The dynamics of biofilm lifecycle are deeply influenced by the surrounding environment and the interactions between sessile and planktonic phenotypes. Bacterial biofilms typically develop in three distinct stages: attachment of cells to a surface, growth of cells into colonies, and detachment of cells from the colony into the surrounding medium. The attachment of planktonic cells from the surrounding environment plays a prominent role in the initial phase of biofilm lifecycle as it initiates the colony formation. During the maturation stage, biofilms harbor numerous microenvironments which lead to metabolic heterogeneity. Such microniches provide conditions suitable for the growth of new species, which are present in the bulk liquid as planktonic cells and can penetrate the porous biofilm matrix. We present a 1D continuum model on the interaction of sessile and planktonic phenotypes in biofilm lifestyle. Such a model is able to reproduce the key role of planktonic cells in the formation and development of biofilms by considering the initial attachment and colonization phenomena. The model is formulated as a hyperbolic–elliptic free boundary value problem with vanishing initial value which considers the concentrations of planktonic and sessile cells as state variables. Hyperbolic equations reproduce the transport and growth of sessile species, while elliptic equations model the diffusion and conversion of planktonic cells and dissolved substrates. The attachment is modeled as a continuous, deterministic process which depends on the concentrations of the attaching species. The growth of new species is modeled through a reaction term in the hyperbolic equations which depends on the concentration of planktonic species within the biofilm. Existence and uniqueness of solutions are discussed and proved for the attachment regime. Finally, some numerical examples show that the proposed model correctly reproduces the growth of new species within the biofilm and overcomes the ecological restrictions characterizing the Wanner–Gujer-type models.

生物膜生命周期的动态深受周围环境以及固着和浮游表型之间的相互作用的影响。细菌生物膜通常在三个不同的阶段发展：细胞附着于表面，细胞生长成集落，以及细胞从集落分离到周围培养基中。来自周围环境的浮游细胞的附着在生物膜生命周期的初始阶段起着重要作用，因为它启动了集落形成。在成熟阶段，生物膜具有许多导致代谢异质性的微环境。这种微生态系统提供了适合新物种生长的条件，这些新物种作为浮游细胞存在于大量液体中并且可以穿透多孔生物膜基质。我们提出了一个关于生物膜生活方式中固着和浮游表型相互作用的一维连续模型。通过考虑初始附着和定植现象，这样的模型能够重现浮游细胞在生物膜形成和发展中的关键作用。该模型被表述为具有消失初始值的双曲线-椭圆自由边界值问题，该问题将浮游生物和固着细胞的浓度视为状态变量。双曲线方程再现固着物种的运输和生长，而椭圆方程模拟浮游细胞和溶解基质的扩散和转化。附着被建模为一个连续的、确定性的过程，它取决于附着物质的浓度。新物种的生长通过双曲线方程中的反应项建模，该方程取决于生物膜内浮游物种的浓度。讨论并证明了附着机制的解的存在性和唯一性。最后，一些数值例子表明，所提出的模型正确地再现了生物膜内新物种的生长，并克服了 Wanner-Gujer 型模型的生态限制。