BOILING-POINT RISE OF CONCENTRATED LACTOSE SOLUTIONS UNDER VACUUM

ABSTRACT: The boiling-point rise (BPR) of lactose solutions determines the effective temperature difference in vacuum evaporators and crystallizers used for whey concentration and crystalline-lactose production. Quantifying BPR for 12.7–68.4 wt% lactose at absolute pressures between 24 and 93 kPa provides a sound basis for sizing heat exchangers, estimating steam demand, and predicting plant performance. This study aimed to measure the BPR of aqueous lactose solutions over industrial concentration and pressure ranges and to propose a single correlation that simultaneously accounts for both variables. α-Lactose monohydrate solutions were prepared gravimetrically and boiled in a flat-bottom flask equipped with a reflux condenser to prevent composition drift. The boiling temperature was recorded using a calibrated thermocouple (±0.6 °C), and absolute pressure was measured with differential pressure transmitters (±4.3 Pa). For each solution, the BPR (ΔT_B) was determined at progressively lower pressures. Data were fitted to the Dürring, Antoine, and Clapeyron equations, as well as to the empirical model of Crapiste & Lozano, using non-linear regression. For mass fractions ≤ 0.294, the BPR was essentially pressure-independent (variation < 0.02 °C). Above this threshold, ΔT_B increased with both concentration and pressure reduction; at w = 0.684, it rose from 1.9 °C (93 kPa) to 2.3 °C (24 kPa). The Dürring slope remained ≈ 1.00 in dilute solutions but deviated by 1.8% at w = 0.684, indicating that ignoring pressure leads to underestimation. The Antoine and Clapeyron equations described each individual concentration accurately (R² ≥ 0.999) but required specific constants for every value of w. The Crapiste–Lozano equation, with parameters α = 1.085 × 10⁻³, β = 1.140 × 10⁻², γ = 3.82 × 10⁻², and δ = 1.284 × 10⁻³, reproduced 99% of the data (RMSE = 0.06 °C), with <10% error in most cases. In the typical evaporation window (w ≥ 0.50), neglecting pressure can underpredict BPR by up to 0.4 °C, reducing the effective temperature difference and lowering evaporator capacity by approximately 8%. The proposed correlation eliminates the need for separate tables, simplifying the design and control of lactose evaporators. These results broaden the available data on pressure-dependent BPR for concentrated lactose solutions and offer a correlation that can serve as a practical starting point for process calculations in vacuum whey concentration