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In this paper, a biofilm growth model on an agar substrate is developed based on mass conservation principles, Fick\u2019s first law, and Monod\u2019s kinetic reaction, by considering nutrient diffusion between biofilm and agar substrate. Our results show biofilm growth evolution characteristics such as biofilm thickness, active biomass, and nutrient concentration in the agar substrate. We quantitatively obtain biofilm growth dependence on different parameters. 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