Faxén's law

Faxén's law relates the force on a rigid sphere in Stokes flow to the undisturbed fluid velocity and its spatial derivatives at the sphere's center.

Stokes flow: Viscous fluid flow in which inertial forces are negligible compared with viscous forces. Faxén's law applies in this low-Reynolds-number regime.
Reynolds number: A dimensionless ratio comparing inertial forces with viscous forces in fluid flow. A small Reynolds number justifies the Stokes-flow setting.
Stokesian dynamics: A simulation method for suspensions that combines near-field lubrication and long-range hydrodynamic interactions. Its particle force calculations use Faxén relations to couple spheres to flow fields.
Håkan Faxén: A Swedish physicist known for foundational work on the motion of particles in viscous fluids. His name is attached to the sphere-force relations.
Stokes equations: The incompressible fluid equations simplified by neglecting inertia. Their linear flow fields provide the undisturbed velocity used in Faxén's relation.
Rigid sphere: A solid sphere whose shape does not deform under applied forces. The law specifies this particle geometry and rigidity.
Suspension (chemistry): A mixture in which solid particles are dispersed through a fluid without dissolving. Faxén's law helps model hydrodynamic forces between suspended particles.
George Gabriel Stokes: A British mathematician and physicist whose work established key results in viscous-fluid mechanics. The creeping-flow equations underlying Faxén's law bear his name.
Laplacian: A differential operator that sums a function's second spatial derivatives. A Laplacian correction captures how velocity varies across the sphere.
Undisturbed flow: The fluid velocity field that would exist without the particle present. Faxén's law samples this field and its derivatives at the sphere center.

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Stokes' lawRelated: It generalizes the basic result to nonuniform ambient flows.