How to Convert Diffusion Rate to Hertz

[amy1vaulhausen]

How to Convert Diffusion Rate to Hertz - Hi, new here.  Does anyone know if it is possible to convert the molecular diffusion rate

to a frequency in hertz?

[chenbeier]

What is the unit of diffusion rate?

For a diffusion coefficient its cm^2* s^-1

 

Hertz is a unit for vibration. 1 Hz  = 1 s^-1

Edited July 3, 2023 by chenbeier

[exchemist]

6 hours ago, amy1vaulhausen said:

How to Convert Diffusion Rate to Hertz - Hi, new here.  Does anyone know if it is possible to convert the molecular diffusion rate

to a frequency in hertz?

This question does not make sense. Ask yourself this question: how can a rate of transfer of a substance, say dissolved salt spreading out through an unstirred liquid, have a frequency? 

[studiot]

 

6 hours ago, amy1vaulhausen said:

How to Convert Diffusion Rate to Hertz - Hi, new here.  Does anyone know if it is possible to convert the molecular diffusion rate

to a frequency in hertz?

Hello Amy, I don't think you mean diffusion rate, perhaps you mean diffusion half life.

The diffusion equation can be as complicated as you wish  ut the simple one can be modelled with a half life (measured in seconds or milliseconds etc) 

Of course 'frequency' is the reciprocal of seconds.

 

see here

How to model mass diffusion with half life - Physics Stack Exchange

Edited July 3, 2023 by studiot

[swansont]

1 hour ago, studiot said:

Of course 'frequency' is the reciprocal of seconds.

Frequency is the reciprocal of period. To have a period, it needs to be periodic. Just because there are units of inverse seconds, it doesn’t mean there is a frequency.

[studiot]

2 hours ago, swansont said:

Frequency is the reciprocal of period. To have a period, it needs to be periodic. Just because there are units of inverse seconds, it doesn’t mean there is a frequency.

Indeed so but periodic does not necessarily mean wave like. It means that something happens every specific time interval called the period.

In the case of a chemical or nuclear reaction this means this something refers to the consumption/ concentration of decaying reactant.

 

But I was really inviting Amy to provide more detail as to what she was really after, not wishing to engage in a semantic discussion.

That way we could help her more successfully.

Edited July 3, 2023 by studiot

[amy1vaulhausen]

4 hours ago, studiot said:

Indeed so but periodic does not necessarily mean wave like. It means that something happens every specific time interval called the period.

In the case of a chemical or nuclear reaction this means this something refers to the consumption/ concentration of decaying reactant.

 

But I was really inviting Amy to provide more detail as to what she was really after, not wishing to engage in a semantic discussion.

That way we could help her more successfully.

Thank you very much for your reply studiot!   

the reason behind my question is based on the diffusion rate in time.

 

Formula ;  t=x^2/2D 

 

see reference ; https://www.physiologyweb.com/calculators/diffusion_time_calculator.html

 

Since a solute will take a range of time to diffuse for a spacial unit with known viscosity and related parameters

and since that time range can be computed in seconds, then if light seconds are used as a distance value and

we convert the distance to a value in hertz, wouldnt we end up with a means to covert rate to a hertzian frequency? 

Am just wondering if there is a standard way to approach this?  A formula to use?  A cycle of time can be converted to

a frequency in hertz.  If we know the amount of time in seconds it takes a solute to diffuse in a specific unit of space

with know characteristics then there must be a way to convert this time period to a hertzian value or at least a range

of frequency values?

[swansont]

41 minutes ago, amy1vaulhausen said:

A cycle of time can be converted to

a frequency in hertz. 

A cycle, yes. But you haven’t described a cyclic system.

 

[studiot]

I have to say I am, like swansont, puzzled by your usage.

I don't know a great deal about physiology so it is new to me that they measure distances in light-seconds (300,000 kilometres).

What sort of organism incorporates those distances ?

 

I further agree with swansont that you need to model a repetitive (not necessarily cyclic) phenomenon, such as the one I mentioned earlier.

 

For instance in medicine, the half life of a drug in a body is given by

Half life, t_0.5  = 0.693* Volume of Distribution / Clearance  = 0.693/kc  where k_c is the elimination rate constant (a form of diffusion constant)

This half life models how much drug is eliminated by the body every time period.

[exchemist]

1 hour ago, amy1vaulhausen said:

Thank you very much for your reply studiot!   

the reason behind my question is based on the diffusion rate in time.

 

Formula ;  t=x^2/2D 

 

see reference ; https://www.physiologyweb.com/calculators/diffusion_time_calculator.html

 

Since a solute will take a range of time to diffuse for a spacial unit with known viscosity and related parameters

and since that time range can be computed in seconds, then if light seconds are used as a distance value and

we convert the distance to a value in hertz, wouldnt we end up with a means to covert rate to a hertzian frequency? 

Am just wondering if there is a standard way to approach this?  A formula to use?  A cycle of time can be converted to

a frequency in hertz.  If we know the amount of time in seconds it takes a solute to diffuse in a specific unit of space

with know characteristics then there must be a way to convert this time period to a hertzian value or at least a range

of frequency values?

You can’t express a distance , which has dimensions of L , in units of 1/T. A light second still has dimensions of distance. The speed of light has dimensions L/T. So a light second, c x t, has dimensions L/T  x T = L, i.e. distance.

There is no cycle of time in a diffusion process. It is not a periodic phenomenon.

Edited July 3, 2023 by exchemist

[chenbeier]

Exactly

[amy1vaulhausen]

 I realize diffusion itself is not periodic, but wouldnt the average "rate" of diffusion through a substance with known parameters be something that could be averaged, ie we could know the time period it takes for diffusion to occur? Wouldnt the time frame be essentially the same for a given solute to diffuse through similiar units of spatial size, viscosity, etc?

[exchemist]

6 hours ago, amy1vaulhausen said:

 I realize diffusion itself is not periodic, but wouldnt the average "rate" of diffusion through a substance with known parameters be something that could be averaged, ie we could know the time period it takes for diffusion to occur? Wouldnt the time frame be essentially the same for a given solute to diffuse through similiar units of spatial size, viscosity, etc?

Diffusion will continue so long as a concentration gradient remains. So it doesn’t generally stop after a definite time interval. It will gradually slow down, asymptotically, as equilibrium concentration throughout is approached.

The concept of the diffusion coefficient is that there is indeed a constant, for given substances and a given concentration gradient, at a given temperature.

[chenbeier]

I think she dont understand what periodical means, like at a pendelum or alterning current.

Diffusion is a process where a compound penetrates through a membran or something like this. This is slowed down by this membran. There is no periodical process. The same you hit the brake of your car and its shows down. It will not accelarte by itself.

[studiot]

@chenbeier  @exchemist

Surely you should also consider the boundary conditions.

Even the simple diffusion equation has periodic solutions with the right conditions.

There are plenty of learned maths papers on the subject.

eg 

Diffusion equation if f and φ are periodic the solution is also periodic - Mathematics Stack Exchange

Periodic solutions in reaction–diffusion equations with time delay - ScienceDirect

 

The point is to find out from Amy what she is trying to do as I still don't follow this and she hasn't responded to my last post.

 

Again a medical example, with more complicated conditions is the calculation of the rate and size of periodic dosing to achieve a 'steady state concentration' in the body.

This also happens when considering Fourier solutions to the heat equation, which is a form of the simple diffusion equation.

 

So @amy1vaulhausen, please,

Why are you working with a physiological calculator and why are you measuring distance in light seconds ?

What conditions are you setting

Edited July 4, 2023 by studiot

[chenbeier]

@Studiot

Quote

Surely you should also consider the boundary conditions.

Even the simple diffusion equation has periodic solutions with the right conditions.

There are plenty of learned maths papers on the subject.

eg 

Diffusion equation if f and φ are periodic the solution is also periodic - Mathematics Stack Exchange

Periodic solutions in reaction–diffusion equations with time delay - ScienceDirect

This is other piece of cake, because a periodical parameter is set in, but this has nothing to do with the diffusion itself.

[exchemist]

1 hour ago, studiot said:

@chenbeier  @exchemist

Surely you should also consider the boundary conditions.

Even the simple diffusion equation has periodic solutions with the right conditions.

There are plenty of learned maths papers on the subject.

eg 

Diffusion equation if f and φ are periodic the solution is also periodic - Mathematics Stack Exchange

Periodic solutions in reaction–diffusion equations with time delay - ScienceDirect

 

The point is to find out from Amy what she is trying to do as I still don't follow this and she hasn't responded to my last post.

 

Again a medical example, with more complicated conditions is the calculation of the rate and size of periodic dosing to achieve a 'steady state concentration' in the body.

This also happens when considering Fourier solutions to the heat equation, which is a form of the simple diffusion equation.

 

So @amy1vaulhausen, please,

Why are you working with a physiological calculator and why are you measuring distance in light seconds ?

What conditions are you setting

What real life scenario would such periodic behaviour correspond to?
 

Or is this just an abstract artifact of the maths that has no real life application?

[studiot]

31 minutes ago, chenbeier said:

@Studiot

This is other piece of cake, because a periodical parameter is set in, but this has nothing to do with the diffusion itself.

The diffusion equation is not only impossible to solve, it is actually meaningless without the boundary conditions, (and I include initial conditions in this).

 

The link Amy provided pays attention to this and describes in some detail some of the possible circumstances including multiple sources   and/ or sinks both time and space and the possibility of both diffusing and transmission media interacting.

It is true that the simple quadratic formula it calculates refers to a single source with no sinks and and an unbounded transmission medium.

Thus it is a very simplistic formula (It is not the diffusion equation) which simply comes up with a rough estimate of how far (x) a diffusing medium would get in time (D), all other things being equal.

but it depends upon these conditions which are  part of the diffusion equation, not something separate from it.

 

To see how diffusion can lead to chemical oscillation read this

Quote

Wikipedia

Belousov–Zhabotinsky reaction - Wikipedia

In a way similar to the Briggs–Rauscher reaction, two key processes (both of which are auto-catalytic) occur; process A generates molecular bromine, giving the red colour, and process B consumes the bromine to give bromide ions.^[14] Theoretically, the reaction resembles the ideal Turing pattern, a system that emerges qualitatively from solving the reaction diffusion equations for a reaction that generates both a reaction inhibitor and a reaction promoter, of which the two diffuse across the medium at different rates.^[15]

 

[exchemist]

33 minutes ago, studiot said:

The diffusion equation is not only impossible to solve, it is actually meaningless without the boundary conditions, (and I include initial conditions in this).

 

The link Amy provided pays attention to this and describes in some detail some of the possible circumstances including multiple sources   and/ or sinks both time and space and the possibility of both diffusing and transmission media interacting.

It is true that the simple quadratic formula it calculates refers to a single source with no sinks and and an unbounded transmission medium.

Thus it is a very simplistic formula (It is not the diffusion equation) which simply comes up with a rough estimate of how far (x) a diffusing medium would get in time (D), all other things being equal.

but it depends upon these conditions which are  part of the diffusion equation, not something separate from it.

 

To see how diffusion can lead to chemical oscillation read this

 

That’s very interesting. I was not aware of these.  I actually think the Briggs-Rauscher reaction may be an even better example as that one does seem to exhibit regular, rather than chaotic, periodicity: https://en.wikipedia.org/wiki/Briggs–Rauscher_reaction

However these processes are not in fact examples of diffusion, but of chemical reactions, in which diffusion inevitably plays a part. I struggle to believe  there are any examples of purely diffusive processes that exhibit periodicity.

 

 

Edited July 4, 2023 by exchemist

[studiot]

I have very scanty knowledge of biochemistry, mainly through reaction kinetics, so I am only guessing what Amy is after, I suspect she has mixed up some terminology somewhere, hence my questions.

 

Anyway here is a short discussion about the maths, set at upper high school level calculus.

 

The diffusion equation and the wave equation connect the distribution in space and time of some quantity and it derivatives with respect to space and time.

The 'solution'' of the equation is an algebraic equation describing the values of this function in time and/or space.

The derivatives involved are first and second derivatives.

The connection enables the evolution in time of a system obeying these equations to be determined. That is the spatial distribution at a given time t.

In general we are looking for continuous functions so functions such as x = t² and x = sin(t) are acceptable but x = tan(t) is not

x = t² is not periodic, but x = sin(t) and x = tan(t) are periodic.

However x = tan(t) is discounted as it is non continuous.

OK so the first derivative will be continuous (but may be zero).

For periodicity to occur there must be 'turning points'.
This involve the second derivative being zero at the points.
Further there must be more than one turning point x = t² has one turning point but this is clearly not enough to generate periodicity.

Now the wave equation involves only second derivatives,
So it is not surprising that periodic solutions predominate.

The diffusion equation involves both first and second derivatives.
So it nis not surprising that non periodic solutions occur most frequently in practice.

But the periodicity or non periodicity is built right into the equation it is not a separate cake as chenbeier puts it.

 

I hope this helps somebody.

[chenbeier]

Quote

But the periodicity or non periodicity is built right into the equation it is not a separate cake as chenbeier puts it.

This I didn't said. I said it is other piece of cake, but its the same cake not a separate  cake. Only a piece of the whole thing.

But I think we should wait for answer of Amy, if she still is interested.

[exchemist]

23 minutes ago, studiot said:

I have very scanty knowledge of biochemistry, mainly through reaction kinetics, so I am only guessing what Amy is after, I suspect she has mixed up some terminology somewhere, hence my questions.

 

Anyway here is a short discussion about the maths, set at upper high school level calculus.

 

The diffusion equation and the wave equation connect the distribution in space and time of some quantity and it derivatives with respect to space and time.

The 'solution'' of the equation is an algebraic equation describing the values of this function in time and/or space.

The derivatives involved are first and second derivatives.

The connection enables the evolution in time of a system obeying these equations to be determined. That is the spatial distribution at a given time t.

In general we are looking for continuous functions so functions such as x = t² and x = sin(t) are acceptable but x = tan(t) is not

x = t² is not periodic, but x = sin(t) and x = tan(t) are periodic.

However x = tan(t) is discounted as it is non continuous.

OK so the first derivative will be continuous (but may be zero).

For periodicity to occur there must be 'turning points'.
This involve the second derivative being zero at the points.
Further there must be more than one turning point x = t² has one turning point but this is clearly not enough to generate periodicity.

Now the wave equation involves only second derivatives,
So it is not surprising that periodic solutions predominate.

The diffusion equation involves both first and second derivatives.
So it nis not surprising that non periodic solutions occur most frequently in practice.

But the periodicity or non periodicity is built right into the equation it is not a separate cake as chenbeier puts it.

 

I hope this helps somebody.

In fact this discussion reminds me that Schrodinger’s “wave” equation in its time-dependent form is actually a diffusion equation. The time-independent form however is a standing wave equation, I understand, hence the way it is often named. But I expect this is straying a long way from the OP question.

Edited July 4, 2023 by exchemist

[sethoflagos]

As there seems to be some link to a physiological context, might the OP be referring to neural firing rates? Not my field but I think it's common knowledge that nerve signals are either on or off, and therefore have to convert stimulus amplitude to frequency as and when required (eg pain receptors etc.). I can see diffusion rates of neurotransmitters etc released during the off and on states possibly playing some part in setting the time period(?). Just a guess. 

Post Script - I just pulled up the calculator link provided by the OP and there's a heavy emphasis on neurotransmitter diffusion. So less of a guess now.

Edited July 4, 2023 by sethoflagos

[amy1vaulhausen]

13 hours ago, studiot said:

I have very scanty knowledge of biochemistry, mainly through reaction kinetics, so I am only guessing what Amy is after, I suspect she has mixed up some terminology somewhere, hence my questions.

 

Anyway here is a short discussion about the maths, set at upper high school level calculus.

 

The diffusion equation and the wave equation connect the distribution in space and time of some quantity and it derivatives with respect to space and time.

The 'solution'' of the equation is an algebraic equation describing the values of this function in time and/or space.

The derivatives involved are first and second derivatives.

The connection enables the evolution in time of a system obeying these equations to be determined. That is the spatial distribution at a given time t.

In general we are looking for continuous functions so functions such as x = t² and x = sin(t) are acceptable but x = tan(t) is not

x = t² is not periodic, but x = sin(t) and x = tan(t) are periodic.

However x = tan(t) is discounted as it is non continuous.

OK so the first derivative will be continuous (but may be zero).

For periodicity to occur there must be 'turning points'.
This involve the second derivative being zero at the points.
Further there must be more than one turning point x = t² has one turning point but this is clearly not enough to generate periodicity.

Now the wave equation involves only second derivatives,
So it is not surprising that periodic solutions predominate.

The diffusion equation involves both first and second derivatives.
So it nis not surprising that non periodic solutions occur most frequently in practice.

But the periodicity or non periodicity is built right into the equation it is not a separate cake as chenbeier puts it.

 

I hope this helps somebody.

 

This is by far the best response and most helpful so far!  Thank you so much for this feedback.  I wanted to provide an answer to those who have

been asking why I am interested in this and I also have some more questions.  The reason I am asking is that I would like to experiment with passing weak electrical  / RF signals through an aqueous solution to see if I can modulate saturation time of a diffusing substance. 

A working example would be for methylene blue ; 

"The average diffusion coefficient was (6.74 ± 1.32) × 10−6 cm2/s for an aqueous solution of methylene blue and (1.93 ± 0.24) × 10−6 cm2/s for a micellar solution of the dye. "

Since ; "The diffusion coefficient determines the time it takes a solute to diffuse a given distance in a medium."

where 

 

• x is the mean distance traveled by the diffusing solute in one direction along one axis after elapsed time t.
• t is the elapsed time since diffusion began. Diffusion time increases with the square of diffusion distance. Diffusion time is inversely proportional to the diffusion coefficient (D).

from ; https://www.physiologyweb.com/calculators/diffusion_time_calculator.html

If Im working with an aqueous solution with a volume of one cubic centimeter that has fixed characteristics ( density, temperature, etc...)

Then unless Im grossly misunderstanding something here, it must generally take the same amount of time for methylene blue to diffuse to a threshold within the

volume of the aqueous solution regardless of how often I repeat the process of introducing the substance into the volume.  There must be a simple formula that will tell me what this time period is - that is all I really want to know.  How long will it take for the substance to distribute in the volume over the distance, ie. from point of origin of introduction of substance to total distance the substance travels in the medium to the point of threshold saturation.  When I know that time period then I should be able to convert that time frame to a frequency.

But I feel I am missing something here, surely its not as easy as just inputing the values to 

Also, I am a newb and when I look at this string ;  [ (6.74 ± 1.32) × 10−6 cm2/s ] 

for methylene blue I dont understand exactly what I am looking at the value ; 6.74 ± 1.32

mean what exactly?  Does this mean a numeric range of 6.74 plus or minus1.32 ?

And the value of [ 10−6 cm2/s ]  this just means the volume of the sample being used?

 

 

 

 

 

[sethoflagos]

2 hours ago, amy1vaulhausen said:

Then unless Im grossly misunderstanding something here, it must generally take the same amount of time for methylene blue to diffuse to a threshold within the

volume of the aqueous solution regardless of how often I repeat the process of introducing the substance into the volume.  There must be a simple formula that will tell me what this time period is - that is all I really want to know.  How long will it take for the substance to distribute in the volume over the distance, ie. from point of origin of introduction of substance to total distance the substance travels in the medium to the point of threshold saturation.  When I know that time period then I should be able to convert that time frame to a frequency.

But I feel I am missing something here, surely its not as easy as just inputing the values to 

No, it's not quite so easy.

The diffusion function you seem to be looking for is an appropriate solution to Fick's 2nd Law for your specific geometry. Have a look at https://en.wikipedia.org/wiki/Fick's_laws_of_diffusion and in particular the section "Example solution 1: constant concentration source and diffusion length".