*Review* **Lattice Boltzmann Method in Modeling Biofilm Formation, Growth and Detachment**

**Mojtaba Aghajani Delavar and Junye Wang \***

> Faculty of Science and Technology, Athabasca University, Athabasca, AB T9S 3A3, Canada; maghajanidelavar@athabascau.ca

**\*** Correspondence: junyew@athabascau.ca; Tel.: +1-7803-944-883

**Abstract:** Biofilms are a complex and heterogeneous aggregation of multiple populations of microorganisms linked together by their excretion of extracellular polymer substances (EPS). Biofilms can cause many serious problems, such as chronic infections, food contamination and equipment corrosion, although they can be useful for constructive purposes, such as in wastewater treatment, heavy metal removal from hazardous waste sites, biofuel production, power generation through microbial fuel cells and microbially enhanced oil recovery; however, biofilm formation and growth are complex due to interactions among physicochemical and biological processes under operational and environmental conditions. Advanced numerical modeling techniques using the lattice Boltzmann method (LBM) are enabling the prediction of biofilm formation and growth and microbial community structures. This study is the first attempt to perform a general review on major contributions to LBM-based biofilm models, ranging from pioneering efforts to more recent progress. We present our understanding of the modeling of biofilm formation, growth and detachment using LBM-based models and present the fundamental aspects of various LBM-based biofilm models. We describe how the LBM couples with cellular automata (CA) and individual-based model (IbM) approaches and discuss their applications in assessing the spatiotemporal distribution of biofilms and their associated parameters and evaluating bioconversion efficiency. Finally, we discuss the main features and drawbacks of LBM-based biofilm models from ecological and biotechnological perspectives and identify current knowledge gaps and future research priorities.

**Keywords:** biofilm; lattice Boltzmann method; cellular automata; individual-based model
