Jialin Wu

Phase misalignment between periodic pollutant emissions and receptor inhalation can fundamentally bias exposure estimations, yet it is rarely quantified in transient assessments. Here we propose Phase-Independent Pollutant Exposure (PIPE), a general exposure metric that removes this temporal randomness by integrating phase-resolved exposure over a phase-difference probability distribution. The phase-dependent exposure function is reconstructed efficiently using a Fourier series surrogate built from sparse samples, enabling deterministic calculation of the expected exposure without resource-demanding Monte Carlo sampling. We demonstrate the framework using a short-range indoor exposure case representative of periodic human emissions resolved by transient computational fluid dynamics (CFD). Results showed that across multiple breathing intensities, breathing/coughing waveforms, interpersonal distances (0.5–1.5 m), and exposure durations, phase-dependent variability was consistently pronounced and accurately captured by the proposed model. Phase differences increased cumulative inhaled exposure by up to 9.58 times, with the largest amplification occurring at close range (0.5 m) under intense breathing. Flow-field analysis indicates that specific phase relationships can suppress turbulent kinetic energy in the inter-person region, limiting dispersion and thereby elevating near-field concentrations and intake. Although phase effects attenuate with time due to accumulation and mixing, they remain non-negligible even over extended contact (up to 60 s). Notably, PIPE is generally lower than exposure under perfectly synchronized phases, but becomes 1.20–4.97 times higher in close-range, high-intensity scenarios. By explicitly accounting for phase uncertainty, PIPE provides a transferable and computationally efficient methodology to stabilize exposure assessment for periodic sources, improving the robustness of process-based risk metrics relevant to environmental and human exposure evaluation.