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?

 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?

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!   

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?