Measuring Brix in Pastes with a 0–32 Refractometer¶

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A Stage B jar has to be reduced to 60–68 °Brix, measured, before it is sealed: that is both the kinetic lever and the safety hurdle (a_w below the growth minimum of the organisms that matter). A 0–32 brewing refractometer cannot read it. The workaround is gravimetric dilution: weigh paste, weigh water, read the slurry, multiply back. The bench below makes that method reliable. It plans the dilution so the reading lands mid-scale, corrects the things a naive ×4 gets wrong, propagates the reading and weighing errors into the answer, and cross-checks the result against the pot weight.

Three definitions matter. °Brix on a refractometer is refractometric dry substance: the prism is calibrated on sucrose, and everything dissolved (invert sugar, amino acids, potassium salts, melanoidins) reads as if it were sucrose. For a cooked paste the number is a Brix equivalent, which is exactly the basis the 60–68 target is expressed in; do not try to turn it into "real sugar". Insoluble pulp does not dissolve and does not read; in the mass balance it behaves like water, in the liquid phase it does not exist, and that gap is the main error in a naive ×4. And a brewing refractometer's SG scale and any wort correction factor are for wort; read the Brix scale and apply no factor.

The procedure¶

1. Weigh the paste on a 0.01 g scale (10.0 g is enough; 50 g if the scale only reads to 1 g).
2. Weigh in distilled or boiled-cooled water by mass, never by volume: ×4 for an expected 60–68 °Brix paste (10.0 g + 30.0 g), ×3 for 40–50.
3. Stir until uniform, a minute or two; pressed liquid or a thin smear, not lumps.
4. Cool to 20 ± 3 °C; the slurry cools on a spoon in a minute. Never read a hot sample.
5. Read the Brix scale and note the raw reading with the masses.
6. Enter the numbers; log the raw reading alongside the result.

The bench¶

It also runs on its own at /assets/apps/brix-dilution-bench/index.html if the frame above is awkward on a phone.

The arithmetic¶

with \(R\) the corrected slurry reading, \(p\) the insoluble-pulp mass fraction and \(m_{pot}\) the current pot contents. \(B_{liquid}\) is what water activity depends on and drives the verdict; \(B_{whole}\) is the right basis for the water still to remove. The two are consistent on their own bases.

Errors combine as \(\delta B / B = \sqrt{(\delta R / R)^2 + (\delta d / d)^2}\) with \(\delta d / d \approx \sqrt{(\delta m_p / m_p)^2 + (\delta m_w / m_w)^2}\). With a ±0.2 °Brix reading at 16.2 and a 0.01 g / 0.1 g pair of scales, a 64.8 °Brix result carries ±0.8; the reading term dominates, which is why the planner puts the reading mid-scale.

The corrections and their size¶

Water activity is estimated two ways (Norrish with sucrose and hexose constants, Money–Born likewise) and shown as the band they span. A Stage B jar is not pure sucrose: glycine and potassium salts depress a_w more than the sugar mapping predicts, collagen peptides and maltodextrin less, so treat 60–68 °Brix as the operational handle and the a_w band as indicative.

The mass-balance cross-check uses the start mass and the start Brix (a runny purée read neat on the 0–32 scale) against the current pot contents: solids are conserved, so \(B_{now} = m_{start} B_{start} / m_{now}\). When it disagrees with the dilution result by more than the combined error, the bench says which assumption is likely wrong: water that entered unaccounted for (lid condensate, a rinse) pushes the mass balance up; a pulp fraction set too high, or a start reading taken on pulp rather than pressed liquid, pushes it down.