scholarly journals A Thin-Film Lubrication Model for Biofilm Expansion Under Strong Adhesion

2021 ◽  
Author(s):  
Alexander K. Y. Tam ◽  
Brendan Harding ◽  
J. Edward F. Green ◽  
Sanjeeva Balasuriya ◽  
Benjamin J. Binder
Keyword(s):  
Thin Film ◽  
Cell Proliferation ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Extensional Flow ◽  
Model Parameters ◽  
Two Dimensional ◽  
Microbial Biofilm ◽  
Biofilm Growth ◽  
Expansion Speed

Understanding microbial biofilm growth is important to public health, because biofilms are a leading cause of persistent clinical infections. In this paper, we develop a thin-film model for microbial biofilm growth on a solid substratum to which it adheres strongly. We model biofilms as two-phase viscous fluid mixtures of living cells and extracellular fluid. The model tracks the movement, depletion, and uptake of nutrients explicitly, and incorporates cell proliferation via a nutrient-dependent source term. Notably, our thin-film reduction is two-dimensional and includes the vertical dependence of cell volume fraction. Numerical solutions show that this vertical dependence is weak for biologically-feasible parameters, reinforcing results from previous models in which this dependence was neglected. We exploit this weak dependence by writing and solving a simplified one-dimensional model that is computationally more efficient than the full model. We use both the one and two-dimensional models to predict how model parameters affect expansion speed and biofilm thickness. This analysis reveals that expansion speed depends on cell proliferation, nutrient availability, cell-cell adhesion on the upper surface, and slip on the biofilm-substratum interface. Our numerical solutions provide a means to qualitatively distinguish between the extensional flow and lubrication regimes, and quantitative predictions that can be tested in future experiments.

scholarly journals A thin-film extensional flow model for biofilm expansion by sliding motility

2019 ◽  
Vol 475 (2229) ◽  
pp. 20190175 ◽  
Author(s):  
Alexander Tam ◽  
J. Edward F. Green ◽  
Sanjeeva Balasuriya ◽  
Ee Lin Tek ◽  
Jennifer M. Gardner ◽  
...  
Keyword(s):  
Thin Film ◽  
Flow Model ◽  
Numerical Solutions ◽  
Extensional Flow ◽  
Model Parameters ◽  
Two Phase ◽  
Experimental Conditions ◽  
Fluid Mixture ◽  
Expansion Speed ◽  
Sliding Motility

In the presence of glycoproteins, bacterial and yeast biofilms are hypothesized to expand by sliding motility. This involves a sheet of cells spreading as a unit, facilitated by cell proliferation and weak adhesion to the substratum. In this paper, we derive an extensional flow model for biofilm expansion by sliding motility to test this hypothesis. We model the biofilm as a two-phase (living cells and an extracellular matrix) viscous fluid mixture, and model nutrient depletion and uptake from the substratum. Applying the thin-film approximation simplifies the model, and reduces it to one-dimensional axisymmetric form. Comparison with Saccharomyces cerevisiae mat formation experiments reveals good agreement between experimental expansion speed and numerical solutions to the model with O ( 1 ) parameters estimated from experiments. This confirms that sliding motility is a possible mechanism for yeast biofilm expansion. Having established the biological relevance of the model, we then demonstrate how the model parameters affect expansion speed, enabling us to predict biofilm expansion for different experimental conditions. Finally, we show that our model can explain the ridge formation observed in some biofilms. This is especially true if surface tension is low, as hypothesized for sliding motility.

A general theory for the dynamics of thin viscous sheets

2002 ◽  
Vol 457 ◽  
pp. 255-283 ◽  
Author(s):  
N. M. RIBE
Keyword(s):  
Evolution Equations ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Extensional Flow ◽  
Constant Thickness ◽  
Scaling Analysis ◽  
Two Dimensional ◽  
Principal Curvatures ◽  
Kinematic Evolution ◽  
Starting Point

A model for the deformation of thin viscous sheets of arbitrary shape subject to arbitrary loading is presented. The starting point is a scaling analysis based on an analytical solution of the Stokes equations for the flow in a shallow (nearly planar) sheet with constant thickness T0 and principal curvatures k1 and k2, loaded by an harmonic normal stress with wavenumbers q1 and q2 in the directions of principal curvature. Two distinct types of deformation can occur: an ‘inextensional’ (bending) mode when [mid ]L3(k1q22 + k2q21)[mid ] [Lt ] ε, and a ‘membrane’ (stretching) mode when [mid ]L3(k1q22 + k2q21)[mid ] [Gt ] ε, where L ≡ (q21 + q22)−1/2 and ε = T0/L [Lt ] 1. The scales revealed by the shallow-sheet solution together with asympotic expansions in powers of ε are used to reduce the three-dimensional equations for the flow in the sheet to a set of equivalent two-dimensional equations, valid in both the inextensional and membrane limits, for the velocity U of the sheet midsurface. Finally, kinematic evolution equations for the sheet shape (metric and curvature tensors) and thickness are derived. Illustrative numerical solutions of the equations are presented for a variety of buoyancy-driven deformations that exhibit buckling instabilities. A collapsing hemispherical dome with radius L deforms initially in a compressional membrane mode, except in bending boundary layers of width ∼ (εL)1/2 near a clamped equatorial edge, and is unstable to a buckling mode which propagates into the dome from that edge. Buckling instabilities are suppressed by the extensional flow in a sagging inverted dome (pendant drop), which consequently evolves entirely in the membrane mode. A two-dimensional viscous jet falling onto a rigid plate exhibits steady periodic folding, the frequency of which varies with the jet height and extrusion rate in a way similar to that observed experimentally.

Electrostatically controlled large-amplitude, non-axisymmetric waves in thin film flows down a cylinder

2013 ◽  
Vol 736 ◽  
Author(s):  
A. W. Wray ◽  
D. T. Papageorgiou ◽  
O. K. Matar
Keyword(s):  
Thin Film ◽  
Field Strength ◽  
Electric Field ◽  
Evolution Equation ◽  
Electric Field Strength ◽  
Numerical Solutions ◽  
Outer Cylinder ◽  
Outer Electrode ◽  
Two Dimensional ◽  
Film Flows

AbstractWe examine the dynamics of a thin film flowing under gravity down the exterior of a vertically aligned inner cylinder, with a co-aligned, concentric cylinder acting as an outer electrode; the space between the outer cylinder and the film is occupied by an inviscid gas. The stability of the interface is studied when it is subjected to an electric field, applied by imposing a potential difference between the two cylinders. Leaky-dielectric theory is used in conjunction with asymptotic reduction, in the large-conductivity limit, to derive a single, two-dimensional evolution equation for the interfacial location, which accounts for gravity, capillarity, and electrostatic effects. A linear stability analysis is carried out which shows that non-axisymmetric modes become more dominant with increasing electric field strength. Our fully two-dimensional numerical solutions of the evolution equation demonstrate qualitative agreement between the trends observed in the nonlinear regime and those predicted by linear theory. These numerical solutions also show that, depending on the electric field strength and the relative proximity of the outer electrode, the interface either remains spatially uniform, or exhibits either axisymmetric or, importantly, non-axisymmetric travelling waves. The effect of wave formation on the interfacial area is investigated in connection with the use of electric fields to control thin film flows to enhance heat and mass transfer rates.

Results from the multi-species Benchmark Problem 3 (BM3) using two-dimensional models

2004 ◽  
Vol 49 (11-12) ◽  
pp. 169-176 ◽  
Author(s):  
D.R. Noguera ◽  
C. Picioreanu
Keyword(s):  
Numerical Solutions ◽  
Mathematical Framework ◽  
Two Dimensional ◽  
Benchmark Problem ◽  
Biofilm Growth ◽  
One Dimensional ◽  
Bulk Substrate ◽  
The One ◽  
Definition Of ◽  
Multidimensional Models

In addition to the one-dimensional solutions of a multi-species benchmark problem (BM3) presented earlier (Rittmann et al., 2004), we offer solutions using two-dimensional (2-D) models. Both 2-D models (called here DN and CP) used numerical solutions to BM3 based on a similar mathematical framework of the one-dimensional AQUASIM-built models submitted by Wanner (model W) and Morgenroth (model M1), described in detail elsewhere (Rittmann et al., 2004). The CP model used differential equations to simulate substrate gradients and biomass growth and a particle-based approach to describe biomass division and biofilm growth. The DN model simulated substrate and biomass using a cellular automaton approach. For several conditions stipulated in BM3, the multidimensional models provided very similar results to the 1-D models in terms of bulk substrate concentrations and fluxes into the biofilm. The similarity can be attributed to the definition of BM3, which restricted the problem to a flat biofilm in contact with a completely mixed liquid phase, and therefore, without any salient characteristics to be captured in a multidimensional domain. On the other hand, the models predicted significantly different accumulations of the different types of biomass, likely reflecting differences in the way biomass spread within the biofilm is simulated.

Instrumentation For Quantitative Microscopy

1977 ◽  
Vol 35 ◽  
pp. 206-209
Author(s):  
B. Ralph ◽  
A.R. Jones
Keyword(s):  
Volume Fraction ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Automatic Data ◽  
Phase Volume Fraction ◽  
Statistical Confidence ◽  
Resultant Data ◽  
Automatic Data Collection ◽  
Third Dimension ◽  
Evolution Of Microstructure

In all fields of microscopy there is an increasing interest in the quantification of microstructure. This interest may stem from a desire to establish quality control parameters or may have a more fundamental requirement involving the derivation of parameters which partially or completely define the three dimensional nature of the microstructure. This latter categorey of study may arise from an interest in the evolution of microstructure or from a desire to generate detailed property/microstructure relationships. In the more fundamental studies some convolution of two-dimensional data into the third dimension (stereological analysis) will be necessary.In some cases the two-dimensional data may be acquired relatively easily without recourse to automatic data collection and further, it may prove possible to perform the data reduction and analysis relatively easily. In such cases the only recourse to machines may well be in establishing the statistical confidence of the resultant data. Such relatively straightforward studies tend to result from acquiring data on the whole assemblage of features making up the microstructure. In this field data mode, when parameters such as phase volume fraction, mean size etc. are sought, the main case for resorting to automation is in order to perform repetitive analyses since each analysis is relatively easily performed.

The relaxation of compressive biaxial strains in SOS via microtwins

1989 ◽  
Vol 47 ◽  
pp. 608-609
Author(s):  
M. E. Twigg ◽  
E. D. Richmond ◽  
J. G. Pellegrino
Keyword(s):  
Thin Film ◽  
Chemical Vapor Deposition ◽  
Molecular Beam Epitaxy ◽  
Compressive Stress ◽  
Vapor Deposition ◽  
Partial Dislocation ◽  
Molecular Beam ◽  
Volume Fraction ◽  
Chemical Vapor ◽  
Silicon Thin Film

For heteroepitaxial systems, such as silicon on sapphire (SOS), microtwins occur in significant numbers and are thought to contribute to strain relief in the silicon thin film. The size of this contribution can be assessed from TEM measurements, of the differential volume fraction of microtwins, dV/dν (the derivative of the microtwin volume V with respect to the film volume ν), for SOS grown by both chemical vapor deposition (CVD) and molecular beam epitaxy (MBE).In a (001) silicon thin film subjected to compressive stress along the [100] axis , this stress can be relieved by four twinning systems: a/6[211]/( lll), a/6(21l]/(l1l), a/6[21l] /( l1l), and a/6(2ll)/(1ll).3 For the a/6[211]/(1ll) system, the glide of a single a/6[2ll] twinning partial dislocation draws the two halves of the crystal, separated by the microtwin, closer together by a/3.

Two-dimensional BN-doped ZnO thin-film deposition by a thermionic vacuum arc system

2020 ◽  
Vol 31 (9) ◽  
pp. 6948-6955
Author(s):  
Mustafa Özgür ◽  
Suat Pat ◽  
Reza Mohammadigharehbagh ◽  
Uğur Demirkol ◽  
Nihan Akkurt ◽  
...  
Keyword(s):  
Thin Film ◽  
Thin Film Deposition ◽  
Film Deposition ◽  
Vacuum Arc ◽  
Zno Thin Film ◽  
Two Dimensional ◽  
Doped Zno ◽  
Thermionic Vacuum Arc

scholarly journals A Multi Objective Evolutionary Algorithm for the Parameters Extraction of Organic Thin Film Transistors Models

Electronics ◽  
2021 ◽  
Vol 10 (8) ◽  
pp. 939
Author(s):  
Rosario Schiano Lo Moriello ◽  
Davide Ruggiero ◽  
Leopoldo Angrisani ◽  
Enzo Caputo ◽  
Francesco de Pandi ◽  
...  
Keyword(s):  
Thin Film ◽  
Evolutionary Algorithm ◽  
Design Stage ◽  
Model Parameters ◽  
Organic Transistors ◽  
Organic Thin Film ◽  
Multi Objective ◽  
Application Fields ◽  
Channel Lengths ◽  
P Type

Thanks to their peculiar features, organic transistors are proving to be a valuable alternative to traditional semiconducting devices in several application fields; however, before releasing their exploitation, simulating their behaviour through adequate circuital models could be advisable during the design stage of electronic circuits and/or boards. Consequently, accurately extracting the parameter value of those models is fundamental to developing useful libraries for hardware design environments. To face the considered problem, the authors present a method based on successive application of Single- and Multi-Objective Evolutionary Algorithm for the optimal tuning of model parameters of organic transistors on thin film (OTFT). In particular, parameters are first roughly estimated to assure the best fit with the experimental transfer characteristics; the estimates are successively refined through the multi-objective strategy by also matching the values of the experimental mobility. The performance of the method has been assessed by estimating the parameters value of both P-type and N-type OTFTs characterized by different values of channel lengths; the obtained results evidence that the proposed method can obtain suitable parameters values for all the considered channel lengths.

scholarly journals A numerical frame work of magnetically driven Powell-Eyring nanofluid using single phase model

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Wasim Jamshed ◽  
Mohamed R. Eid ◽  
Kottakkaran Sooppy Nisar ◽  
Nor Ain Azeany Mohd Nasir ◽  
Abhilash Edacherian ◽  
...  
Keyword(s):  
Differential Equations ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Dissipative Flow ◽  
Uniform Medium ◽  
Heat Transport Properties ◽  
Flow Heat ◽  
Frame Work ◽  
Slippery Surface ◽  
Nanoparticle Shapes

AbstractThe current investigation aims to examine heat transfer as well as entropy generation analysis of Powell-Eyring nanofluid moving over a linearly expandable non-uniform medium. The nanofluid is investigated in terms of heat transport properties subjected to a convectively heated slippery surface. The effect of a magnetic field, porous medium, radiative flux, nanoparticle shapes, viscous dissipative flow, heat source, and Joule heating are also included in this analysis. The modeled equations regarding flow phenomenon are presented in the form of partial-differential equations (PDEs). Keller-box technique is utilized to detect the numerical solutions of modeled equations transformed into ordinary-differential equations (ODEs) via suitable similarity conversions. Two different nanofluids, Copper-methanol (Cu-MeOH) as well as Graphene oxide-methanol (GO-MeOH) have been taken for our study. Substantial results in terms of sundry variables against heat, frictional force, Nusselt number, and entropy production are elaborate graphically. This work’s noteworthy conclusion is that the thermal conductivity in Powell-Eyring phenomena steadily increases in contrast to classical liquid. The system’s entropy escalates in the case of volume fraction of nanoparticles, material parameters, and thermal radiation. The shape factor is more significant and it has a very clear effect on entropy rate in the case of GO-MeOH nanofluid than Cu-MeOH nanofluid.

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