Difference between revisions of "Team:Vilnius-Lithuania/Model"

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<p>Phase-field models are mathematical models used for solving interfacial problems. They are based on the generalized free-energy functional approach (lattice Boltzmann), meaning that the system evolution is driven by the minimisation of free energy. Important thing to note is that sharp fluid interfaces in the models are replaced by a thin transition region where the interfacial forces are distributed in a smooth manner. This provides model an easy treatment of topological variations at the interface1. In order to describe phases in numerical form, equations use phase variables ϕ. In three-phase systems, phase variables are described as ϕi , where i = A, B, C, and the variable is equal to 1 in the phase i and 0 outside.</p>
 
<p>Phase-field models are mathematical models used for solving interfacial problems. They are based on the generalized free-energy functional approach (lattice Boltzmann), meaning that the system evolution is driven by the minimisation of free energy. Important thing to note is that sharp fluid interfaces in the models are replaced by a thin transition region where the interfacial forces are distributed in a smooth manner. This provides model an easy treatment of topological variations at the interface1. In order to describe phases in numerical form, equations use phase variables ϕ. In three-phase systems, phase variables are described as ϕi , where i = A, B, C, and the variable is equal to 1 in the phase i and 0 outside.</p>
 
<p>Typically used phase-field models for two and three phase fluid systems couple fourth order nonlinear advection-diffusion equations, called Cahn-Hilliard equations, which represent the evolution of the phase variables with the Navier-Stokes equations for the fluid motion 2 . Equations (1), (2) and (3) form the traditional Cahn-Hilliard equation, and Eq. (4) is Navier-Stokes equation - both of them are used in our calculations on COMSOL</p>
 
<p>Typically used phase-field models for two and three phase fluid systems couple fourth order nonlinear advection-diffusion equations, called Cahn-Hilliard equations, which represent the evolution of the phase variables with the Navier-Stokes equations for the fluid motion 2 . Equations (1), (2) and (3) form the traditional Cahn-Hilliard equation, and Eq. (4) is Navier-Stokes equation - both of them are used in our calculations on COMSOL</p>
<p>  <div class="image-container"><img src="https://static.igem.org/mediawiki/2018/f/fe/T--Vilnius-Lithuania--dv_eq1_Model.png"></div>
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<p>  <div class="image-container"> <img src="https://static.igem.org/mediawiki/2018/1/1a/T--Vilnius-Lithuania--dv_eq21_Model.png"></div>
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<p>  <div class="image-container"> <img src="https://static.igem.org/mediawiki/2018/c/c8/T--Vilnius-Lithuania--dv_eq3_Model.png"></div>
 
<p>  <div class="image-container"> <img src="https://static.igem.org/mediawiki/2018/c/c8/T--Vilnius-Lithuania--dv_eq3_Model.png"></div>
 
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<p>  <div class="image-container"> <img src="https://static.igem.org/mediawiki/2018/f/fb/T--Vilnius-Lithuania--dv_eq4_Model.png"></div>
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<p>M0 is the mobility tuning parameter that determines the relaxation time of interface and the time scale of diffusion in C-H equation. It should be noted, that interfacial diffusion (the Gibbs-Thomson effect) is inevitable in phase phase field method because the diffusion term is used in the right side of Eq. (1). Due to this, prolonged simulations of our system result in spheres diffusing and constantly changing their size (Fig. 1.). Because of that, we have chosen to analyze only the first few spheres formed in every simulation as their size proved to be most accurate.</p>
 
<p>M0 is the mobility tuning parameter that determines the relaxation time of interface and the time scale of diffusion in C-H equation. It should be noted, that interfacial diffusion (the Gibbs-Thomson effect) is inevitable in phase phase field method because the diffusion term is used in the right side of Eq. (1). Due to this, prolonged simulations of our system result in spheres diffusing and constantly changing their size (Fig. 1.). Because of that, we have chosen to analyze only the first few spheres formed in every simulation as their size proved to be most accurate.</p>

Revision as of 18:35, 7 November 2018

Modeling

Mathematical model

Mathematical models and computer simulations provide a great way to describe the function and operation of BioBrick Parts and Devices. Synthetic Biology is an engineering discipline, and part of engineering is simulation and modeling to determine the behavior of your design before you build it. Designing and simulating can be iterated many times in a computer before moving to the lab. This award is for teams who build a model of their system and use it to inform system design or simulate expected behavior in conjunction with experiments in the wetlab

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