Equivalent HTST pasteurisation schedules for ice cream mixes between 80 and 90°C: Comparison of Bigelow and Arrhenius models

Abstract

Background

Commercial dairy pasteurisation relies on High-Temperature Short-Time (HTST) systems designed around equivalent time–temperature schedules. These are traditionally interpreted using the Bigelow model, which assumes a constant z-value over the operating range. Arrhenius-based approaches, which introduce temperature-dependent z-values, have been suggested as a better alternative to the classical constant-z Bigelow relationship.

Aim

To determine whether Arrhenius modelling provides a practical advantage over Bigelow for calculating equivalent HTST pasteurisation schedules for ice cream mixes.

Methods

Paired HTST schedules from the US Pasteurised Milk Ordinance (PMO) (80.0°C/25 s and 83.0°C/15 s) and New Zealand DPC 3 (79.5°C/15 s and 85.5°C/10 s) were used to derive process z-values from established dairy pasteurisation criteria. Equivalent holding times between 80 and 90°C were calculated using Bigelow and Arrhenius models. Agreement was assessed using mean absolute error and maximum relative divergence. UK statutory schedules spanning low-temperature long-time (LTLT), HTST and ultra-high-temperature (UHT) processing were also examined to assess the limitations of extrapolating process-derived z-values across different thermal regimes.

Results

Bigelow z-values derived from the US and New Zealand schedules were 13.52°C and 34.07°C, respectively. Across 79.5–90°C, Bigelow and Arrhenius predictions were closely aligned, with mean absolute differences ≤0.037 s and maximum relative divergences <1.4%. Thus, temperature-dependent z-values provided no meaningful practical advantage within the evaluated HTST range. In contrast, z-values derived across UK LTLT, HTST and UHT schedules varied substantially (approximately 5.2–79.3°C), indicating that process-derived z-values should not be treated as universal microbial kinetic constants or extrapolated across distinct processing regimes.

Industrial Implications

For dairy HTST processing within the evaluated range, the Bigelow model provides an adequate and simpler basis for calculating equivalent pasteurisation schedules. Process-derived z-values should be restricted to the temperature range and processing regime from which they are derived.