$10$ mg$/$L monodisperse particle suspensions with initially $($a$)$ all $10$ nm spherical particles and $($b$)$ all $1$m spherical particles. Assume that the only removal mechanism of the particles is through collision and attachment to other particles $($i$.$e$.,$ ignore collisions with larger particles formed by earlier particle$-$particle interactions$).$ The process is occurring with alpha$=1,$ particle densities of $1\mathrm{.}2$ g$/$cm$3,$ a velocity gradient of $251/$s$,$ and temperature of $25\backslash$deg C$.$

a$)$ For each particle size give the half$-$life.

b$)$ Indicate the dominant flocculation process for each particle size.