The fate of biofouled microplastics in the ocean

Overview

There are an estimated 5.25 trillion plastic pieces floating in the global oceans (Salvador Cesa et al., 2017), with approximately 1.5 million tonnes of microplastics polluting the ocean each year. There is an observed size-based preferential loss of this plastic from the ocean surface into the water column, however, we still lack a full understanding of the mechanisms behind this process (Kooi et al., 2017). This hinders our ability to map the distribution of microplastics in the ocean, monitor their ecological impact or plan for partial removal. However, we have recently made progress in developing a mathematical description of one important process, biofouling (the accumulation of algae on the surface of microplastics) and its role in the vertical movement of floating debris (Kreczak et al., 2021). One of the key findings of the work is that particle properties are the biggest factor in determining the particular excursions that microplastics make beneath the free surface.

However, this study neglected inertial effects, such as added mass and history effects, which result from the lagging boundary layer development of an accelerating particle. It also did not consider the effects of non-spherical geometries. In a recent review (Sevilla, 2021), we discovered that history effects could only be neglected for microplastics of 55micron diameter and less in regular ocean conditions. Given that microplastics are defined as any plastic debris with diameter 1micron – 5mm (Jambeck et al., 2015), there remains a considerable range of microplastics whose dynamics should include an analysis of the history force (see figure, reproduced from Wagner, M. et al. (2014) – scale bar is 1mm). This project aims to investigate the influence of inertial and geometric effects on the migration and ultimate fate of biofouled particles in the ocean.

Research objectives
The overall aim of this project is to gain a deeper fundamental understanding of the role of inertial and geometric effects on the migration of biofouled particles in the ocean. To do this the following tasks will be carried out.
1. Reformulate our model (Kreczak et al., 2021) to include inertial forces for spherical particles;
a. Non-dimensionalise and collect data to estimate the ranges of various parameters in the model relevant to microplastics.
2. Perform perturbation analysis with small parameters in the problem (e.g., Stokes number);
a. Recover our previous model as the zeroth-order approximation.
b. Find the first-order corrections to our previously-derived analytical solutions.
3. Extend the original modelling to include the effects of non-spherical geometries.

Methodology

The student will survey most prevalent microplastics polluting the environment and collect data for computing the envisioned parametric ranges for the mathematical modelling (Objective 1).
The student will formulate the mathematical model to include inertial forces. This model will be non-dimensionalised and a zeroth-order perturbation analysis will be sought to ensure that we recover published results. Once verified, the student will perform perturbation analysis up to the first order (Objective 2). The student will construct a numerical scheme to solve the full set of equations including inertial terms (Objective 3).
The student will examine the effects of non-sphericity by reformulating the problem using prolate spheroids rather than simple spheres. This model will be non-dimensionalised and a zeroth-order perturbation analysis will be sought to ensure that we recover published results. Once verified, the student will perform perturbation analysis up to the first order (Objective 4). The student will construct a numerical scheme to solve the full set of equations including the effects of a non-spherical particle geometry (Objective 5).

Project Timeline

Year 1
Literature review

  1. Research the most prevalent microplastics in the environment.
  2. Data collection to feed into parametric ranges for mathematical modelling. (Objective 1).

Mathematical modelling

  1. Formulate mathematical problem including inertial forces.
  2. Perform zeroth-order perturbation analysis on model and verify that we recover the low-order model (Kreczak et al., 2021).
Year 2

Mathematical modelling

  1. Perform first-order perturbation analysis on model to investigate the influence of inertial forces. (Objective 2).

Numerical modelling

  1. Construct numerical scheme to solve the full set of equations.
  2. Verify the code using analytical solutions derived previously.
  3. Perform parametric analysis and identify key regions of the parametric space.
  4. Investigate deeply into specific parametric ranges. (Objective 3).

Mathematical modelling

  1. Formulate mathematical problem including non-spherical geometric effects.
  2. Perform zeroth-order perturbation analysis on model and verify that we recover the low-order model (Kreczak et al., 2021).
Year 3

Mathematical modelling

  1. Perform first-order perturbation analysis on model to investigate the influence of non-sphericity. (Objective 4).

Numerical modelling

  1. Construct numerical scheme to solve the full set of equations.
  2. Verify the code using analytical solutions derived previously.
  3. Perform parametric analysis and identify key regions of the parametric space.
  4. Investigate deeply into specific parametric ranges. (Objective 5).

Write-up publications, present results

Year 3.5

Write up and complete PhD thesis. Submit final publications.

Training
& Skills

The student will be supported by the existing PhD students and postdocs based in the supervisors’ teams at Heriot-Watt and Newcastle Universities. This will create a superb environment to learn new skills and access the experience gained by their peers.

The student will receive significant training in Asymptotic Analysis and Numerical Methods through the Scottish Mathematical Sciences Training Centre (SMSTC).

The student will receive leading-edge scientific training in fluid mechanics at the von Karman Institute.

Dissemination of results: The student will learn to present their work at leading scientific conferences such as the annual American Physical Society Division of Fluid Dynamics meeting (USA).

References & further reading

Jambeck, J. R., Geyer, R., Wilcox, C., Siegler, T. R., Perryman, M., Andrady, A., Narayan, R., & Law, K. L. (2015). Plastic waste inputs from land into the ocean. Science, 347(6223), 768-771. https://doi.org/10.1126/SCIENCE.1260352

Kooi, M., Nes, E. H. van, Scheffer, M., & Koelmans, A. A. (2017). Upsand Downs in the Ocean: Effects of Biofoulingon Vertical Transport of Microplastics. Environmental Science & Technology, 51(14), 7963. https://doi.org/10.1021/ACS.EST.6B04702

Kreczak, H., Willmott, A. J., & Baggaley, A. W. (2021). Subsurface dynamics of buoyant microplastics subject to algal biofouling. Limnology and Oceanography, 66(9), 3287-3299. https://doi.org/10.1002/LNO.11879

Salvador Cesa, F., Turra, A., & Baruque-Ramos, J. (2017). Synthetic fibers as microplastics in the marine environment: A review from textile perspective with a focus on domestic washings. In Science of the Total Environment. https://doi.org/10.1016/j.scitotenv.2017.04.172

Sevilla, C. (2021). Basset-Boussinesq history term in ocean wave induced microplastic pollution. Unpublished. Heriot-Watt Unviersity.

Wagner, M., Scherer, C., Alvarez-Muñoz, D. et al. (2014) Microplastics in freshwater ecosystems: what we know and what we need to know. Environmental Sciences Europe 26(12). https://doi.org/10.1186/s12302-014-0012-7

Further Information

Apply Now