1. Introduction
Biofilms are complex aggregates of microorganisms embedded in a matrix of extracellular polymeric substances (EPS) (Flemming & Wingender, 2010; Hall-Stoodley et al., 2004). Biofilms are ubiquitous in the natural environment, and have profound impacts on engineering systems and human health (Chen et al., 2014; Hall-Stoodley et al., 2004). For example, biofilm detachment in the food industry and drinking water systems may cause pathogen-related diseases (Shaheen et al., 2019; Shen et al., 2015; Wéry et al., 2008). The EPS matrix, which is a major component of biofilms, protects bacteria from unfavorable environments and chemical stresses (Desmond et al., 2018; Flemming & Wingender, 2010; Simões et al., 2009; Sutherland, 2001), and provides mechanical stability.
Most biofilms develop in flowing aqueous environments, where the flow provides a mechanical loading on the biofilm. The hydrodynamic conditions may result in biofilm deformation, erosive detachment (small particle loss from the biofilm exterior), or sloughing (major biofilm loss) (Blauert et al., 2015; Jafari et al., 2018; Paul et al., 2012; J. B. Xavier et al., 2005). On the other hand, the biofilm’s physical response to mechanical forces, such as deformation and detachment, may affect their structure, composition, porosity, mass transfer characteristics, and fluid dynamic forces (Laspidou & Rittmann, 2004; Purevdorj et al., 2002; Stoodley et al., 2002, 1999). The interactions of hydrodynamics and biofilms are affected by the biofilm’s mechanical properties. Thus, in order to control biofilms effectively, it is critical to understand biofilm mechanical properties and their impact on stress-induced deformation and detachment.
Biofilms behave as viscoelastic materials (Jones et al., 2011; Klapper et al., 2002; Towler et al., 2003), which allows them to adapt and form versatile structures under fluid flow (Hall-Stoodley et al., 2004). This also affects their detachment. However, biofilms are complex, both in microbial ecology, morphology, and EPS chemical composition. This provides them with a great spatial variability (i.e., heterogeneity) of mechanical properties, as well as a potentially large differences between mechanical properties among different biofilms (Böl et al., 2012; Galy et al., 2012; Pavissich et al., 2020; Shaw et al., 2004). This is further complicated by the large variety of experimental techniques used to measure mechanical properties, and the different types of parameters obtained. This makes it difficult to compare the results of different studies (Böl et al., 2012; Gloag et al., 2019; Tallawi et al., 2017). Additionally, while an increasing body of researchers is reporting on biofilm mechanical properties, it is not clear how to use them to predict biofilm deformation and detachment. Having well characterized mechanics and suitable models could allow more effective control of engineered, medical, and other biofilms.
In recent years, researchers have developed mathematical models that incorporate biofilm mechanical behavior, allowing the prediction of biofilm deformation (e.g., Ehret & Böl, 2013; Laspidou et al., 2005; Picioreanu et al., 2018, 2001; Stewart, 1993). Several previous studies (e.g., Picioreanu et al., 2001; Radu et al., 2010; Stewart, 1993; Xavier et al., 2005) focused on the biofilm development considering shear-induced detachment via cohesive strength, or with empirical detachment rate. These models treated biofilms as rigid bodies without deformation (Klapper & Dockery, 2010).
Detachment is a natural process controlled by the biofilm’s mechanical properties (i.e., cohesive strength). However, in cases where biofilm deformation is of interest, it is more accurate to include the effects of deformation on the fluid flow regime, as with fluid-structure interaction models. In order to achieve this, many researchers have simplified biofilms as purely elastic solids, since the short-term response of biofilms is mostly elastic (Dupin et al., 2001; Picioreanu et al., 2018; Taherzadeh et al., 2010). However, viscous behavior may be significant when the time scales are similar to biofilm relaxation (Alpkvist & Klapper, 2007; Liou et al., 2019). For example, Towler et al. (2007) developed a numerical model based on Burger’s material law to describe the biofilm viscoelastic behavior under fluid flows. Alpkvist and Klapper (2007) applied the particle-based immersed boundary method to demonstrate biofilm deformation and detachment under fluid flows. Traditional fluid-structure interaction models can capture the physical behavior accurately, with certain limitations.
Unfortunately, the direct coupling of the fluid domain to the solid domain creates significant computational difficulties, especially for tracking the interface (Mokbel et al., 2018; Rubenstein et al., 2015). Configuration changes, such as large deformations or particle breakup, are difficult to capture with these models. Thus, alternative models are necessary to overcome these limitations.
Multi-phase models have been applied to biofilm studies by treating biofilms as fluids (Alpkvist et al., 2006; Tierra et al., 2015; Zhang et al., 2008b). In particular, phase field (PF) models have been proposed to predict biofilm deformation and detachment (Tierra et al., 2015; Zhang et al., 2008a, 2008b; Zhao et al., 2016). In PF models, the phase-field variable, based on the free energy of the system, controls the morphological changes of the interface without the consideration of boundary tracking (Gao et al., 2009; Zheng & Karniadakis, 2016). Besides, using the Eulerian PF models avoids mesh limitations for large deformations (Gao et al., 2009; Zheng & Karniadakis, 2016). Also, by assuming the biofilm is a viscous or viscoelastic fluid, biofilm detachment due to mechanical stresses can be achieved.
While PF models have the potential to accurately simulate biofilm large deformation and detachment, there are few validation studies. Even with the experimental studies of PF models being reported in other fields (Bai et al., 2017; Han et al., 2015; Nguyen et al., 2016; Pham et al., 2017; Wen et al., 2000), the experimental validation of a PF biofilm model is lacking.
In our study, we determined biofilm mechanical properties experimentally, input them into a continuum PF model, and showed the model can accurately predict biofilm deformation under fluid flow. For this purpose, the Oldroyd-B constitutive equation was used to model biofilm viscoelastic behavior. A synthetic biofilm made of microbial cells embedded in alginate was initially used for model validation, as it is more homogeneous. Further studies were then carried out on aPseudomonas aeruginosa biofilm. This study opens the use of PF continuum modeling for a wide range of biofilm applications.