[Paper Review] A threshold model of plastic waste fragmentation: New insights into the distribution of microplastics in the ocean and its evolution over time

Matthieu George, Frédéric Nallet+1 more|PubMed|Jul 9, 2023

Microplastics and Plastic PollutionEnvironmental Science3 citations

TL;DR

This paper proposes a threshold fragmentation model explaining the bimodal size distribution of microplastics in the ocean, where particles below a critical size (around 1 mm) fragment inefficiently due to physical limits. Using a size-dependent fragmentation efficiency and exponential waste input, the model reproduces the observed abundance peak near 1 mm and predicts a time-invariant power-law scaling with exponent ν ≈ 1.8, reconciling discrepancies in observed microplastic trends over time.

ABSTRACT

Plastic pollution in the aquatic environment has been assessed for many years by ocean waste collection expeditions around the globe or by river sampling. While the total amount of plastic produced worldwide is well documented, the amount of plastic found in the ocean, the distribution of particles on its surface and its evolution over time are still the subject of much debate. In this article, we propose a general fragmentation model, postulating the existence of a critical size below which particle fragmentation becomes extremely unlikely. In the frame of this model, an abundance peak appears for sizes around 1 mm, in agreement with real environmental data. Using, in addition, a realistic exponential waste feed to the ocean, we discuss the relative impact of fragmentation and feed rates, and the temporal evolution of microplastics (MP) distribution. New conclusions on the temporal trend of MP pollution are drawn.

Motivation & Objective

• To explain the observed bimodal size distribution of microplastics in the ocean, particularly the abundance peak near 1 mm and the deficit in the 150–1000 µm range.
• To resolve the contradiction between theoretical fragmentation models (which predict power-law scaling) and environmental data (which show a peak and subsequent decline).
• To investigate how time-dependent waste input and fragmentation efficiency jointly shape the temporal evolution of microplastic size distribution.
• To quantify the impact of fragmentation threshold effects on long-term microplastic accumulation patterns in marine environments.

Proposed method

• Proposes a threshold fragmentation model where particles below a critical size (p_max) cannot fragment further, introducing a physical limit to size reduction.
• Models fragmentation as a stochastic process with size-dependent efficiency, where larger particles fragment more readily than smaller ones.
• Introduces inflation in the fragmentation process (τ = 7% per year) to simulate real-world time-dependent waste input and aging effects.
• Uses a discrete size-class model with logarithmic spacing across 28 size classes, tracking abundance over time (n ≤ 40) and generation (g ≤ 40).
• Applies a sugar-lump model with random initial size dispersity in length and width, while thickness is fixed, to simulate realistic plastic debris geometry.
• Derives analytical expressions for cumulative abundance (S_n) under both standard and inflated fragmentation models, enabling comparison with observed power-law scaling.

Experimental results

Research questions

• RQ1 Why does the observed microplastic size distribution exhibit a broad peak near 1 mm, followed by a decline and then a secondary increase below 150 µm?
• RQ2 How does the introduction of a physical fragmentation threshold affect the time-invariant nature of the size distribution predicted by classical fragmentation models?
• RQ3 What is the role of time-varying waste input (exponential feed) in shaping the temporal evolution of microplastic abundance and size distribution?
• RQ4 To what extent does the fragmentation efficiency dependence on size explain the observed power-law scaling with exponent ν ≈ 1.8 in real oceanic data?
• RQ5 How do inflation effects (7% annual increase in fragmentation efficiency) alter the scaling behavior and cumulative abundance over time?

Key findings

• The model reproduces the observed abundance peak near 1 mm by introducing a physical threshold below which fragmentation becomes highly inefficient.
• With a 7% annual inflation rate in fragmentation efficiency, the model predicts a time-invariant power-law scaling of microplastic abundance with size, with exponent ν ≈ 1.8, closely matching environmental observations.
• The cumulative abundance S_n follows an exponential growth pattern for n > p_max, indicating that the system reaches a quasi-steady state in size distribution despite ongoing fragmentation.
• The model shows that the time-invariant feature of the size distribution is preserved in terms of scaling behavior, though the exponent ν is slightly reduced compared to the classical model (ν < 2).
• The inclusion of size-dependent fragmentation efficiency explains the observed deficit of microplastics between 150 µm and 1 mm, resolving a long-standing discrepancy in the literature.
• Simulations using the sugar-lump model confirm that distinguishing between generation (g) and size class (p) indices is essential due to non-100% fragmentation efficiency, especially near the atomic limit.