Particle Tracing Module

Track Charged Particles and Particles in Fluid Flow

Particle tracing is a numerical method for computing the paths of individual particles by solving their equations of motion over time. Unlike many of the other methods used in the COMSOL Multiphysics® software, particle tracing solves for a number of discrete trajectories, rather than a continuous field.

The particles you simulate could represent ions, electrons, biological cells, grains of sand, projectiles, water droplets, bubbles, or even planets or stars. Depending on what kind of particles are being modeled, you can choose from a variety of built-in forces that affect their motion. For example, you might predict how electrons move in electric and magnetic fields, or how dust settles due to gravity and atmospheric drag. You can also control the initial position and velocity of released particles and specify what happens to the particles when they hit boundaries in the geometry.

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A mixer model showing the particle trajectories in the Rainbow color table.

Charged Particle Tracing

Accurately predicting the motion of ions or electrons in applied fields is essential to the design of spectrometers, electron guns, and particle accelerators. The applied fields might be user defined or taken from a previous analysis. Such fields can be stationary, time dependent, or solved for in the frequency domain. You can apply any number of different fields, allowing you to superpose stationary and time-harmonic fields in the same simulation.

Particle motion seldom takes place in a perfect vacuum. You can turn any particle tracing model into a Monte Carlo collision model, giving the particles some chance to collide with molecules in the surrounding gas. This might cause particles to change direction or even undergo reactions such as ionization and charge exchange.

The simplest charged particle tracing models involve unidirectional (one-way) coupling, where the fields are solved and then used to define forces on the particles. If the charged particles are in a beam of sufficiently high current, it might then be necessary to consider the bidirectional (two-way) coupling, where the particles can perturb the field. Built-in analysis types are available to conveniently set up bidirectionally coupled models.

Particle Tracing for Fluid Flow

The dispersion and evaporation of airborne water droplets, the migration of biological cells in a lab-on-a-chip device, and the impact of sediment on the walls of oil and gas pipelines are all examples of particle tracing for fluid flow.

For particles in a fluid, the most important forces are often drag and gravity. Depending on the application, additional forces such as electric, magnetic, thermophoretic, and acoustic radiation forces may also be applied. The particle motion might involve a random component if the fluid is turbulent or if the particles are small enough that Brownian motion is significant.

Particles might all have the same size or they may be sampled from a size distribution. Optionally, you can model particle heating or cooling by their surroundings, or cause particles to gain or lose mass as they propagate.

For larger particles, a full inertial treatment of the equations of motion accurately predicts how each particle will accelerate in the surrounding fluid. The fluid velocity can be typed in manually or taken from a previous analysis. Some approximate methods are also available to significantly reduce simulation time, especially for small particles with negligible inertia.

Mathematical Particle Tracing

As an alternative to the built-in functionality for charged particle tracing and particle tracing for fluid flow, the Particle Tracing Module includes a general-purpose interface for solving any particle equation of motion you might want to specify. You can include any number of user-defined release features, boundary conditions, domain conditions, and forces.

The options for specifying forces on the particles include using Newton's second law of motion or, indirectly, by specifying a Lagrangian or a Hamiltonian for the particle system.

What You Can Model with the Particle Tracing Module

Simulate the behavior of particles within a variety of applications.

A close-up view of a mass spectrometer model with four electrodes.

Mass Spectrometry

Track ions through a superposition of DC and AC fields.

A close-up view of a microchannel model with separating particles.

Separation and Filtration

Release and separate particles with a nonuniform size distribution.

A close-up view of a CVD chamber with injected particles.

Droplets and Sprays

Model dispersion and evaporation of small droplets in the surrounding air.

A close-up view of a micromixer model with particles mixing.


Visualize the mixing of different particle species.

A close-up view of an acoustic levitator model showing the suspended particles.


Couple to an acoustic pressure field solved for in the frequency domain.

A close-up view of a multipactor model showing the electron trajectories.

Secondary Emission

Model exponential electron growth due to energetic particle–wall collisions.

A close-up view of a circular model showing the particles and concentration.

Diffusive and Advective Transport

Combine deterministic and random forces on particles.

A close-up view of a pipe elbow model showing the velocity in particles.


Plot the rate of erosive wear as particles strike boundaries.

Features and Functionality in the Particle Tracing Module

The Particle Tracing Module provides specialized tools for tracing particles in fluids and for tracking ions or electrons in external fields.

A close-up view of the Particle Properties settings and a microprobe plot in the Graphics window.

Variety of Particle Release Features

A particle release feature allows you to assign the initial particle position and velocity. You can choose to release particles from selected domains, boundaries, edges, or points in the geometry. For finer control over the initial positions, you can also type in an array of coordinates or you can load the initial positions and velocities from a text file. Specialized release features can be used to launch nonlaminar ion and electron beams of specified emittance, model thermionic emission of electrons from a hot cathode, or release a spray of liquid droplets from a nozzle.

A close-up view of the Nonresonant Charge Exchange settings and a charge exchange cell model in the Graphics window.

Monte Carlo Collision Modeling

As ions and electrons propagate, they may randomly collide with ambient gas molecules in their surroundings. You can set up Monte Carlo collision models in which every particle has a probability to collide with molecules in the surrounding gas, based on velocity, gas density, and collision cross-section data. The collisions might be elastic or they could be ionization or charge exchange reactions where new particle species, like secondary electrons, are introduced into the model.

A close-up view of the Model Builder with the Electric Particle Field Interaction node highlighted and an electron beam model in the Graphics window.

Coupled Particle–Field Interactions

Charged particles naturally attract or repel each other, depending on whether their charges have opposite signs or the same sign. This is fundamentally why a beam of electrons tends to diverge, or spread out, as the beam propagates forward.

You can model the repulsion or attraction between particles in two different ways. For a small number of charged particles, you can define the Coulomb force directly. For a larger population of particles, you can compute the volumetric space charge density, then use it to perturb the electric potential in the particles' surroundings. Alternating between calculation of the electron trajectories and the resulting electric potential is an example of self-consistent bidirectionally coupled particle–field interaction modeling.

A close-up view of the Model Builder with the Particle Tracing for Fluid Flow node highlighted and a pipe elbow model in the Graphics window.

Track Particles in Laminar or Turbulent Flows

To save computational resources when modeling turbulent fluid flows, a common simulation technique is to solve the Reynolds-averaged Navier–Stokes (RANS) equations, which predict the average behavior of the turbulent fluctuations in fluid velocity by solving for additional transport variables, rather than computing the exact velocity at every position and every time.

When tracking particles in a turbulent fluid using RANS, you can model the drag force by treating it as a combination of two terms: one contribution from the mean flow and one contribution from the velocity fluctuations or eddies. You can randomly sample these eddies from a distribution based on the average turbulent kinetic energy, using built-in discrete random walk and continuous random walk models.

A close-up view of the Mathematical Particle Tracing settings and an ideal cloak model in the Graphics window.

Formulate and Solve Custom Equations of Motion

You can set up user-defined forces in a Newtonian formulation of the particle equations of motion, specify the particle velocity directly in a massless formulation, or enter a user-defined Lagrangian or Hamiltonian.

To solve the time-dependent equations of particle motion, the COMSOL® software offers a range of different solvers, including robust implicit solvers that can solve even very stiff equations of motion, as well as fast, accurate Runge–Kutta methods. A default time-stepping algorithm is assigned based on the functional form of the particle equations of motion, but the choice of solver is completely transparent and can be modified easily by the user.

A close-up view of the Wall settings and an RF coupler model in the Graphics window.

Customizable Particle–Wall Interactions

As particles move through the simulation domain, they will automatically detect any collisions with surfaces in the surrounding geometry. When a particle hits a wall, you can control its behavior: particles might stop moving, disappear, reflect diffusely or specularly, or fly off in a user-defined direction. You can also assign multiple kinds of wall interaction at the same surface and specify a probability for each of them, or some other condition that must be satisfied for a certain type of wall interaction to be applied. Alternatively, particle collisions with the walls can trigger secondary particle emission: the introduction of new model particles into the geometry.

A close-up view of the Particle Properties settings and a dielectrophoretic separation model in the Graphics window.

Define Multiple Species with Different Properties

When tracking particles in a fluid, the particle density and size must be specified in order to correctly apply the drag and gravity forces. Depending on what other forces are considered in the model, it may be necessary to enter additional information such as relative permittivity, thermal conductivity, or even dynamic viscosity (when modeling liquid droplets). You can either enter the particle material properties directly or load them from an extensive built-in library of material properties.

It is easy to model different kinds of particles in the same geometry at the same time. You can define multiple species in the same model, each with its own distinct material properties. Alternatively, if the particles are made of the same material but appear in varying sizes, you can sample the mass or diameter of the released particles from a distribution.

A close-up view of the Model Builder with the Space Charge Limited Emission node highlighted and a Pierce electron gun model in the Graphics window.

Self-Consistent Space-Charge Limited Emission Modeling

Modern electron gun design requires an accurate description of the particle velocity and electric field in the vicinity of the cathode or plasma source where particles are first released at relatively low kinetic energy. You can use built-in features to model the space-charge limited emission of electrons from a cathode or a higher-fidelity treatment of thermionic emission if the thermal distribution of released electron velocities is found to have a significant effect on the solution.

A close-up view of the Bidirectionally Coupled Particle Tracing settings and an electron beam model in the Graphics window.

Relativistic Particle Tracing

When the particle speed approaches the speed of light, classical Newtonian mechanics require some modification to accurately describe the particle motion. The Particle Tracing Module includes the option to account for special relativity when tracking very fast particles. A beam of relativistic particles can create appreciable electric and magnetic fields around itself, so a fully self-consistent model includes both electric and magnetic particle–field interactions.

A close-up view of the Model Builder with the Poincaré Maps node highlighted and a magnetic lens model in the Graphics window.

Visualize and Animate Particle Trajectories

You can visualize the instantaneous particle positions as points, arrows, or comet tails and render their paths as lines, tubes, or flat ribbons. You can color the trajectories with any expression that is defined on the particles or in the space they occupy. Some additional postprocessing tools include Poincaré maps to show the intersection of particle trajectories with a plane, and phase portraits to visualize the evolution of the particles in momentum space.

You can easily combine different types of plots in the same plot group, then animate the particle motion. Plots and animations can be exported to a file, or you can export the raw solution data for further analysis. Built-in operators and variables provide a convenient overview of the particle statistics.

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