or momemtum, they are all the same. A very dear
chemist friend was faced with a problem of an object not drying fast
enough. Here response: turn up the temperature in the oven. My
response: turn up the fan speed. Guess who was right?
John
Edward Green
Mean free path.
> Admittedly there may be Brownian motion issues, though; the
> mean free path is about 3.34 * 10^-9 m.
Ah. You pre-cognated my mind. :-)
> This means that on
> average a molecule can travel 6.99 * 10^-12 seconds before
> it hits something. If the average distance varies as the
> cube root of time [*], this suggests that the water molecule
> will only get to, on average, about 3.34 * 10^-9 * (1/(6.99 * 10^-12))^(1/3) =
> 1.75 * 10^-5 m after 1 second. (There is also a probability
> distribution, mentioned below.)
>
> http://www.rwc.uc.edu/koehler/biophys/8a.html
>
> So maybe that fan is useful after all. :-) A fan moving the air
> 1.75 * 10^-5 m / s would be a very slow fan indeed.
> [*] For whatever reason, mathematical random walks vary as the
> square root of time on 2-D, but I'm not entirely clear on
> the 3-D variant. The aforementioned webpage isn't all that
> clear, either. :-)
Huh. Good question. Since I once got a satisfactory grade in a
course called "stochastic processes", I really should know off the top
of my head ... which reminds me ... not to change the topic ... one
must watch what instrument the barber is getting out when one asks for
"a little off the top", or says something off-the-top-of-one's-head
around a headsman.
As for the behavior on n-dimensional random walks, whatever the
dimension, what one gets is a diffusion equation: one should be able
to figure out the scaling from there.
The Ghost In The Machine
<bg8b89$1ji$2...@bob.news.rcn.net>:
Well, it is sci.physics. I suppose at some point I could
start insulting people but then I'd have to move the equations
to alt.flame, and at least here I think the audience either
can appreciate them, critique them, verify them, or (apparently
for the most part) just ignore them. :-)
Besides, I'd turn into Ghost Flambee... :-) It's not pretty. :-)
>
> I don't enough to do what you just did. I was thinking more about
> saturation and concentration...oh...that's what you were talking
> about w.r.t. Brownian motion...no..that's not it. On a humid day,
> with no wind, the "concentration" of the stuff evaporing out of
> the paint is concentrated low to the ground; thus, the new stuff
> has no place to go. Ed was talking about this with his store
> at customer capacity.
That's probably about right. It's clear that it takes time to
diffuse -- though apparently not much, if one leaves a perfume
bottle open. :-)
>>[*] For whatever reason, mathematical random walks vary as the
>> square root of time on 2-D, but I'm not entirely clear on
>> the 3-D variant. The aforementioned webpage isn't all that
>> clear, either. :-)
>
> 2-D gives you two choices each time. 3-D should give you three.
That's my thinking, yes.
>
> /BAH
>
>
> Subtract a hundred and four for e-mail.
--
Edward Green
...
> It's clear that it takes time to
> diffuse -- though apparently not much, if one leaves a perfume
> bottle open. :-)
There is a standard observation that while mean free path slows things
down in ... well, in the mean ... a few molecules are going to cover
much larger distances. And given very odoriferous molecules, a few is
all it takes.
Ken Muldrew
>In sci.physics, jmfb...@aol.com
>>>[*] For whatever reason, mathematical random walks vary as the
>>> square root of time on 2-D, but I'm not entirely clear on
>>> the 3-D variant. The aforementioned webpage isn't all that
>>> clear, either. :-)
>>
>> 2-D gives you two choices each time. 3-D should give you three.
>
>That's my thinking, yes.
In 1 dimension <x^2> = 2Dt (where D is now the diffusion constant
rather than the dimension), in 2 dimensions, <r^2> = 4Dt and in 3
dimensions <r^2> = 6Dt (where x and r represent distance from the
origin and t is time). The relationship is with the square root of
time for each case.
Ken Muldrew
kmul...@ucalgary.ca
Edward Green
Is it:
(1) supposed to be obvious to the most casual observer;
(2) non-obvious, but a story you might like to tell; or
(3) a challenge to the reader;
to explain why the prefactor is 2d, where d is the dimensionality?
For that matter, repeat the question for why the quantity growing
linearly with time is the mean square. Hmm... I even have some kind
of glimmer on that one: variance of independent increments adds;
variance is a second moment.
Well hot damn ... that even gives a distant glimmer of how to answer
the first question ... but I want to hear your input, first. ;-)
Ken Muldrew
>kmul...@ucalgary.ca (Ken Muldrew) wrote in message news:<3f2a8c7d...@news.ucalgary.ca>...
>> The Ghost In The Machine <ew...@sirius.athghost7038suus.net> wrote:
>>
>> >In sci.physics, jmfb...@aol.com
>> >>>[*] For whatever reason, mathematical random walks vary as the
>> >>> square root of time on 2-D, but I'm not entirely clear on
>> >>> the 3-D variant. The aforementioned webpage isn't all that
>> >>> clear, either. :-)
>> >>
>> >> 2-D gives you two choices each time. 3-D should give you three.
>> >
>> >That's my thinking, yes.
>>
>> In 1 dimension <x^2> = 2Dt (where D is now the diffusion constant
>> rather than the dimension), in 2 dimensions, <r^2> = 4Dt and in 3
>> dimensions <r^2> = 6Dt (where x and r represent distance from the
>> origin and t is time). The relationship is with the square root of
>> time for each case.
>
>Is it:
>
>(1) supposed to be obvious to the most casual observer;
>
>(2) non-obvious, but a story you might like to tell; or
>
>(3) a challenge to the reader;
>
>to explain why the prefactor is 2d, where d is the dimensionality?
(2) or (3)
The 1/2 is there for convenience and d is simply due to independence
of the motion along each dimension. Consider a 1 dimensional random
walk with step length dx and time interval dt. The displacement of the
particle after n time intervals is given by
x(n) = x(n-1) +/- dx
If we were to perform a random walk with N particles, the average
displacement would be given by the sum of the individual displacements
divided by N.
<x(n)> = 1/N i=1_sum_N[x_i(n)]
where i_sum_N is a sigma with i=1 on the bottom and N on the top
Substituting we get
<x(n)> = 1/N i=1_sum_N[x_i(n-1) +/- dx]
The "+/-" term becomes zero because, on average, the particle stays
where it is (obviously). To see how the particles spread out with time
we need to look at the root mean square displacement.
x^2(n) = x^2(n-1) +/- 2dx[x(n-1)] + dx^2
The mean is given by
<x^2(n)> = 1/N i=1_sum_N[x_i^2(n-1) +/- 2dx[x_i(n-1) + dx^2]]
Since the "+/-" term goes to zero we can write
<x^2(n)> = <x^2(n-1)> + dx^2
Since x_i(0) = 0, it follows that <x^2(1)> = 1dx^2, <x^2(2)> =
2dx^2,...,<x^2(n)> = ndx^2, and since each step occurs in time dt, the
elapsed time is ndt
<x^2> = (t/dt)dx^2 = dx^2/dt
Since dx and dt are constants, we can stick them into a single
constant:
D = dx^2/(2 dt)
The factor of 1/2 is there to make Fick's equation cleaner.
So now we have
<x^2> = 2Dt
for each independent dimension.
Exercise for the reader: relate this to thermal motion and use the
equipartition theorem to get an equation for dt in terms of
macroscopic measureable quantities.
Ken Muldrew
kmul...@ucalgary.ca