Brownian Force
Use the Brownian Force node to account for diffusion of suspended particles in a fluid according to Einstein’s theory. When using this feature, a random force is applied on each particle at each time step. This force accounts for the random motion of molecules in the vicinity of the particle. The Brownian Force is most significant for submicron particles and can usually be ignored for larger particles.
Supported formulations:
•
Newtonian,
•
Newtonian, first order, and
•
Newtonian, ignore inertial terms.
When the Brownian Force is included in a model, the Update scaled absolute tolerance check box is cleared in the Time-Dependent solver settings. This prevents the solver from taking extremely small time steps to try to compensate for the random nature of the force.
Model Input
The model input for the Temperature T (SI unit: K) is always shown in the settings window for this feature, even if there are no material properties that depend on it.
Brownian Force
Enter a value or expression for the Dynamic viscosity μ (SI unit: Pa·s). If a physics interface is present that computes the dynamic viscosity it can be selected directly from the list, or the value or expression can come from the selected material.
Advanced Settings
Use the Particles to affect list to apply the force to specific particles. The available settings are the same as for the Force node.
The random number generator used in COMSOL Multiphysics uses seeding so that the same results are obtained every time the model is solved. When adding forces that are random in nature, this is not always desirable. When the Arguments for random number generation setting is User defined, you can use the Additional input argument to random number generator field in conjunction with a Parametric Sweep to perform a Monte Carlo simulation. For example, use the following steps:
1
From the Home toolbar click a Parameters () node. Or in the Model Builder, right-click Global Definitions () and add a Parameters node.
2
Add a parameter with Name, for example, ds and set the Expression to 1.
3
In the Brownian Force feature, set the Additional input argument to random number generator to ds.
4
Add a Parametric Sweep to the current Study and set the Parameter name to ds.
5
Set the Parameter values to be an array whose length is equal to the number of times the model should be solved. For example, to solve the model 5 times, set the Parameter values to 1 2 3 4 5.
When 2 (the default) is selected from the Wall accuracy order list in the physics interface Advanced Settings section, the Brownian force may cause particles to undergo extremely large accelerations after they are released or when they interact with walls. This is due to the second-order Runge–Kutta extrapolation using the random force to predict the particle position at the end of the current time step. To prevent this unphysical behavior, consider selecting 1 from the Wall accuracy order list when modeling Brownian motion.
•
 About Parameters, Variables, Variable Utilities, Physics Utilities, and Expressions and Parametric Sweep in the COMSOL Multiphysics Reference Manual.
•
Brownian Force in the theory section.
Brownian Motion: Application Library path Particle_Tracing_Module/Verification_Examples/brownian_motion