Stop Bath.. How important?

[faberryman]

As to Pyro and stop baths, I do not use one, water only.

The reason being, I spent a fair bit of time experimenting to find the true film ratings and, developing times for my favourite films in Pyro 510.
The information available to me at the time was No Acid Stop Bath.
I know my parameters for my films developed in 510 and a homebrewed Kodak fixer. I don't want to go over the same ground again using an acid stop bath.

This is an easy one. The instructions for 510 Pyro say not to use stop bath, which is consistent with manufacturers of other pyrogallol based developers, although some say you can use water or an alkali stop bath. So, if you follow the 510 Pyro instructions, you would refrain from using stop bath.

Please note that James Lane, owner of Zone Imaging, is a marketing guy pretending to be a photo chemist, and you should question everything on his company's website except the price. Don't trust. Verify.

 

[Sirius Glass]

On working out the appropriate concentration of acetic acid and indicator? Is it really more than a high school chemistry problem? Ah well, I’ve no reason to dispute it if it is documented.

It has been documented, while your assertions seem to be based on what you want them to be with nothing to back them up.

What would you see? Sometimes I can’t tell if you are joking.

I am saying that you are not equipped and neither is most of the rest of us, to measure the difference. Using your logic, nothing is true unless you want it to be true. It is time for you to scientifically prove otherwise.

 

[faberryman]

I realise I need to reply to this with personal experience.

I used to use Tetenal Emofin as my standard (it is no longer made). With the thin Delta emulsions I started to notice lots of tiny blemishes. I read somewhere that the reason might have been the use of a stop bath, because Bath 2 of that product was strongly alkali and could cause a physically violent reaction (it was said). So I stopped using stop bath on my films. After a while, I realised that my blemishes were white in the positive, so they couldn’t have been missing bits of emulsion blown away by micro-explosions. I improved the filtration on my water supply and all chemicals, and the problem vanished. That’s why I said ‘may’ in my post above. It’s a widespread notion, but I’ve seen no definite proof.

I was unable to locate the manufacturer's directions for Emofin film developer. Did you have them and read them? What did they say? Other two bath developers, like Diafine and Barry Thornton two bath developer, say not to use stop bath, so I would be surprised if the directions for Emofin said to use stop bath. If the directions didn't say to use a stop bath and you used it anyway, then the use of stop bath would be on my troubleshooting checklist. I would also consider that, since Emofin film developer is a powder, perhaps the developer was not fully dissolved, and that particles of developer may have gotten stuck in the emulsion. The same consideration would apply if you mixed your fixer from powder.

Nevertheless, I realised that the amount of unused developer in bath 2 of my Emofin must have been very small, so a stop bath was probably not doing much anyway. That reasoning applies equally to the Barry Thornton 2 bath developer that I now use. I'm sure I could use a stop bath because I use metaborate in bath 2; but if I used a stronger alkali (there are several options mentioned by Thornton) I might wonder about that acid-alkali theory until I’d done a few films.

The directions for Barry Thornton two bath developer say not to use stop bath. Case closed.

If I use a mainstream developer like ID-11, I use a stop bath.

My default is to follow the directions, unless someone can give me a verifiable good reason not to. Some random guy on the internet telling me that it is not necessary to use stop bath when developing film and I can save a nickle, without more, does not meet my threshold for credibility.

 

[faberryman]

The number of developer molecules carried over to the fixer will be essentially the same, regardless of whether one uses an acid-based stop bath of just plain water. It will only depend on the volume of liquid used in the stop bath, so if you use the same amount of liquid for the stop bath you will transfer the same number of molecules to the fixer, regardless of whether the stop bath is acidic or roughly pH neutral.

This analysis assumes that the developer carryover comes from the film of solution adhering to the surface of the film and the developer tank and reel. It does not include developer molecules that might be trapped inside the emulsion. There might be some subtle effect with regard to how many developer molecules might be removed from the actual film emulsion itself, but given the small volume occupied by the emulsion there must be very few developer molecules trapped in the emulsion, and even then one would have to propose that they are more easily removed under mild acidic conditions than under roughly pH neutral conditions.

I do not know how to calculate the number of carry over film developer molecules. My guess is that there are a lot of variables. Your analysis "depends" and "assumes", so I don't know how accurate your conclusion is. I am sure that someone, perhaps you, could calculate the number of carry over film developer molecules accurately and tell us how much is too much. It seems that there are at least two issues involving carry over film developer molecules. First, the continued effect of the carry over film developer molecules on development, and second, the effect of carry over film developer molecules on the longevity of fixer. It all gives me a headache, so I am going to use stop bath when directed, and forego saving a nickle.

 

[alanrockwood]

Here's a quick sample calculation to more fully explain what I meant in my last post. In this sample calculation I will not be discussing developer molecules that are in the emulsion itself, only those that are in the liquid residue clinging to the reels and walls of the development tank.

Suppose you are using 500 ml of developer and that in that 500 ml there are 10,000 developer molecules. Yes, I know there are more than that. I'm just using that number to make the calculations easy for illustration purposes.

Assume that after the development stage is completed you pour out 495ml of the developer solution, leaving 5ml clinging to the reels and walls of the tank. That's 1% of the original volume. In that 1% there will be 100 molecules of developer. (1% of 10,000 molecules is 100 molecules.) At this point I will split the analysis into two scenarios.

In scenario one we add 495ml of water to the tank and agitate to mix it with the 5ml of residue from the previous step. There will be 100 molecules of developer in the 500ml of resulting solution. We pour out that solution, leaving 5ml of residue in the tank. In that 5ml there will be an average of 1 molecule of developer. That's the number of developer molecules carried over into the fixer.

In scenario two we add 495ml of acid stop bath into the tank and agitate to mix it with the 5ml of residue from the previous step. There will be 100 molecules of developer in the 500ml of resulting solution. We pour out that solution, leaving 5ml of residue left in the tank. In that 5ml there will be 1 molecule of developer. That's the number of molecules carried over into the fixer. That's exactly the same number of developer molecules carried over as in scenario 1.

If you started with the a different number of developer molecules the carryover ratios will be the same as those described above. For example, if you started with a 100 trillion molecules in 500ml of developer you end up with 10 billion developer molecules carried over into the fixer, regardless of whether you were using a water stop bath or an acid stop bath. The carryover ratio is 0.01% of the original number of molecules.

Suppose there was 10ml instead of 5ml of solution carryover for each step. That would change the fraction of molecules carried over into fixer from 0.01% to 0.04%, independent of whether you use an acid stop bath or a water stop bath.

Conclusion: the number of molecules carried over into the fixer is independent of whether one uses an acid stop bath or a water stop bath.

As noted above, this analysis does not include a discussion of developer molecules that are actually trapped in the gelatin at the beginning of the stop-bath step. However, to argue that an acid stop bath produces less carryover into the fixer one would somehow have to say that, first of all, there are enough developer molecules trapped in the gelatin to matter (which I think it unlikely), and second of all, that an acid stop bath is more efficient in extracting those molecules into solution than a water stop bath, which as far as I am aware has never even been discussed, let alone been proven.

 

[MattKing]

Stop bath changes the pH, and the carried over developer is therefore effectively neutralized before it gets into the fixer, where neutralized developer has little or no deleterious effect.

 

[alanrockwood]

Stop bath changes the pH, and the carried over developer is therefore effectively neutralized before it gets into the fixer, where neutralized developer has little or no deleterious effect.

If you look at the pKa values of common developers you will see that it is not necessary for a solution to be acidic in order to neutralize developers. A neutral pH is plenty good enough to do that. For example, the pKa of 4 aminophenol (the developer in Rodinal) is 10.30. (I believe that the pKa of metol is about the same.) A developer with a pKa of 10 will only be 0.1% ionized at pH 7. A developer of pKa 10.3 will be be only 0.05% ionized at pH 7.

However, it doesn't really matter what percentage of molecules are ionized before they enter the fixer because as soon as they hit the fixer they will assume their equilibrium value at whatever the pH of the fixer is.

Now, there is an effect that I deliberately avoided discussing, and that is the fact that the pH of the solution carried over will slightly alter the pH of the fixer. The operative word here is "slightly". I doubt if it is a strong enough effect to make a practical difference.

 

[faberryman]

Here's a quick sample calculation to more fully explain what I meant in my last post. In this sample calculation I will not be discussing developer molecules that are in the emulsion itself, only those that are in the liquid residue clinging to the reels and walls of the development tank.

Suppose you are using 500 ml of developer and that in that 500 ml there are 10,000 developer molecules. Yes, I know there are more than that. I'm just using that number to make the calculations easy for illustration purposes.

Assume that after the development stage is completed you pour out 495ml of the developer solution, leaving 5ml clinging to the reels and walls of the tank. That's 1% of the original volume. In that 1% there will be 100 molecules of developer. (1% of 10,000 molecules is 100 molecules.) At this point I will split the analysis into two scenarios.

In scenario one we add 495ml of water to the tank and agitate to mix it with the 5ml of residue from the previous step. There will be 100 molecules of developer in the 500ml of resulting solution. We pour out that solution, leaving 5ml of residue in the tank. In that 5ml there will be an average of 1 molecule of developer. That's the number of developer molecules carried over into the fixer.

In scenario two we add 495ml of acid stop bath into the tank and agitate to mix it with the 5ml of residue from the previous step. There will be 100 molecules of developer in the 500ml of resulting solution. We pour out that solution, leaving 5ml of residue left in the tank. In that 5ml there will be 1 molecule of developer. That's the number of molecules carried over into the fixer. That's exactly the same number of developer molecules carried over as in scenario 1.

If you started with the a different number of developer molecules the carryover ratios will be the same as those described above. For example, if you started with a 100 trillion molecules in 500ml of developer you end up with 10 billion developer molecules carried over into the fixer, regardless of whether you were using a water stop bath or an acid stop bath. The carryover ratio is 0.01% of the original number of molecules.

Suppose there was 10ml instead of 5ml of solution carryover for each step. That would change the fraction of molecules carried over into fixer from 0.01% to 0.04%, independent of whether you use an acid stop bath or a water stop bath.

Conclusion: the number of molecules carried over into the fixer is independent of whether one uses an acid stop bath or a water stop bath.

As noted above, this analysis does not include a discussion of developer molecules that are actually trapped in the gelatin at the beginning of the stop-bath step. However, to argue that an acid stop bath produces less carryover into the fixer one would somehow have to say that, first of all, there are enough developer molecules trapped in the gelatin to matter (which I think it unlikely), and second of all, that an acid stop bath is more efficient in extracting those molecules into solution than a water stop bath, which as far as I am aware has never even been discussed, let alone been proven.

Let's assume for the sake of argument that your analysis is absolutely correct in every respect. I will ask the same questions I asked in post 1161 which no one has yet seen fit to address:

Why has Kodak included using stop bath in its film processing instructions since time immemorial? Did they have any scientific evidence for doing so or did they just make it up out of thin air so they could sell stop bath and make more money? Have materials changed over time eliminating the need for stop bath, and Kodak never got around to updating its directions? Did Kodak pay PE to recommend using stop bath on this forum? He seemed like a pretty knowledgeable guy. How else did he lead us astray? Do any books on film processing say stop bath is unnecessary, or is it just people on photo forums?

Here are two bonus questions:

What purposes, if any, does using stop bath serve, other than stopping development? Are there any benefits to using stop bath?

If you would care to address those, I would be most appreciative.

 

[alanrockwood]

Let's assume for the sake of argument that your analysis is absolutely correct in every respect. I will ask the same questions I asked in post 1161 which no one has yet seen fit to address:

Why has Kodak included using stop bath in its film processing instructions since time immemorial? Did they have any scientific evidence for doing so or did they just make it up out of thin air so they could sell stop bath and make more money? Have materials changed over time eliminating the need for stop bath, and Kodak never got around to updating its directions? Did Kodak pay PE to recommend using stop bath on this forum? He seemed like a pretty knowledgeable guy. How else did he lead us astray? Do any books on film processing say stop bath is unnecessary, or is it just people on photo forums?

Here are two bonus questions:

What purposes, if any, does using stop bath serve, other than stopping development? Are there any benefits to using stop bath?

If you would care to address those, I would be most appreciative.

Excellent question(s) to which I do not have answers, nor have I seen any data answering the question(s).

 

[Sirius Glass]

Here's a quick sample calculation to more fully explain what I meant in my last post. In this sample calculation I will not be discussing developer molecules that are in the emulsion itself, only those that are in the liquid residue clinging to the reels and walls of the development tank.

Suppose you are using 500 ml of developer and that in that 500 ml there are 10,000 developer molecules. Yes, I know there are more than that. I'm just using that number to make the calculations easy for illustration purposes.

Assume that after the development stage is completed you pour out 495ml of the developer solution, leaving 5ml clinging to the reels and walls of the tank. That's 1% of the original volume. In that 1% there will be 100 molecules of developer. (1% of 10,000 molecules is 100 molecules.) At this point I will split the analysis into two scenarios.

In scenario one we add 495ml of water to the tank and agitate to mix it with the 5ml of residue from the previous step. There will be 100 molecules of developer in the 500ml of resulting solution. We pour out that solution, leaving 5ml of residue in the tank. In that 5ml there will be an average of 1 molecule of developer. That's the number of developer molecules carried over into the fixer.

In scenario two we add 495ml of acid stop bath into the tank and agitate to mix it with the 5ml of residue from the previous step. There will be 100 molecules of developer in the 500ml of resulting solution. We pour out that solution, leaving 5ml of residue left in the tank. In that 5ml there will be 1 molecule of developer. That's the number of molecules carried over into the fixer. That's exactly the same number of developer molecules carried over as in scenario 1.

If you started with the a different number of developer molecules the carryover ratios will be the same as those described above. For example, if you started with a 100 trillion molecules in 500ml of developer you end up with 10 billion developer molecules carried over into the fixer, regardless of whether you were using a water stop bath or an acid stop bath. The carryover ratio is 0.01% of the original number of molecules.

Suppose there was 10ml instead of 5ml of solution carryover for each step. That would change the fraction of molecules carried over into fixer from 0.01% to 0.04%, independent of whether you use an acid stop bath or a water stop bath.

Conclusion: the number of molecules carried over into the fixer is independent of whether one uses an acid stop bath or a water stop bath.

As noted above, this analysis does not include a discussion of developer molecules that are actually trapped in the gelatin at the beginning of the stop-bath step. However, to argue that an acid stop bath produces less carryover into the fixer one would somehow have to say that, first of all, there are enough developer molecules trapped in the gelatin to matter (which I think it unlikely), and second of all, that an acid stop bath is more efficient in extracting those molecules into solution than a water stop bath, which as far as I am aware has never even been discussed, let alone been proven.

Stop bath neutralizes the developer in the gelatin period. That is a fact. This is part of stop bath's purpose. Water rinsing will not do that.

 

[koraks]

A neutral pH is plenty good enough to do that

But since plain water isn't buffered, a water "stop" bath won't yield a neutral pH. It'll be decidedly alkaline due to developer carryover the moment it's swirled around in the tank.
Your reasoning does however illustrate why a stop bath that's buffered around a neutral pH does indeed work like an acidic stop bath.

In the end, it's still splitting hairs of course. Legions of people have used a water rinse instead of a stop bath in film development. If there were any structural problems with this, we would have known by now.

Until we instate a stop bath police, that is. They'll patrol your darkroom equipped with pH meters and titration equipment. Punishments will be harsh, and very acidic.

 

[alanrockwood]

But since plain water isn't buffered, a water "stop" bath won't yield a neutral pH. It'll be decidedly alkaline due to developer carryover the moment it's swirled around in the tank.
Your reasoning does however illustrate why a stop bath that's buffered around a neutral pH does indeed work like an acidic stop bath.

In the end, it's still splitting hairs of course. Legions of people have used a water rinse instead of a stop bath in film development. If there were any structural problems with this, we would have known by now.

Until we instate a stop bath police, that is. They'll patrol your darkroom equipped with pH meters and titration equipment. Punishments will be harsh, and very acidic.

Good point about buffering.

This brings up a question. Does developer carryover into fixer harm the fixer because of the developer molecules that are transferred to the fixer or because it tends to raise the pH of the fixer?

Returning to the issue of buffering, a dilution factor of 100x (as per my hypothetical calculation when 5ml of developer solution is diluted with 495 ml of water) will drastically reduce the buffering capacity of the buffer. It may be worth considering how plays into the question.

 

[koraks]

Does developer carryover into fixer harm the fixer because of the developer molecules that are transferred to the fixer or because it tends to raise the pH of the fixer?

I'm not sure, really. What I think happens is that something in the carried-over developer reacts with the thiosulfate to liberate sulfur, which then combines with still unfixed silver halides, producing a silver sulfide stain that can't be removed. However, if it's the developer itself or part of the adjuvant package (e.g. carbonates etc.) that does this, I don't know. Perhaps a combination of both?

PS & NB: in the above, with staining, I'm referring primarily to prints, not film!

 

[alanrockwood]

PS & NB: in the above, with staining, I'm referring primarily to prints, not film!

Thanks for the clarification. All of my comments pertain to film, not prints.

 

[snusmumriken]

I was unable to locate the manufacturer's directions for Emofin film developer. Did you have them and read them? What did they say? Other two bath developers, like Diafine and Barry Thornton two bath developer, say not to use stop bath, so I would be surprised if the directions for Emofin said to use stop bath. If the directions didn't say to use a stop bath and you used it anyway, then the use of stop bath would be on my troubleshooting checklist. I would also consider that, since Emofin film developer is a powder, perhaps the developer was not fully dissolved, and that particles of developer may have gotten stuck in the emulsion. The same consideration would apply if you mixed your fixer from powder.

Yes I have the instructions (below). No stop bath stage is listed in the developing/fixing procedure, but under 'Special Comments' they say "The use of a stop bath (INDICET or 2 to 3% acetic acid) before fixing raises the yield of the fixer." One can reasonably conclude that in Tetenal's view a stop bath was optional with this developer.

I thought the same as you about particles, hence my decision to filter everything carefully; and that solved things, as stated.

Some random guy on the internet telling me that it is not necessary to use stop bath when developing film and I can save a nickle, without more, does not meet my threshold for credibility.

Nor mine - see post #1082. Still, the emulsion pin-hole theory was plausible enough for me to experiment with leaving out the (optional) stop bath.

The directions for Barry Thornton two bath developer say not to use stop bath. Case closed.

In his article 'Fine negatives automatically', BT mentions stop bath only when warning not to use a rinse or stop bath between Bath A and Bath B. Are there other directions somewhere?
If he did advise against it, I imagine it was on the basis of reasoning, rather than millions of dollars of research on his part.

all you will learn by seeing prints is that the photographer at least sometimes gets a printable negative and makes a decent job of printing it. I don’t see how you’d be able to tell whether they used stop bath on the film or not?

You would have to look at the molecular level.

For sure the print is - as Ilford expressed it in their Manual - the consummation of the photographer's journey. But what could anyone see in the molecular structure of a print that would cast any light on the role of a stop bath in processing the film?

 

[faberryman]

For sure the print is - as Ilford expressed it in their Manual - the consummation of the photographer's journey. But what could anyone see in the molecular structure of a print that would cast any light on the role of a stop bath in processing the film?

With all love and respect, all you will learn by seeing prints is that the photographer at least sometimes gets a printable negative and makes a decent job of printing it. I don’t see how you’d be able to tell whether they used stop bath on the film or not? Prolific output with consistent quality might be a different matter, I grant you.

For sure the print is - as Ilford expressed it in their Manual - the consummation of the photographer's journey. But what could anyone see in the molecular structure of a print that would cast any light on the role of a stop bath in processing the film?

Here is what I said in post 1161:

"Of course, I'm fine with everyone doing whatever they want. As always, show me your prints."

The last sentence in not meant to be read literally. Are you familiar with the quote "Show me the money." from the movie Jerry McGuire?

As I previously mentioned, my default is to follow the instructions. I give the film and chemical manufacturers with their warehouses full of scientists the benefit of the doubt over random people on the internet, however well intentioned, offering up thought experiments and anecdotal information, even if it means I won't save a nickle. Still, I remain open-minded about the issue, which is why I participate in the thread from time to time.

 

[snusmumriken]

The last sentence in not meant to be read literally. Are you familiar with the quote "Show me the money." from the movie Jerry McGuire?

Nope, sorry, never seen it. I guess it must be the same idea as The proof of the pudding is in the eating? (Who thought that one up?) But I don't know: I don't look at photos by Irving Penn or Sebastaio Salgado and think "There's someone who is sound on stop baths."

Nearly 1200 posts! I bet if we did a poll, we'd find that folk were equally content with their negatives whether they use stop bath or not.

 

[faberryman]

But I don't know: I don't look at photos by Irving Penn or Sebastaio Salgado and think "There's someone who is sound on stop baths."

I don't think about technicalities on first viewing, but I am interested in process, and subsequently do view the image closeup, and think about how the artist may have achieved the look of the photograph.

Nearly 1200 posts! I bet if we did a poll, we'd find that folk were equally content with their negatives whether they use stop bath or not.

Ignorance is bliss - on both sides of the issue.

 

[Sirius Glass]

Nor mine - see post #1082. Still, the emulsion pin-hole theory was plausible enough for me to experiment with leaving out the (optional) stop bath.

Pin holes arise in poorer films and/or when the stop bath solution is not properly mixed, that is too strong.

 

[MattKing]

Nope, sorry, never seen it. I guess it must be the same idea as The proof of the pudding is in the eating? (Who thought that one up?) But I don't know: I don't look at photos by Irving Penn or Sebastaio Salgado and think "There's someone who is sound on stop baths."

Nearly 1200 posts! I bet if we did a poll, we'd find that folk were equally content with their negatives whether they use stop bath or not.

I've never thought the issue was whether the resulting negatives were better - assuming correct use of stop bath vs. correct use of a running water stop.
It is both simpler and easier to achieve correct results when stop bath is employed. Balanced of course, against the need to have and employ an additional chemical.
In addition, there is a benefit in respect to how well, and for how many rolls, the fixer is usable.
I've always thought the thread title should be "Stop Bath. How useful, and how necessary?".

 

[Xylo]

It's funny because I have the feeling that the stop bath has very deep roots. Lets not forget that back in the old days, the gelatin emulsion wasn't as well hardened as it is today. We all know that an alkaline PH will help soften the emulsion. So if you have an already soft emulsion, (even though it isn't hardening) using an acidic stop bath would have benefits.

Also, Kodak have always been sticklers when it comes to ensuring the optimal performance of their products. When the emulsions used to be quite thick, it made sense to halt development using chemicals rather than relying on diffusion of the chemicals in water.

And not everybody uses an alkaline fixer (which didn't exist when the stop bath was invented), so it still is relevant for some people. I have the feeling that using an unbuffered fixer without first using a stop bath would reduce it's life pretty dramatically.

Though I must admit that with the advancements in chemistry, the use of the stop bath is not as important as it once was...

 

[snusmumriken]

Pin holes arise in poorer films and/or when the stop bath solution is not properly mixed, that is too strong.

Do you have a reference for that, please?

 

[Sirius Glass]

Do you have a reference for that, please?

Stuff I learned here from others. I have never had the problem, but then I use Kodak film, Ilford film and Rollei IR 400 and not the post Soviet manufacturer. I also mix chemicals to the manufacturers' specifications.

 

[faberryman]

I have been giving my "save a nickle" comment some thought. It is not meant to be read literally. I intend it to mean save a nominal amount of money.

Anyway, I looked up the price and dilution directions for Kodak Indicator Stop Bath, and, if my calculations are correct, it costs $0.16 per roll if used one shot. Of course, you can reuse the stop bath until it turns purple, so the cost savings of not using it could be considerably less per roll than $0.16. I have no interest in running an experiment to find out. Perhaps someone does and can report back.

And since water bath advocates are into saving nominal amounts of money, let's consider fixer. I think the directions for some fixers tell you how many rolls you can process for a given amount of fixer. For goodness sake, don't trust them. Just continue to use the fixer until your hypo check drops indicate it is exhausted. You may be able to squeeze out a few, or many, more rolls. If you don't want to bother testing, you can just use it as long as you want, and when your prints turn bad you'll know the actual number of rolls the fixer can process. In the same vein, if you use your fixer one-shot, ignore the directions, and dilute it more and more until your prints turn bad. Then dial the dilution back a little and you are good to go.

I have the same advice with respect to hypo clearing agent. Just ignore the instructions and reuse it and/or increase the dilution until your prints turn bad. Then you'll know what you can get away with. Sure it many take five or ten years for your prints to go bad, but you can always reprint the images you made, so there is very little risk.

If you follow these suggestion, you will be well on your way to financial security.

 

[faberryman]

Here's a quick sample calculation to more fully explain what I meant in my last post. In this sample calculation I will not be discussing developer molecules that are in the emulsion itself, only those that are in the liquid residue clinging to the reels and walls of the development tank.

Suppose you are using 500 ml of developer and that in that 500 ml there are 10,000 developer molecules. Yes, I know there are more than that. I'm just using that number to make the calculations easy for illustration purposes.

Assume that after the development stage is completed you pour out 495ml of the developer solution, leaving 5ml clinging to the reels and walls of the tank. That's 1% of the original volume. In that 1% there will be 100 molecules of developer. (1% of 10,000 molecules is 100 molecules.) At this point I will split the analysis into two scenarios.

In scenario one we add 495ml of water to the tank and agitate to mix it with the 5ml of residue from the previous step. There will be 100 molecules of developer in the 500ml of resulting solution. We pour out that solution, leaving 5ml of residue in the tank. In that 5ml there will be an average of 1 molecule of developer. That's the number of developer molecules carried over into the fixer.

In scenario two we add 495ml of acid stop bath into the tank and agitate to mix it with the 5ml of residue from the previous step. There will be 100 molecules of developer in the 500ml of resulting solution. We pour out that solution, leaving 5ml of residue left in the tank. In that 5ml there will be 1 molecule of developer. That's the number of molecules carried over into the fixer. That's exactly the same number of developer molecules carried over as in scenario 1.

If you started with the a different number of developer molecules the carryover ratios will be the same as those described above. For example, if you started with a 100 trillion molecules in 500ml of developer you end up with 10 billion developer molecules carried over into the fixer, regardless of whether you were using a water stop bath or an acid stop bath. The carryover ratio is 0.01% of the original number of molecules.

Suppose there was 10ml instead of 5ml of solution carryover for each step. That would change the fraction of molecules carried over into fixer from 0.01% to 0.04%, independent of whether you use an acid stop bath or a water stop bath.

Conclusion: the number of molecules carried over into the fixer is independent of whether one uses an acid stop bath or a water stop bath.

As noted above, this analysis does not include a discussion of developer molecules that are actually trapped in the gelatin at the beginning of the stop-bath step. However, to argue that an acid stop bath produces less carryover into the fixer one would somehow have to say that, first of all, there are enough developer molecules trapped in the gelatin to matter (which I think it unlikely), and second of all, that an acid stop bath is more efficient in extracting those molecules into solution than a water stop bath, which as far as I am aware has never even been discussed, let alone been proven.

I re-read your example. Why are you bothering to use carry over developer molecules? Why not just say, as in your example, out of 500ml of developer, you will have 5ml of carry over developer, or 1%. 1% ain't much, so nothing to worry about. That seems to be the essence of your argument. All that carryover developer molecules stuff is just unnecessary window dressing.

Query: what are your scientific credentials, particularly in the field of chemistry?