Predicting a Wide Range of Fractal Dimensions of Salt-Induced\nAggregates in Water Using a Random Forest Model

Salt-induced colloidal aggregates\ncan significantly influence contaminant\nfate and transport in natural and engineered systems. These aggregates’\nfractal dimensions (<i>d</i><sub><i>f</i></sub>), ranging from 1.4 to 2.2, depend on various system variables. However,\nthe quantitative relationship between these variables and <i>d</i><sub><i>f</i></sub> of aggregates has not been\nfully explored, especially in predicting a wide range of <i>d</i><sub><i>f</i></sub>. Here, we developed a random forest\nmodel capable of predicting the complete range of aggregate <i>d</i><sub><i>f</i></sub> using just four simple physical\nand chemical parameters of the aggregating system as inputs. The model\naccurately predicts the <i>d</i><sub><i>f</i></sub> of aggregates formed by colloids of different sizes, ranging from\nnano to micro sizes, after being trained and tested on appropriate\ndata sets. Ionic strength (IS) has the most significant influence\non the <i>d</i><sub><i>f</i></sub> of aggregates\nformed by microsized particles followed by the relative hydrodynamic\nradius of aggregates (<i>R</i><sub><i>h</i></sub>/<i>R</i><sub><i>p</i></sub>), particle concentration\n(<i>C</i><sub><i>p</i></sub>), and primary particle\nradius (<i>R</i><sub><i>p</i></sub>). For aggregates\nformed by both nano- and microsized particles, IS still has a strong\ninfluence on the <i>d</i><sub><i>f</i></sub>,\nwith the significance of <i>R</i><sub><i>p</i></sub> increasing. All four inputs are negatively correlated with\npredicting the <i>d</i><sub><i>f</i></sub> of\naggregates. The predictions align well with the physical interpretations.