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.