Laminar Flow and Particle Tracing Equations
For an incompressible single-phase fluid in the laminar flow regime, the Navier–Stokes equations can be reduced to the following:
where
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u (SI unit: m/s) is the fluid velocity,
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p (SI unit: Pa) is the pressure,
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ρ (SI unit: kg/m3) is the density,
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μ (SI unit: Pa·s) is the dynamic viscosity, and
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F (SI unit: N) is the total volume force.
In the following, let FV denote the contribution of particle motion to the total volume force acting on the fluid.
The equation of motion of particles in the fluid can be written as
where
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mp is the particle mass (SI unit: kg)
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v is the velocity of the particle (SI unit: m/s)
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FD is the drag force (SI unit: N),
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Fg is the gravitational force (SI unit: N), and
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Fext is any other external force (SI unit: N).
Several different expressions for the drag force are available; these are described in the section Particle Motion in a Fluid in Theory for the Particle Tracing for Fluid Flow Interface.