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In a mixture of a cylindrical particle and the carrier fluid, what exactly particle inertia refer to? (let's neglect gravitation force and Brownian motion).

When the size of particles are small (particle Reynolds number around unity), it is often assumed that the force on the particle is a linear function of slip velocity (no need to integrate the viscous stress over the surface of a particle).

However, in some cases, one can also neglect particle inertia. I want to understand which factor(s) exactly can justify the assumption (size, shape, $Re_p$, etc.)?

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