Surface Erosion Equations for Degradation Analysis of Several Common Three-Dimensional Shapes of Plastic Materials

Equations were derived for the biodegradative erosion of the surfaces of arbitrarily-sized circular and square objects, i.e., the decrease in volume caused by the catalytic activity of enzymes secreted by microorganisms attached to the object surfaces. Surface erosion is the primary mode of biodegradation for polyhydroxyalkanoate (PHA) objects resting on the ocean floor. Although the derivations were motivated by a need to assess the time-varying biodegradation and ultimate disintegration of PHA tubes and straws in the benthic environment, generality was maintained during the mathematical development such that the resulting equations are also applicable to other circular and square objects, including cylindrical rings, discs, and solid rods, and square plates, cubes, and prisms. Moreover, the equations are applicable to abiotic degradation via physical erosion, not just to biotic degradation caused by microbes. Surface erosion is expressed in terms of the ratio of the instantaneous mass to the initial mass, which is generally nonlinear with respect to time. The value of this ratio and the relative dimensions of the object establish a surface erosion function and its evolution over the lifetime of the object. Hence, the rate of degradation is not constant in the theory, but rather is prescribed by the irregular mass loss and the original geometry of the 3D object.