Why household crystallisation yields cap where they do

Household and small-scale sugar makers commonly recover much less crystal from a pan of concentrated syrup than the sugar it contains, and the shortfall is often blamed on technique. This paper shows, by mass balance, that most of the shortfall is structural. From a stated massecuite of 100 kg at 93% solids and 85% purity — 79.05 kg of sucrose and 13.95 kg of non-sucrose solids — the theoretical first-strike crystal yield, with the mother liquor exhausted to 40% purity, is 69.75 kg of sucrose, which is 88.2% of the sucrose present and 69.8% of the massecuite mass. The remaining 9.30 kg of sucrose, 11.8% of the total, stays dissolved in 30.25 kg of mother liquor and cannot be removed by any amount of stirring, cooling, or draining, because the non-sucrose solids hold it in a liquor of that purity. Retention then taxes the result a second time: draining in cloth or a basket leaves 18.0% of the mother liquor on the crystals, 5.44 kg, dropping product purity to 95.0%, while a household basket centrifuge leaving 5.0% gives a product purity of 98.5%. After a stated handling loss and washing off the retained liquor, the practical single-strike cap for a drained, washed product is 66.68 kg, which is 84.4% of the sucrose and 66.7% of the massecuite. Reboiling the mother liquor recovers only 3.32 kg in a second strike and 1.33 kg in a third, taking cumulative recovery to 74.4 kg, or 94.1%, at the cost of two further boils. The paper also derives the sap-to-syrup rule from mass balance: litres of sap per litre of syrup equals 87.1 divided by the sap sugar percentage, so 2.0% sap requires 43.6 litres per litre of syrup. All separation equipment figures are SIMULATED, NOT MEASURED.