## Particle Tracing Module Updates

For users of the Particle Tracing Module, COMSOL Multiphysics^{®} version 5.6 includes a dedicated feature for evaporation of liquid droplets, easier use of the *Material* node to define particle material properties, and a new *Newtonian, ignore intertial* formulation to model small particles in a viscous fluid. Read more about the particle tracing features below.

### Droplet Evaporation

A dedicated *Droplet Evaporation* node can now be used to treat the model particles as liquid droplets that evaporate in the surrounding gas. The evaporation rate is computed based on the saturation vapor pressure at the droplet surface and the diffusion coefficient of the droplet vapor into the surrounding gas. The *Droplet Evaporation* node supports a simplified Maxwell diffusion model, a more detailed Stefan–Fuchs model, and an option to specify the evaporation constant directly.

Usually, evaporating droplets approach a steady-state temperature (called the wet-bulb temperature), based on the temperature of the surrounding gas. If you know the steady-state temperature, you can specify it directly. Alternatively, if you are using the Stefan–Fuchs evaporation model and solving for particle temperature, you can model the droplet heat-up period as well as the steady-state evaporation. This can be useful when the surrounding air is much hotter than the droplets being released into it, since the heat-up time might represent a significant fraction of the total droplet lifetime.

*Droplet evaporation example*

*Evaporation of water droplets as they are carried away in the surrounding air. The particle size and color expression are proportional to the particle mass.*

### Particle Properties from Material

In the *Particle Tracing for Fluid Flow* interface, the particle material properties can now be taken from a *Material* node instead of being specified directly. This change allows the Material Libraries to be used more effectively in particle tracing models. It also gets rid of some redundancy when several different forces use the same material property: You only have to specify this property a single time.

By default, every *Particle Tracing for Fluid Flow* model requires the particle density to be specified. Depending on what additional forces and other features are added to the model, other material properties might also be required. For example, the *Dielectrophoretic Force* domain condition requires the particle relative permittivity and electrical conductivity. These will automatically be taken from the same material used to define the particle density. You also have the option to make any material property user defined, instead of getting it from the Material Libraries. When using the new *Droplet Evaporation* node to treat model particles as evaporating droplets, you can also take the properties of the vapor phase from another *Material* node.

*Demonstrating how to get particle properties from the material libraries*

*Typical usage where particle density is taken from the built-in quartz glass from the Material Libraries.*

### New Formulation for Tracing Small Particles in Fluids

A new particle tracing formulation is available for the *Particle Tracing for Fluid Flow* interface. Called the *Newtonian, ignore inertial terms* formulation, it solves first-order equations for the particle position while assuming that the drag force counterbalances all other forces on the particles. In essence, this ignores the particle acceleration when particles are first inserted into the fluid.

Ordinarily, the time step size you need to resolve particle acceleration in a fluid scales with the square of the particle diameter. As a result, a full inertial treatment of very small particles (around tens of microns or smaller, depending on the fluid) requires extremely small time steps, and running the study can become rather slow. The new *Newtonian, ignore inertial terms* formulation allows much larger time steps to be taken without incurring any additional numerical instability. You can see this new feature in the Dielectrophoretic Separation of Platelets from Red Blood Cells and Particle Trajectories in a Laminar Static Mixer models.

*Example using the Newtonian, ignore inertial terms formulation*

*Physics interface settings and equation display when the*Newtonian, ignore inertial terms

*formulation is selected.*

### Number Density Calculation

The new *Number Density Calculation* feature can be used to compute the number density of particles within the simulation domain. The density is averaged over each domain mesh element.

*RF coupler*

*Gas molecules in an RF coupler. The number density is shown as a slice plot through the middle of the geometry, on a logarithmic scale. The highest number density is at the left end (red) where molecules enter the geometry.*

### Improved Convective Heating and Cooling

When solving for particle temperature, there are now two different ways to apply convective heating or cooling to the particles. First, you can specify the heat transfer coefficient *h* directly. Alternatively, specify the particle Nusselt number, Nu, and the thermal conductivity of the fluid *k*; the heat transfer coefficient will then be computed automatically.

### Random Sampling of Mass, Temperature, and Other Variables

When you initialize auxiliary dependent variables on particles, you can sample their initial values deterministically or, new with COMSOL Multiphysics^{®} version 5.6, randomly. When using the random option, you can sample from built-in normal, lognormal, or uniform distributions. For the *Particle Tracing for Fluid Flow* interface, you can also sample the initial particle mass or diameter from these distributions. When sampling the diameter, there is a built-in option to enter the Sauter mean diameter, a common way to describe the size distribution of aerosol particles. The Sauter mean diameter, along with other new variables for describing the particle size distribution, are also available in postprocessing.

*Particles*

*Particles are released with a lognormal diameter distribution. Such distributions are much easier to set up in COMSOL Multiphysics*

^{®}version 5.6 than in previous versions of the software.### Easier Sampling from Uniform Distributions

When you initialize auxiliary dependent variables on particles, if the initial values are sampled from a uniform distribution, you now specify the maximum and minimum value in the distribution. Previously, it was necessary to specify a mean and standard deviation. This also applies to initial values of particle mass and diameter in the *Particle Tracing for Fluid Flow* interface.

### Random Sampling of Vacuum Wavelength, Frequency, and Other Variables

When you initialize auxiliary dependent variables on particles, you can sample their initial values deterministically or, new with version 5.6, randomly. When using the random option, you can sample from built-in normal, lognormal, or uniform distributions. You can also sample deterministically or randomly from a wavelength or frequency distribution if the rays are polychromatic.

### Improvements to the Space Charge Limited Emission Multiphysics Coupling

The *Space Charge Limited Emission* multiphysics coupling node, used with the *Charged Particle Tracing* interface, has significant stability improvements and performance upgrades. This feature uses fewer degrees of freedom compared to previous versions, and the accuracy of this feature is also significantly improved in 2D axisymmetric models. You can see this functionality in the Pierce Electron Gun and Child's Law Benchmark models.

### Velocity Offset for Thermal Re-Emission

The *Thermal Re-Emission* node, which causes molecules to be adsorbed onto a surface and then released back into the simulation domain with a thermal velocity distribution, now allows you to set a wall velocity. When tracing particles in a rotating frame of reference, there is a built-in option to offset the wall velocity by the reference frame velocity, effectively making the wall stationary with respect to the inertial (or laboratory) frame. You can see this feature in the updated Turbomolecular Pump model.

### Ionization Node Improvements

The *Ionization* node, which is added to the *Collisions* node in the *Charged Particle Tracing* interface, has been improved. You can now separately control whether or not the primary electron, secondary electron, and ionized species are released following each ionization reaction.

### Accumulators on Particle Collisions

In Monte Carlo collision models using the *Charged Particle Tracing* interface, you can now define a domain variable (called an accumulated variable) that the particles contribute to every time they undergo a collision with the background gas. This effectively lets you track the number density of collisions throughout the simulation domain.

*Example of accumulators on particle collisions*

*The colored line shows a particle in a rarefied background gas; its color expression is proportional to the number of gas molecules it has hit. Every time it undergoes a collision, it increases the value of an accumulated variable in the mesh element where the collision took place, indicated by the grayscale field.*

### New and Updated Tutorial Models

COMSOL Multiphysics^{®} version 5.6 brings a new "Pierce Electron Gun" tutorial for the *Charged Particle Tracing* interface and a significantly improved "Turbomolecular Pump" tutorial for modeling vacuum systems.

#### Pierce Electron Gun

*Pierce electron gun model*

*Electrons in the Pierce electron gun start at the cathode (bottom) and accelerate as they reach the anode (top). The background contours (perfectly horizontal within the beam) show the electric potential while the streamlines show the direction of the electric field.*

Application Library Title:

*pierce_electron_gun*

Download from the Application Gallery

#### Turbomolecular Pump

*Turbomolecular pump model results*

*The updated turbomolecular pump model showing the maximum compression ratio and speed factor of the pump, which agree better with the literature in the updated version.*

Application Library Title:

*turbomolecular_pump*

Download from the Application Gallery