Postfragmentation density function for bacterial aggregates in laminar flow

Abstract

The postfragmentation probability density of daughter flocs is one of the least well-understood aspects of modeling flocculation. We use three-dimensional positional data of Klebsiella pneumoniae bacterial flocs in suspension and the knowledge of hydrodynamic properties of a laminar flow field to construct a probability density function of floc volumes after a fragmentation event. We provide computational results which predict that the primary fragmentation mechanism for large flocs is erosion. The postfragmentation probability density function has a strong dependence on the size of the original floc and indicates that most fragmentation events result in clumps of one to three bacteria eroding from the original floc. We also provide numerical evidence that exhaustive fragmentation yields a limiting density inconsistent with the log-normal density predicted in the literature, most likely due to the heterogeneous nature of K. pneumoniae flocs. To support our conclusions, artificial flocs were generated and display similar postfragmentation density and exhaustive fragmentation.

An inverse problem for a class of conditional probability measure-dependent evolution equations

“…In particular, we are interested in the propensity of suspended bacterial aggregates to fragment in a flowing system. The model proposed in [29] uses knowledge of the hydrodynamics to predict a breakage event and thus the post fragmentation density Γ. With this work, we now have a tool to bridge the gap between the experimental and microscale modeling efforts for fragmentation.…”

“…In [29], we found that the resulting post-fragmentation density for small parent flocs resembles a Beta distribution with α = β = 2 (see Figure 1a for an illustration). Therefore, the first artificial data set was generated from the forward problem by assuming model rates given in (22)–(23) and a post-fragmentation density function a Beta distribution with α = β = 2, $${\mathrm{\Gamma }}_{\text{true}}false(x,yfalse)={\mathrm{𝟙}}_{false[0,yfalse]}false(xfalse)\frac{6xfalse(y-xfalse)}{y^3}.$$ As in Section 4.1, we chose exponential initial size-distribution b 0 ( x ) = 10 3 exp( x ) on Q = [0, 1] for t f = 10.…”

“…In the literature, it is widespread to assume that this distribution is is normally distributed for all parent floc size [55, 66]. However, in [29], we focused only on the fragmentation and developed a microscale mathematical model which contradicts this result and predicted that the distribution is non-normal and conditionally dependent on parent size. Thus it is clear that there is a need for a methodology to identify this conditional distribution from available data.…”

Variable viscosity and density biofilm simulations using an immersed boundary method, part II: Experimental validation and the heterogeneous rheology-IBM

“…To ensure that the biofilm is not attached to the plates and is sufficiently far from the plate to induce a rotating, or tumbling motion, these simulations only include bacteria that are greater than 8.8 µm from either plate at the start. With the physical parameters we use, the bacteria aggregation rotates and is deformed by the fluid shear forces exerted by the fluid [6]. In Blaser et al [3], analytical results on the frequency at which a solid ellipsoid will rotate in shear flow are provided.…”

Sticky surface: sphere–sphere adhesion dynamics

“…The present study is geared towards tracking the size distribution of spherical floc aggregates in stagnant fluid conditions [29]. The spherical particles within the flocs adhere through well-defined disc-like patches covered with binding ligands.…”