Brownian Force
The Brownian Force feature adds a Brownian force term Fb (SI unit: N) to the total force on the particles:
(5-14)
where
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Δt (SI unit: s) is the time step taken by the solver
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rp (SI unit: m) is the particle radius
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T (SI unit: K) is the absolute fluid temperature
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μ (SI unit: Pa·s) is the fluid dynamic viscosity,
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kB = 1.380649 × 10−23 J/K is the Boltzmann constant, and
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ζ (dimensionless) is a normally distributed random number with a mean of zero and unit standard deviation.
As explained in Ref. 25, independent values for ζ are chosen in all directions. A different value of ζ is created for each particle, at each time step for each component of the Brownian force. The Brownian force leads to spreading of particles from regions of high particle density to low density.
The fluid viscosity required by the Brownian force must be consistent with the one supplied in the Drag force. Furthermore, the specific form of the Brownian force given above is only consistent if the Drag law is set to Stokes.