Danger of microplastics for marine ecosystem is recognized and a large number of research works from various viewpoints have been conducted worldwide. However, those about the fragmentation model of plastic pieces under marine environment is limited. The fragmentation of secondary microplastics is estimated to progress primary at beaches. A lot of surveys about the number density of secondary microplastics at beaches have been performed, but the results usually lack the information about the degree of fragmentation; i.e., the progress level from virgin plastics to fully fragmented stage. In this work, by considering the physical process of fragmentation, the time dependent equation describing the number density distribution of the secondary microplastics is derived. The steady state solution for the equation has the form; f(x)=Cx–(β+n+1). Here, f: the number density distribution function, C: the integral constant,x : the size of fragment,β: the exponent of fragmentation rate, n: the dimension of fragmentation (n=1~3). The previous beach surveys showed the value 1.6 to 4.6 for the exponent ofx that correponds to β+n+1. The causes of the difference in the exponent numbers are discussed with the author’s model. The degree of fragmentation of the four types of the secondary microplastics collected at the Yoshizaki Beach in Japan is also evaluated as an another example.
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