Step fermentation idea- can this work?

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I'd call it recreation rather than experimentation, as long as your having fun...
Mark
 
My initial thought is that yeast can't go on multiplying (dividing themselves) over and over despite addition of fresh wort, about 3-4 splits and they've depleted their initial reserve of 'nutrients' and should be entering the stationary phase and settling out rather than being force fed sugars from additional wort pitches (a bit like under pitching)
I'm sure someone far more learned will weigh in soon with the science.

Not so: I routinely put yeast through about 17 generations and that was in grape juice, which is a much poorer growth medium than is wort.

To make up enough yeast to pitch 300 kl of grape juice we used a kilo of dried yeast ( ~ 6 * 10^12 cells) and grew it up unitl we had about 8000 l at . 10^8 cells / ml (about 10^18 cells total). That's about 17 doublings (log2(1.667 x 10^5) = 17.35).

Wine yeast is also much more sensitive to sterol status as it has to cope with higher alcohol at higher temperatures. The lipid bilayer is a liquid crystal and as such it has a melting point. Alcohol becomes far more toxic to the cell above this melting point because it can cross the membrane more easily. One of the principal functions of ergosterol is to increase this melting point.
 

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