# Lagrangian Modeling of Marine Microplastics Fate and Transport: The State of the Science
## 3 Physical Properties and Processes
### Biofouling and Degradation (Physical Transformation Processes)  
According to previous studies, microplastic particles are subjected to some natural transformation processes including fouling, degradation, and mechanical breakdown during their residence time in an aquatic ecosystem that may lead to changes in their physical properties [58]. Biofouling is controlled by different ambient environmental factors such as temperature, salinity, and the availability of sunlight, which is necessary for biofilm (including fine and ultrafine organisms and plankton) growth [76]. On the other hand, particles become more brittle and break apart into smaller pieces as a result of mechanical degradations by weathering, wave actions, interaction with other particles, the seabed, and the shore [110]. Degradation is typically a slow process that takes over 50 years to be fully completed for plastics since they are highly resistant to weathering [7, 110]. However, in the swash zone [111] and some energetic coastal areas (e.g., salt marshes), natural abrasives including sediment and rock are present, and the degradation may be completed sooner, even within 8 weeks based on [112], thereby affecting seasonal microplastics' transport. The main equations employed in the reviewed models in this study for considering biofouling and degradation processes are provided in Table 3. It should be noted that none of the reviewed models are capable of simulating different types of aggregation.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multicolumn{2}{c}{**Mathematical or Empirical**} & \multirow{2}{*}{**Application**} & \multirow{2}{*}{**Defining Parameters**} & \multirow{2}{*}{**Employed in**} & \multirow{2}{*}{**Ref.**} \\ \hline \(1\) & & & & \\ \(v_{s}=c^{n}\times\left[A_{0}+A_{1}sin\left(\frac{2\pi(t+0)}{t}\right)\right]\) & & Settling velocity & & \\  & & & & \\  & & & & \\  & & & & \\  & & & & \\ \hline \(2\) & \(v_{s}=\frac{\pi}{2R}d_{s}^{3}(38.1+0.93d_{s}^{12/7})^{-7/8}\) & Settling velocity & & & \\  & & spherical particles & & \\  & & & & \\  & & & & \\ \hline \(3\) & \(d_{s}=2R(g(\rho_{p}-\rho_{w})/\rho_{w}\theta^{2})^{1/3}\) & Dimensionless diameter of the particle & & & \\  & & the particle & & \\  & & & the same units \((\text{gm}^{-3})\) & \\ \hline \(4\) & \(v_{s}=\frac{\pi}{2}\frac{1}{3}g\frac{(\rho_{p}-\rho_{w})}{\rho_{w}}\frac{2R |}{55.288+12.691}\) & Settling velocity of cylindrical particles & & \(L\) indicates the length of cylinders (mm) & \\ \hline \(5\) & & & & \(d\) is particle diameter \((\text{mm})\), \(\rho_{p}\left(\text{gm}^{-3}\right)\) & \\  & & & and \(\rho_{w}\) (\(\text{gm}^{-3}\)) indicate the density of the particle and the surrounding medium, respectively, \(g\) is the gravitational acceleration \((\text{ms}^{-2})\) and, \(C_{D}\) represents drag coefficient. & [98] \\ \hline \(6\) & \(\begin{array}{l}C_{D}\\ =\frac{24}{R_{p}}(\frac{1-\
u}{R_{p}}+1)^{0.25}\\ +\frac{24}{R_{p}}(\frac{1}{2R_{p}}+0.6595)\Psi^{-R_{p}}\eta^{0.08}\\ +\frac{1}{1+\frac{0.0502\
u}{2R_{p}}\eta^{5.05}}\end{array}\) & & & \\  & & & & \\ \hline \end{tabular}
\end{table}
Table 2: Various equations used for the modeling of hydrodynamic aspects in the reviewed models *.