Mathematical Models for Biofilms on the Surface of Monuments

Clarelli, Fabrizio; Russo, Cristiana Di; Murialdo, Largo S. Leonardo; Natalini, Roberto

doi:10.1142/9789814280303_0020

Cited by 4 publications

(4 citation statements)

References 7 publications

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“…without vacuum, following [3,12], we can decomposẽ T φ = −φP I + φT φ andm φ = P ∇ x φ + m φ , where P is the hydrostatic pressure, T φ is the excess stress tensor, m φ is the excess interaction force and I is the identity matrix. In line with previous works [11,38,39], we assume that the body forces are negligible. So, equation (3.13) can be written as:…”

Section: Force Balance Equationsmentioning

confidence: 90%

A time-space model for the growth of microalgae biofilms for biofuel production

Polizzi

Bernard

Ribot

2017

Journal of Theoretical Biology

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Section: Force Balance Equationsmentioning

confidence: 90%

A time-space model for the growth of microalgae biofilms for biofuel production

Polizzi

Bernard

Ribot

2017

Journal of Theoretical Biology

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“…leading to α k+1 f u k+1 f + α k+1 p u k+1 p = 0. Finite difference simulations based either on (34) (including results with two or three space dimensions) or (35) are presented in [16,17] for models describing biofilms formations, which share many similarities with the system we are dealing with. We also refer the reader to [7] for two-dimensional simulations in the Finite Volume framework, still based on a direct discretization of the elliptic equation (34).…”

Section: Discretization Of the Correction Stepmentioning

confidence: 99%

“…The proof of Proposition 2.4 follows exactly from the same manipulations we did for the kinetic model, the counterpart (43) being obtained by multiplying the particle momentum balance equation (16) by p u p and using the mass balance equation (15) to transform the inertia terms.…”

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confidence: 93%

Multifluid Flows: A Kinetic Approach

2015

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We propose a numerical scheme for the simulation of fluid-particles flows with two incompressible phases. The numerical strategy is based on a finite volume discretization on staggered grids, with a flavor of kinetic schemes in the definition of the numerical fluxes. We particularly pay attention to the difficulties related to the volume conservation constraint and to the presence of a close-packing term which imposes a threshold on the volume fraction of the disperse phase. We are able to identify stability conditions on the time step to preserve this threshold and the energy dissipation of the original model. The numerical scheme is validated with the simulation of sedimentation flows

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“…The modeling of biofouling involves a complex non-linear treatment because of the unpredictable behavior of microorganisms and their relationship with building materials and environment conditions. Biofouling on solid substrata was recently proposed to predict the growth of microorganisms on the surface of monuments, and a nonlinear hyperbolic-elliptic partial differential equation was used [32][33][34]. The dynamic biofilm growth in porous media at a microscopic scale was developed by implementing a growth of the biofilm in irregular domains by considering the thickness of the substrates as an independent variable [35].…”

Section: Introductionmentioning

confidence: 99%

On the Modelling of Algal Biofouling Growth on Nano-TiO2 Coated and Uncoated Limestones and Sandstones

Graziani

Quagliarini

2018

Coatings

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Algal biofouling on archaeological and historic materials, as well as in modern building façade, is a common phenomenon that occurs when microorganisms of various nature adhere to the material, forming biological stains and patinas. It can significantly deteriorate the aesthetic and even mechanical quality of historic and archaeological artifacts. Thus, predicting the colonization progress of algae on treated and untreated materials can be helpful to establish appropriate schedules and methods of maintenance. In this way, the aim of this research was to modelize the algal colonization on nano-TiO 2 coated and uncoated stone surfaces, usually found in historic and archaeological artifacts, by following Avrami's theory. Particular attention was paid on correlating the model with some properties of the substrate, like roughness and porosity. Biofouling was tested on two sandstones and three limestone with different intrinsic characteristics (porosity, roughness) by means of an accelerated lab-scale test. A suspension of green alga Chlorella mirabilis and cyanobacteria Chroococcidiopsis fissurarum was used as biofouling. Digital image analysis was carried out in order to find the attachment rate and the growth of algal spots. Results show that the attachment specific rate increased linearly with time, and the assumption of a constant growth rate was acceptable. A good agreement between the simulation and the experimental results was obtained with a maximum error of 0.59%.

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Mathematical Models for Biofilms on the Surface of Monuments

Cited by 4 publications

References 7 publications

A time-space model for the growth of microalgae biofilms for biofuel production

A time-space model for the growth of microalgae biofilms for biofuel production

Multifluid Flows: A Kinetic Approach

On the Modelling of Algal Biofouling Growth on Nano-TiO2 Coated and Uncoated Limestones and Sandstones

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