inertialess

Inertialess is an adjective used in physics and engineering to describe systems or models in which inertia, or resistance to changes in motion due to mass, is negligible compared with other forces such as viscous drag or external fields. In such regimes the equations of motion simplify because the acceleration term becomes small or vanishes, and the motion is governed primarily by a balance of forces.

In practice, the inertialess, or overdamped, limit is often taken in situations of low Reynolds number fluid flow or highly viscous environments. For a particle of mass m moving with velocity v under a force F, the full equation m dv/dt = F reduces to a relation where velocity adjusts instantaneously to force: γ v ≈ F, with γ representing viscous drag. This leads to dynamics described by overdamped models, such as Brownian dynamics or Langevin equations in which inertial terms are neglected.

Applications and contexts include colloidal suspensions, microparticles in viscous fluids, and microfluidic systems where viscous forces dominate. In these settings, researchers model motion and diffusion assuming immediate force balance, while stochastic forces due to thermal fluctuations can remain important. Optical traps and electrical tweezers often operate in the inertialess regime, where particle responses are governed by drag and applied forces rather than acceleration.

Limitations of the inertialess approximation arise when forces vary rapidly, masses are not negligible, or inertial effects become comparable to dissipative forces (for example at higher speeds, larger scales, or higher Reynolds numbers). In such cases a full inertial term is necessary for an accurate description.

See also: inertia, overdamped dynamics, low Reynolds number, Stokes flow, Langevin equation, Brownian dynamics.