Uh oh, I had no idea that a Paterson tank would contain so much air. If you're using 500 ml of developer with a full liter of air above it I'm skeptical that replenishment is gonna be successful beyond 2 or 3 processing runs. Based on some estimates I made a few weeks back, that 2:1 air/developer volume is gonna contain nearly enough oxygen to kill it off. (I'm presuming that the rate of oxidation is slow enough to withstand several process cycles before the developer becomes badly hurt.) Keep in mind that I'm largely guessing, but if I had to make a bet...
I was wild guessing on the volume. See below for a tested answer -- still with some uncertainty, but better than my guess. BTW, I've been using my Paterson with Xtol replenished, used about a liter of replenisher so far (that's 14 rolls, roughly) and there's been no change. neither color change in the developer (aside from a little blue dye picked up from Fomapan when I forgot to prewash) nor change in the negatives. I know color developer has much less preservative than Xtol stock solution, but is oxidation that much worse over a short period?
So why not fill the Paterson tank with developer? Instead of just covering the film. Then you don’t have to deal with the oxidation issue.
There's a limit to how much developer will fit and still give inversion action, but it should be "up to the red ring" -- there'll still be enough air inside the inversion cap to ensure the vigorous agitation inversion produces in Paterson tanks. Looks like, for the 3-reel size, we're looking at about 200 ml air to 1400 ml of liquid, best case. However, see below, there may be another way.
This inspired a quick experiment.
Using a three reel Paterson Super System 4 tank, with the central core installed but no reels (to save having to dry them), one litre of water fills right up to very near the top of the light-proof cavity. The airspace above the cavity (where the inverted developer flows into) holds a further 400 ml of water before one needs the inversion cap to stop it from over-flowing into the sink. Based on an eyeball estimate, I would estimate that there is a further 100-200 ml of airspace above the water at that time.
So without reels and film, one litre of developer plus 500 - 600 ml of air above it.
With reels and film displacing some of that developer up into the airspace, I would expect the air above the developer would be down to 400-500 ml.
So one litre of developer and ~500 ml of air above it.
The determination of how much air/developer inter-mixing happens is probably worth at least a masters thesis - the channel through which the fluid flows is quite constricted, and the turbulence would be complex. And that submerged, narrow channel would require another very complex determination if one used the full Paterson tank with continuous rotary agitation.
Numbers on the relative volumes are helpful. Roundly 100-150 ml of unavoidable air space relative to 1300-1400 ml of developer, but I think there may be a better way.
We always talk about inversion, and that's how I've agitated ever since I got my first stainless tank, but the first time I ever developed film, and several months later when I first developed unsupervised (still age ten), I had a tank that could not be inverted without just pouring the contents out -- an old FR tank, as I recall, same design as the Yankee adjustable tanks from the 1950s to 1970s. Those tanks used a "swizzle stick" of one sort or another -- either a knurled extension on the top of the reel core or an insert (often a thermometer in an oval housing) that mated with an oval or spline inside the core, to twist the reel and film back and forth in the more or less stationary solution. This produced perfectly fine negatives back then, and my Yankee Agitank, (which I agitate by either sliding the tank fairly sharply left and right along the counter (with the long side facing me) or by tilting on the narrow leg base so alternating edges contact the work surface) also gives good results (at least with B&W film and chemistry -- haven't ever used sheet film in color emulsion).
The Paterson also includes a "swizzle stick" -- and while the one for my older 2-reel tank has long since been lost, my 3-reel tank was purchased new just a few weeks ago and the swizzle stick is safe in the drawer under my darkroom counter.
If I use the swizzle stick to agitate, the solution doesn't get aggressively mixed with air bubbles, it's only in contact with air at a relatively calm surface, and there's no impetus for that air to turn over and present fresh oxygen to the interface. Yes, nitrogen is lighter than air (barely), but density difference on this kind of scale ought to be safe to ignore over three and a quarter minutes. Convection can likely also be ignored over this kind of time frame, both because the design of the tank limits convection to going both in and out through the outer edge (the "pour out" area" -- the "pour in" funnel is inside the core and that's submerged) and because there isn't enough temperature differential (no worse than about 35F) to produce a very strong density variation. I'm neither a fluid interface physicist, nor a photo chemist or organic chemist, but it seems to me that oxidation during a development cycle with "swizzle stick" agitation ought to be at least an order of magnitude less than it would be during the same cycle (time, temperature, and frequency/length of agitation) with inversion.
