ABSTRACT
We obtain exact polynomial solutions for two-dimensional coherent complex scalar fields propagating through arbitrary aberrated shift-invariant linear imaging systems. These solutions are used to model nodal-line dynamics of coherent fields output by such systems.
ABSTRACT
This study investigates the functional correspondence between porescale hydrodynamics, mass transfer, pore structure and biofilm morphology during progressive biofilm colonization of a porous medium. Hydrodynamics and the structure of both the porous medium and the biofilm are experimentally measured with 3D particle tracking velocimetry and micro X-ray Computed Tomography, respectively. The analysis focuses on data obtained in a clean porous medium after 36â¯h of biofilm growth. Registration of the particle tracking and X-ray data sets allows to delineate the interplay between porous medium geometry, hydrodynamic and mass transfer processes on the morphology of the developing biofilm. A local analysis revealed wide distributions of wall shear stresses and concentration boundary layer thicknesses. The spatial distribution of the biofilm patches uncovered that the wall shear stresses controlled the biofilm development. Neither external nor internal mass transfer limitations were noticeable in the considered system, consistent with the excess supply of nutrient and electron acceptors. The wall shear stress remained constant in the vicinity of the biofilm but increased substantially elsewhere.
Subject(s)
Biofilms/growth & development , Hydrodynamics , Porosity , Rheology , Stress, Mechanical , X-Ray MicrotomographyABSTRACT
[This corrects the article DOI: 10.1371/journal.pone.0180374.].
ABSTRACT
X-ray tomography is a powerful tool giving access to the morphology of biofilms, in 3D porous media, at the mesoscale. Due to the high water content of biofilms, the attenuation coefficient of biofilms and water are very close, hindering the distinction between biofilms and water without the use of contrast agents. Until now, the use of contrast agents such as barium sulfate, silver-coated micro-particles or 1-chloronaphtalene added to the liquid phase allowed imaging the biofilm 3D morphology. However, these contrast agents are not passive and potentially interact with the biofilm when injected into the sample. Here, we use a natural inorganic compound, namely iron sulfate, as a contrast agent progressively bounded in dilute or colloidal form into the EPS matrix during biofilm growth. By combining a very long source-to-detector distance on a X-ray laboratory source with a Lorentzian filter implemented prior to tomographic reconstruction, we substantially increase the contrast between the biofilm and the surrounding liquid, which allows revealing the 3D biofilm morphology. A comparison of this new method with the method proposed by Davit et al (Davit et al., 2011), which uses barium sulfate as a contrast agent to mark the liquid phase was performed. Quantitative evaluations between the methods revealed substantial differences for the volumetric fractions obtained from both methods. Namely, contrast agent-biofilm interactions (e.g. biofilm detachment) occurring during barium sulfate injection caused a reduction of the biofilm volumetric fraction of more than 50% and displacement of biofilm patches elsewhere in the column. Two key advantages of the newly proposed method are that passive addition of iron sulfate maintains the integrity of the biofilm prior to imaging, and that the biofilm itself is marked by the contrast agent, rather than the liquid phase as in other available methods. The iron sulfate method presented can be applied to understand biofilm development and bioclogging mechanisms in porous materials and the obtained biofilm morphology could be an ideal basis for 3D numerical calculations of hydrodynamic conditions to investigate biofilm-flow coupling.
