Pitching a second packet of yeast

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You want as much oxygen in your wort as possible at the moment you pitch the yeast

Sorry to be the naysayer but this isn't true.

Firstly, you want enough oxygen for the yeast to be able to make enough ergosterol and fatty acids to survive the alcohol they will generate, generally around 10 - 15 mg/l O2. You don't want more than that, it just invites problems including premature staling. For reference "as much oxygen as possible" is around 40 mg/l under normal conditions.

Secondly, it's obviously better to add the oxygen to the yeast rather than to the wort, so ideally you want oxygen level at pitch to be zero and to add the oxygen after pitching.

I am aware that commercial breweries often add oxygen before pitching but that doesn't make it ideal: in fact it's due to operational considerations including solubility. Adding the O2 in line from castout to fermenter vastly increases the amount that goes into solution, a commercial operation won't accept the 90% loss that's common with home brew setups.
 
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Sorry to be the naysayer but this isn't true.

Firstly, you want enough oxygen for the yeast to be able to make enough ergosterol and fatty acids to survive the alcohol they will generate, generally around 10 - 15 mg/l O2. You don't want more than that, it just invites problems including premature staling. For reference "as much oxygen as possible" is around 40 mg/l under normal conditions.

Secondly, it's obviously better to add the oxygen to the yeast rather than to the wort, so ideally you want oxygen level at pitch to be zero and to add the oxygen after pitching.

I am aware that commercial breweries often add oxygen before pitching but that doesn't make it ideal: in fact it's due to operational considerations including solubility. Adding the O2 in line from castout to fermenter vastly increases the amount that goes into solution, a commercial operation won't accept the 90% loss that's common with home brew setups.

Totally understand this, but for the homebrewer, getting much more than 15mg/l of O2 into solution would take considerable effort and/or waste a lot of O2.

If you're just sticking aeration stone into the wort after pitch, and giving it a squirt of O2 for a minute or two, you wont have any issues. You would have to pump A LOT of O2 through the wort to get close saturation. As you have said, most of it is lost to the atmosphere anyway.

Do you think that excessive 02 is a really a concern for the home brewer using an aeration stone?
 
I think it's a minor concern.

When I was using an O2 bottle + sinter setup I had a couple of brews that show evidence of oxidation which I sheeted back to the oxygen. One of them was definitely my fault, I oxygenated the wrong cube for the wrong time.

Where this might be of concern is that I'm talking obvious, "cardboard", lipid oxidation here. More subtle effects such as loss of evanescent aromas would not be evident but the beer would be less enjoyable.
 
Just something i found looking up the topic:
https://byo.com/bock/item/958-keys-to-aeration-advanced-brewing

Some interesting points based on what you said were:
At sea level and freezing (32 °F or 0 °C) pure water can hold up to 14.6 milligrams per liter (mg/L, equivalent to parts per million, or ppm) of dissolved oxygen
Minimum level is considered to be 5 mg/L, and the optimum demand for oxygen by some yeast strains at higher specific gravities increases to as much as 12–13 mg/L
Major American lager brewers, for example, strive for a dissolved oxygen level of 9-10 mg/L in their wort.
Pitch a large population of healthy yeast and aerate the chilled wort well.

So not sure what you mean by 40mg/L as it says that the higher the SG the less oxygen the wort can hold?
 
The stated maximum (~15 mg/l @ 0 oC) is for water in equilibrium with air at atmospheric pressure*.

Henry's law applies, so for O2 at STP the equilibrium point is higher. For O2 under pressure, the equilibrium point is higher again. The Henry's law coefficient reduces with temperature** so at typical pitching temps the equilibria are a bit lower.

As previously, large breweries go for a certain DO2 level due to operational constraints. You actually don't want any DO2 at all, you want the oxygen to be taken up by the yeast.

The presence of sugar limits the solubility of oxygen due to the "salting out" effect, basically dependent on the fraction of volume of the fluid which is water (in which O2 is soluble) vs sugars and salts (in which O2 is not soluble). As a rough round guide, in a normal wort of about 12 oP the O2 solubility will be around 15% lower than that of water. If you are using oxygenation rather than aeration this effect is not important for any practical wort gravity, you will still be able to get enough oxygen into solution.

* I think part of the reason for the confusion is that people are used to solubilities of solids. Solubilities of gases are completely different, best example is that gas solubilities decrease with increasing temperature while solid solubilities increase. This is because they are governed by different mechanisms.

**For this you need the Van T'Hoff equation
 
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