ELECTRODEPOSITION MODELING USING COUPLED PHASE-FIELD AND LATTICE BOLTZMANN APPROACH

2013 ◽  
Vol 25 (01) ◽  
pp. 1340018 ◽  
Author(s):  
D. V. PATIL ◽  
K. N. PREMNATH ◽  
D. DESAI ◽  
SANJOY BANERJEE
Keyword(s):  
Free Energy ◽  
Phase Field ◽  
Lattice Boltzmann ◽  
Order Parameter ◽  
Chemical Deposition ◽  
Energy Functional ◽  
Time Step ◽  
Ginzburg Landau ◽  
Two Phases ◽  
Boltzmann Method

In this paper, a coupled phase-field (PF) and lattice Boltzmann method (LBM) is presented to model the multiphysics phenomenon involving electro-chemical deposition. The deposition (or dissolution) of the electrode is represented using variations of an order-parameter. The time-evolution of an order-parameter is proportional to the variation of a Ginzburg–Landau free-energy functional. Further, the free-energy densities of the two phases are defined based on a dilute or an ideal solution approximation. An efficient LBM is used to obtain the converged electro-static potential field for each physical time-step of the evolution of the PF variable. The coupled approach demonstrates the applicability of the LBM in a multiphysics scenario. The numerical validation for the coupled approach is performed by the simulation of the electrodeposition process of Cu from CuSO 4 solution.

GROWTH KINETICS IN THE Φ6N-COMPONENT MODEL: NONCONSERVED ORDER PARAMETER

1994 ◽  
Vol 08 (18) ◽  
pp. 1115-1124
Author(s):  
F. CORBERI ◽  
U. MARINI BETTOLO MARCONI
Keyword(s):  
Free Energy ◽  
Growth Kinetics ◽  
Order Parameter ◽  
Energy Functional ◽  
Component Model ◽  
Ginzburg Landau ◽  
Free Energy Functional ◽  
Spherical Limit ◽  
Component Order ◽  
Component Order Parameter

The dynamics of a system with a nonconserved N-component order parameter described by a Ginzburg–Landau free energy functional containing a sixth order nonlinearity is discussed in the spherical limit. The model displays a richer behavior than the well-studied Φ4 case. In particular it shows interesting properties regarding metastability, a feature which is absent in the spherical Φ4 model.

scholarly journals Research on Human Erythrocyte’s Threshold Free Energy for Hemolysis and Damage from Coupling Effect of Shear and Impact Based on Immersed Boundary-Lattice Boltzmann Method

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Zhong Yun ◽  
Chuang Xiang ◽  
Liang Wang
Keyword(s):  
Free Energy ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Coupling Effect ◽  
Threshold Value ◽  
Blood Pump ◽  
Immersed Boundary ◽  
Threshold Limit ◽  
Spring Network Model ◽  
Boltzmann Method

Researches on the principle of human red blood cell’s (RBC) injuring and judgment basis play an important role in decreasing the hemolysis in a blood pump. In the current study, the judgment of hemolysis in a blood pump study was through some experiment data and empirical formula. The paper forms a criterion of RBC’s mechanical injury in the aspect of RBC’s free energy. First, the paper introduces the nonlinear spring network model of RBC in the frame of immersed boundary-lattice Boltzmann method (IB-LBM). Then, the shape, free energy, and time needed for erythrocyte to be shorn in different shear flow and impacted in different impact flow are simulated. Combining existing research on RBC’s threshold limit for hemolysis in shear and impact flow with this paper’s, the RBC’s free energy of the threshold limit for hemolysis is found to be 3.46 × 10 − 15  J. The threshold impact velocity of RBC for hemolysis is 8.68 m/s. The threshold value of RBC can be used for judgment of RBC’s damage when the RBC is having a complicated flow of blood pumps such as coupling effect of shear and impact flow. According to the change law of RBC’s free energy in the process of being shorn and impacted, this paper proposed a judging criterion for hemolysis when the RBC is under the coupling effect of shear and impact based on the increased free energy of RBC.

A Meshfree-Based Lattice Boltzmann Approach for Simulation of Fluid Flows Within Complex Geometries

2018 ◽  
pp. 188-222 ◽  
Author(s):  
Sonam Tanwar
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Moving Boundary ◽  
Fluid Flows ◽  
Computational Domain ◽  
Time Step ◽  
Boundary Problems ◽  
Complex Process ◽  
Element Free ◽  
Boltzmann Method

This chapter develops a meshless formulation of lattice Boltzmann method for simulation of fluid flows within complex and irregular geometries. The meshless feature of proposed technique will improve the accuracy of standard lattice Boltzmann method within complicated fluid domains. Discretization of such domains itself may introduce significant numerical errors into the solution. Specifically, in phase transition or moving boundary problems, discretization of the domain is a time-consuming and complex process. In these problems, at each time step, the computational domain may change its shape and need to be re-meshed accordingly for the purpose of accuracy and stability of the solution. The author proposes to combine lattice Boltzmann method with a Galerkin meshfree technique popularly known as element-free Galerkin method in this chapter to remove the difficulties associated with traditional grid-based methods.

Simulation of Interface Deformation in Shear Flow Using Binary Fluid Lattice Boltzmann Model

2002 ◽  
Author(s):  
Naoki Takada ◽  
Akio Tomiyama ◽  
Shigeo Hosokawa
Keyword(s):  
Shear Flow ◽  
Lattice Boltzmann ◽  
Fluid Model ◽  
Kinetic Equations ◽  
Three Dimensional ◽  
Lattice Boltzmann Model ◽  
Repulsive Interaction ◽  
Binary Fluid ◽  
Two Phases ◽  
Boltzmann Method

In this paper, we describes the simulations of two- and three-dimensional interfacial motions in shear flow based on the lattice Boltzmann method (LBM), in which a macroscopic fluid flow results from averaging collision and translation of mesoscopic particles and an interface can be reproduced in a self-organizing way by repulsive interaction between particles. A new scheme in the binary fluid model is proposed to simulate motions of immiscible two phases with different mass densities, and examined in numerical analysis of bubble motions under gravity in a circular tube and deformation of bubble under shear stress. For higher Reynolds numbers, a finite difference-based lattice Boltzmann scheme is applied to the kinetic equations of particle to improve numerical stability, which can capture break-up motions of bubble. Parallel computing in LBM is also discussed briefly for efficient speeding up.

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