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Lattice Boltzmann Method

The animation which I am proposing here will be a 2D animation and can be developed in JAVA or Flash. 0. Lattice Boltzmann Method. ME410:Microfluidics. - Swati Priyam. 1. Basic Keywords Used:

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Lattice Boltzmann Method

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  1. The animation which I am proposing here will be a 2D animation and can be developed in JAVA or Flash. 0

  2. Lattice Boltzmann Method ME410:Microfluidics -Swati Priyam 1

  3. Basic Keywords Used: • Particle: A small object that behaves as a whole unit in terms of its transport and properties. • Real Molecule: Molecules which actually exist and can move in any direction with varying velocities as and when required. It is a molecule which moves according to the various laws of physics. • Simulated Molecule: Molecules that mimic but do not exactly follow the motion of real molecules. The movements of such molecules can be restricted along any direction. 2

  4. Basic Keywords Used(Continued): • Lattice: A regular, periodic configuration of points, particles, or objects throughout an area or a space, especially the arrangement of ions or molecules in a crystalline solid. • Boundary Conditions: These are conditions which are based on continuity arguments and support observation made at very small scales in micro fluidics. • Probability Function( ): This is the probability of finding a particle in any of the nine defined positions in a lattice at any instant of time according to the Lattice Boltzmann Theory. 3

  5. Lattice Boltzmann Method: This is a particle based method. This mainly involves two basic steps: Movement of Particles Collision of Particles Boundary conditions have to be specified in this method. The movement of the various particles depends upon the boundary conditions. 4

  6. Interactive Animation for Lattice Boltzmann Method: Basic Arrangement of simulated particles in a Lattice: Particles 5

  7. Interactive Animation for Lattice Boltzmann Method: Animation(9 Lattices) Initial Setup Initial Numbering 2 Simulated Motion Lattice Direction of motion of individual particles 0 Simulated Motion 8 6

  8. Lattice Boltzmann Method(Contd.) Initial Setup: When this button is pressed, the blank screen will have many lattices. Our animation has nine different lattices shown for providing ease of movement of the particles. C Lattice Lattice Step 0 Step 1 7

  9. Lattice Boltzmann Method(Contd.) Initial Numbering: This button when pressed, one of the various lattices ( the central one in our case) is highlighted in a different color. And all the numbers are given to the different positions of the particle in a lattice. This is shown properly in the next slide.(slide 9 ) As shown , the central particle is the rest particle(0). The other particles are given numbers with respect to their positions. Thus this button provides proper numbering. 8

  10. 6 2 5 3 0 1 7 4 8 Step 2 9

  11. Lattice Boltzmann Method(Contd.) Direction of motion of individual particles: For this a drop down table will be available where all the 9 particle positions are mentioned. On selecting any one, the display will change automatically. The particle at the position mentioned will have an arrow leading out from it which gives the direction in which the particle is supposed to move. For example, • On selecting 0, that particle will be highlighted. But as it won’t move( rest particle), there will be no arrow leading out from it.( Slide 11 ) • On selecting any other position, there will be an arrow which shows the direction of movement of this particle.(Slide 12 & 13 ) 10

  12. For particle 0, 6 5 2 3 0 1 4 8 Step 3 7 11

  13. For Particle 1, 5 6 2 3 0 1 Step 3 7 4 8 12

  14. For particle 6, 5 6 2 3 0 1 7 4 8 Step 3 13

  15. Lattice Boltzmann Method(Contd.) Simulated Motion of All Particles: This button when pressed will show the motion of all the particles to the corresponding lattices through the use of curved arrows. The position of the particles change. 1,3 will show horizontal movements to the corresponding lattices to their right and left respectively. 2,4 will show vertical movements to their corresponding lattices to their top and bottom respectively. 5 will move to north-east, 6 will move north-west, 7 will move south-west and 8 will move south-east to the corresponding lattices. This is shown in the next slide. 14

  16. Lattice Boltzmann Method(Contd.) 6 2 5 Movement of particles has been shown after one . 6 2 5 3 3 1 0 1 7 4 8 Step 4 7 8 4 15

  17. Lattice Boltzmann Method: Questionnaire: 1) What is the advantage of using simulated molecules over real molecules? A: The sample space reduces when we use simulated particles making the analysis and study of the motion and collision of these particles much easier. 2) According to LBM, in what direction does a particle in the north-east corner of the lattice(pos. 5 in our diag.) move to? Can it in any way go to a lattice north west to the current lattice? A: A particle in the north-east corner will move to the north east in corresponding time periods( ). Its motion is strictly restricted. It cannot move into the north-west lattice. 16

  18. Further links and references: • ME410 lecture notes 13-B • http://en.wikipedia.org/wiki/LatticeBoltzmann_methods 17

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