Particle Tracing Module
Analyze the Behavior of Particles with the Particle Tracing Module
Extend the Functionality of the COMSOL Environment with Particle Tracing
The Particle Tracing Module extends the functionality of the COMSOL environment for computing the trajectory of particles in a fluid or electromagnetic field, including particleparticle, fluidparticle, and particlefield interactions. You can seamlessly combine any applicationspecific module with the Particle Tracing Module for computing the fields that drive particle motion. Particles can have mass or be massless. The movement is governed by either the Newtonian, Lagrangian, or Hamiltonian formulations from classical mechanics. Boundary conditions can be imposed on the particles on the walls of the geometry to allow particles to freeze, stick, bounce, disappear, or reflect diffusely. Userdefined wall conditions may also be specified, where the post collision particle velocity is typically a function of the incoming particle velocity and the wall normal vector. Secondary particles released when an incoming particle strikes a wall can be included. The number of secondary particles and their velocity distribution function can be functions of the primary particle velocity and the wall geometry. Particles can also stick to the wall according to an arbitrary expression or a sticking probability. Additional dependent variables can be added to the model which allows you to compute quantities like particle mass, temperature, or spin.
Particles can be released on boundaries and domains uniformly, according to the underlying mesh, as defined by a grid or according to an arbitrary expression. A wide range of predefined forces is available to describe specifically how the particles interact with the fields. You can then add arbitrary forces as defined by a suitable expression. It is also possible to model the twoway interaction between the particles and the fields (particlefield interaction), as well as the interaction of particles between each other (particleparticle interaction).
Animations
Additional Images:
Powerful Processing Tools
Powerful processing tools allow for sophisticated visualization of the computed particle trajectories. Particle trajectories can be represented by points, comet tails, arrows, lines, tubes, or ribbons. Animations can easily be created and viewed directly in the graphical user interface (GUI) or exported to file. The particle trajectories can be colored with arbitrary expressions that can depend on the particles, the fields, or any combination of the two. In cases where the trajectory of many particles are simulated, it is possible to filter out specific particle trajectories according to a logical expression. The group behavior of the particles can be projected onto a lower dimension and visualized using Poincaré maps or phase portraits. It is also possible to perform operations on the particles to compute and plot the maximum, minimum, average, or integral of some quantity over all the particles. The particle trajectory data itself can be evaluated and written to the Results table or exported to a file. You can conveniently visualize the velocity and energy distributions of the particles, using 1D or 2D histograms.
Charged Particles in Electric and Magnetic Fields
Charged particles, such as electrons, individual ions, or small ion clusters, are affected by three primary forces in electric and magnetic fields:
 The electric force, which arises either due to a gradient in the electric potential or due to a timevarying magnetic vector potential. Particles with negative charge move in the opposite direction to the electric field, and particles with positive charge move in the same direction as the electric field. The electric force does work on these particles.
 The magnetic force, which does no work on the charged particles but can significantly alter their trajectory. The magnetic force often results in “banana” orbits for charged particles, causing them to orbit around magnetic field lines with a distance proportional to their mass.
 Collisional forces, which occur when charged particles collide with a background gas. The higher the background pressure, the more important the collisional forces.
If the number density of charged species is less than around 10^{13} 1/m^{3}, the effect of the particles on the fields can be neglected. This allows you to compute the fields independently from the particle trajectories. The fields are then used to compute the electric, magnetic, and collisional forces on the particles. The fact that the particle trajectories can be computed in their own study allows efficient and computationally inexpensive iterative solvers to be used.
Solving for Particle Tracing
For each particle, an ordinary differential equation is solved for each component of the position vector. This means that three ordinary differential equations are solved for each particle in 3D, and two in 2D. At each time step, the forces acting on each particle are queried from the computed fields at the current particle position. If particleparticle interaction forces are included in the model, they are added to the total force. The particle position is then updated, and the process repeats until the specified end time for the simulation is reached. Since the Particle Tracing Module uses a very general formulation for computing particle trajectories, the Particle Tracing interfaces can be used to model charged particle motion in electromagnetic fields, large scale planetary and galactic movement, and particle motion in laminar, turbulent, and twophase fluid systems.
Studying Particle Tracking in a Fluid
The motion of microscopic and macroscopicsized particles is typically dominated by the drag force acting on particles immersed in a fluid. There are two phases in the system: a discrete phase consisting of bubbles, particles, or droplets, and a continuous phase in which the particles are immersed. In order for the particle tracking approach to be valid, the system should be a dilute or dispersed flow. This means that the volume fraction of the discrete phase should be much smaller than the volume fraction of the continuous phase (generally less than 1%). When the volume fraction of the particles is not small, the fluid system is categorized as a dense flow and you are required to take a different modeling approach. It is important to realize that, with the particle tracking approach, particles do not displace the fluid they occupy.
In a sparse flow, the continuous phase affects the motion of the particles, but not vice versa. This is often referred to as “oneway coupling”. When modeling such a system, it is usually most efficient to solve for the continuous phase first, then to compute the trajectories of the dispersed phases.
In a dilute flow, the continuous phase affects the motion of the particles, and the particle motion in turn disrupts the continuous phase. This is often referred to as “twoway coupling”. In order to model this effect, you must compute the continuous phase and disperse phase simultaneously. Thus, the computational demand is significantly higher when modeling dilute flows than when modeling sparse flows.
Product Features
 Charged Particle Tracing interface to model ion and electron trajectories in electric and magnetic fields including elastic collisions with a background gas
 Particle Tracing for Fluid Flow interface to model the motion of microscopic and macroscopic particles in a fluid
 Mathematical Particle Tracing interface, which offers complete freedom over the equations solved
 Massless, Newtonian, Lagrangian, and Hamiltonian formulations
 Predefined forces to facilitate model setup
 Electric
 Magnetic
 Collisional
 Lift
 Drag
 Brownian
 Thermophoretic
 Gravity
 Acoustophoretic
 Dielectrophoretic
 Magnetophoretic
 Userdefined forces
 Fictitious forces for rotating frames
 Particlefield interactions
 Particleparticle interactions
 Reinitialization of the particle velocity vector based on some logical expression allows for general purpose Monte Carlo modeling
 Particle release mechanisms
 Meshbased where a specific number of particles are released in each mesh element
 Uniform distribution of particles on a given boundary
 Expression based which allows the density of particles to be greater in specific locations
 Grid
 Thermionic emission of electrons
 Boundary conditions
 Freeze
 Stick
 Bounce
 Disappear
 General reflection
 Diffuse scattering
 Periodic conditions
 Symmetry
 Secondary emission
 Sticking probabilities
 Postprocessing
 Particle trajectory plots (lines, tubes, points and comet tails)
 Color trajectories with arbitrary expressions
 Filter particles to plot
 Animations
 Poincaré sections and maps
 Phase portraits
 Compute maximum, minimum, average and integrals over all particles
 Write particle data to tables
 Export particle data
 1D and 2D histograms
 Transmission probabilities
 Add auxiliary dependent variables to compute particle mass, spin, etc.
 Fully compatible with moving mesh
Application Areas
 Mass spectrometry
 Beam physics
 Brownian motion
 Ion optics
 Ion mobility spectrometry
 Fluid flow visualization
 Sprays
 Aerosol dynamics
 Mixers
 Secondary emission
 Separation and filtration
 Ion energy distribution function visualization
 Acoustophoresis
 Classical mechanics
Electron Beam Divergence Due to Self Potential
When modeling the propagation of charged particle beams at high currents, the space charge force generated by the beam significantly affects the trajectories of the charged particles. Perturbations to these trajectories, in turn, affect the space charge distribution. The Charged Particle Tracing interface can use an iterative procedure to ...
Laminar Static Particle Mixer Designer
In static mixers, a fluid is pumped through a pipe containing stationary mixing blades. This mixing technique is well suited for laminar flow mixing, because it generates only small pressure losses in this flow regime. When a fluid is pumped through the channel, the alternating directions of the crosssectional blades mix the fluid as it passes ...
Rotating Galaxy
This tutorial model shows how to add customized particleparticle interaction forces. In this example the gravitational force between 2500 stars in a galaxy is modeled. The galaxy initially rotates as a rigid body, then begins to change shape due to gravitational forces.
Einzel Lens
An Einzel lens is an electrostatic device used for focusing charged particle beams. It may be found in cathode ray tubes, ion beam and electron beam experiments, and ion propulsion systems. This particular model consists of three axially aligned cylinders. The outer cylinders are grounded, while the cylinder in the middle is held at a fixed ...
Ion Cyclotron Motion
This model computes the trajectory of an ion in a uniform magnetic field using the Newtonian, Lagrangian and Hamiltonian formulations available in the Mathematical Particle Tracing interface.
Dielectrophoretic Separation of Platelets from Red Blood Cells
Dielectrophoresis (DEP) occurs when a force is exerted on a dielectric particle as it is subjected to a nonuniform electric field. DEP has many applications in the field of biomedical devices used for biosensors, diagnostics, particle manipulation and filtration (sorting), particle assembly, and more. The DEP force is sensitive to the size, ...
Particle Trajectories in a Laminar Static Mixer
In static mixers, also called motionless or inline mixers, a fluid is pumped through a pipe containing stationary blades. This mixing technique is particularly well suited for laminar flow mixing because it generates only small pressure losses in this flow regime. This example studies the flow in a twistedblade static mixer. It evaluates the ...
Ideal Cloak
This model demonstrates the use of optical tracing for studying optically large gradientindex structures with anisotropic optical properties. Additionally, the model introduces a smoothing technique for handling discontinuities of refractive index on curved surfaces, which are typical in conventional optical devices such as lenses.
Brownian Motion
Transport which is purely diffusive in nature can be modeled using a Brownian force. This model shows how to add such a force in the Particle Tracing for Fluid Flow physics interface. Particle diffusion in a fluid is modeled with the diffusion equation and the Particle Tracing for Fluid flow interfaces and the results are compared.
Charge Exchange Cell Simulator
A charge exchange cell consists of a region of gas at an elevated pressure within a vacuum chamber. When an ion beam interacts with the higherdensity gas, the ions undergo charge exchange reactions with the gas which then create energetic neutral particles. It is likely that only a fraction of the beam ions will undergo charge exchange ...
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Multipurpose Products
 Optimization Module
 Uncertainty Quantification Module
 Material Library
 Particle Tracing Module
 Liquid & Gas Properties Module
Interfacing Products
 LiveLink™ for MATLAB^{®}
 LiveLink™ for Simulink^{®}
 LiveLink™ for Excel^{®}
 CAD Import Module
 Design Module
 ECAD Import Module
 LiveLink™ for SOLIDWORKS^{®}
 LiveLink™ for Inventor^{®}
 LiveLink™ for AutoCAD^{®}
 LiveLink™ for Revit^{®}
 LiveLink™ for PTC^{®} Creo^{®} Parametric™
 LiveLink™ for PTC^{®} Pro/ENGINEER^{®}
 LiveLink™ for Solid Edge^{®}
 File Import for CATIA^{®} V5

Multipurpose Products
 Optimization Module
 Uncertainty Quantification Module
 Material Library
 Particle Tracing Module
 Liquid & Gas Properties Module
Interfacing Products
 LiveLink™ for MATLAB^{®}
 LiveLink™ for Simulink^{®}
 LiveLink™ for Excel^{®}
 CAD Import Module
 Design Module
 ECAD Import Module
 LiveLink™ for SOLIDWORKS^{®}
 LiveLink™ for Inventor^{®}
 LiveLink™ for AutoCAD^{®}
 LiveLink™ for Revit^{®}
 LiveLink™ for PTC^{®} Creo^{®} Parametric™
 LiveLink™ for PTC^{®} Pro/ENGINEER^{®}
 LiveLink™ for Solid Edge^{®}
 File Import for CATIA^{®} V5