scholarly journals Fluid flow and pressure effects in phase-field models for solidification

2007 ◽  
Author(s):  
M. Conti
Keyword(s):  
Fluid Flow ◽  
Phase Field ◽  
Pressure Effects ◽  
Phase Field Models

Prediction of biofilm deformation and detachment using shear rheometry, phase-field modeling, and OCT

2020 ◽  
Author(s):  
Mengfei Li ◽  
Karel Matouš ◽  
Robert Nerenberg
Keyword(s):  
Mechanical Properties ◽  
Fluid Flow ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Viscoelastic Behavior ◽  
Biofilm Control ◽  
Viscoelastic Parameters ◽  
Water Solvent ◽  
Phase Field Models

<p>In many environmental systems, such as membrane filtration systems, biofilm control is essential, but costly and requiring harsh chemicals. More effective biofilm control may be obtained using a “materials science” approach.  Biofilms can be characterized as viscoelastic materials, and biofilm “disruptors” can be characterized for their weakening effect on biofilm mechanical strength. By using a novel mathematical model that incorporates biofilm mechanical properties, fluid flow, and diffusion and reaction of disruptors, better cleaning strategies can be devised.</p> <p> </p> <p>Phase-field models, where the biofilm is treated like a viscoelastic fluid, are one of the few types of models that can predicting deformation and detachment based on mechanical properties. While several related studies have proposed phase-field models for predicting biofilm deformation, there has not been any validation of these models with experimental data. As a first step towards developing a material science strategy for biofilm control, this study validated the ability of a phase-field model to capture biofilm viscoelastic behavior.</p> <p> </p> <p>In this study, a two-dimensional continuum biofilm model was implemented with finite element method (FEM) using COMSOL Multiphysics (COMSOL v5.4, Comsol Inc, Burlington, MA). We applied the phase-field model with the Cahn-Hilliard equation to simulate biofilm mechanical behavior under fluid flow. The Oldroyd-B model, the simplest viscoelastic constitutive model, was applied to capture biofilm viscoelasticity. The biofilm was modeled as an incompressible viscoelastic fluid, with EPS and a water solvent. The phase-field physics were adapted from previous studies and applied to biofilm-fluid interactions. Two types of incompressible, immiscible fluids (EPS and water solvent) were studied as two components of a single fluid, with a fluid-fluid interface between the two.</p> <p> </p> <p>Homogeneous alginate was used as a synthetic biofilm for the experimental validation. The viscoelastic parameters of alginate were obtained by shear rheometry using stress relaxation tests. In experimental tests, the deformation behavior was observed in real time using optical coherence tomography (OCT). By importing the 2-D geometry from OCT and viscoelastic parameters from rheometry, the model was simulated and compared with real deformation in the flow cell.</p> <p> </p> <p>With the applied constant flow (Re=6), biofilm demonstrated viscoelastic behavior.The same behavior was observed in modeling as well. By tracking the movements of several locations of the biofilm geometry, it was concluded that the deformation of alginate biofilms was consistent with the computational results of phase-field models. The relative error between experiment and model for this certain location were 12.8%. Heterotrophic counter-diffusional biofilms cultured in membrane-aerated biofilm reactors were also tested in this study, with a relative error of 22.2%.</p> <p> </p> <p>In conclusion, the phase-field model, coupled with Oldroyd-B equation, could properly capture biofilm viscoelastic behavior. In a complex system, the phase-field model could be used as a tool to characterize the viscoelastic parameters from the observed deformation. With this information, the model can be used to predict the required disruptor dose to achieve high amounts of biofilm removal with a minimal amount of chemical addition. This can reduce operating costs and minimize the use of harsh chemicals.</p>

Phase-Field Simulation of Binary Alloy Crystal Growth Prepared by a Fluid Flow

2015 ◽  
Vol 833 ◽  
pp. 11-14
Author(s):  
Ming Chen ◽  
Xiao Dong Hu ◽  
Dong Ying Ju
Keyword(s):  
Fluid Flow ◽  
Crystal Growth ◽  
Binary Alloy ◽  
Phase Field ◽  
Field Method ◽  
Phase Field Method ◽  
Al Alloy ◽  
Structural Pattern ◽  
Fluid Field ◽  
Phase Field Models

Phase field method (PFM) was employed to investigate the crystal growth of Mg-Al alloy, on the basis of binary alloy model, the fluid field equation was coupled into the phase-field models, and the marker and cell (MAC) method was used in the numerical calculation of micro structural pattern. In the cast process, quantitative comparison of different anisotropy values that predicted the dendrite evolution were discussed in detail, and when the fluid flow rate reaches a high value, we can see the remelting of dendrite arms.

scholarly journals Spectral Approximation of Fractional PDEs in Image Processing and Phase Field Modeling

2017 ◽  
Vol 17 (4) ◽  
pp. 661-678 ◽  
Author(s):  
Harbir Antil ◽  
Sören Bartels
Keyword(s):  
Image Processing ◽  
Phase Field ◽  
Differential Operators ◽  
Mathematical Tool ◽  
Phase Field Models ◽  
Field Modeling ◽  
Regularity Properties ◽  
Fractional Pdes ◽  
Fractional Differential ◽  
Fractional Differential Operators

AbstractFractional differential operators provide an attractive mathematical tool to model effects with limited regularity properties. Particular examples are image processing and phase field models in which jumps across lower dimensional subsets and sharp transitions across interfaces are of interest. The numerical solution of corresponding model problems via a spectral method is analyzed. Its efficiency and features of the model problems are illustrated by numerical experiments.

scholarly journals Minimization and Eulerian Formulation of Differential Geormetry Based Nonpolar Multiscale Solvation Models

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Zhan Chen
Keyword(s):  
Phase Field ◽  
Phase Field Model ◽  
Lagrangian Formulation ◽  
Global Minimizer ◽  
Solvation Model ◽  
Phase Field Models ◽  
Eulerian Formulation ◽  
Solvation Models ◽  
Similarity And Difference ◽  
Nonpolar Solvation

AbstractIn this work, the existence of a global minimizer for the previous Lagrangian formulation of nonpolar solvation model proposed in [1] has been proved. One of the proofs involves a construction of a phase field model that converges to the Lagrangian formulation. Moreover, an Eulerian formulation of nonpolar solvation model is proposed and implemented under a similar parameterization scheme to that in [1]. By doing so, the connection, similarity and difference between the Eulerian formulation and its Lagrangian counterpart can be analyzed. It turns out that both of them have a great potential in solvation prediction for nonpolar molecules, while their decompositions of attractive and repulsive parts are different. That indicates a distinction between phase field models of solvation and our Eulerian formulation.

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