Törmäysaika

Törmäysaika, or the collision time, is the average time interval between successive collisions experienced by a particle in a system. It is a fundamental quantity in kinetic theory and transport phenomena, providing a link between microscopic interactions and macroscopic properties such as viscosity, diffusion, and thermal conductivity.

In a simple dilute gas of particles that interact as hard spheres, the collision rate per particle is often written as Γ = n σ v_rel, where n is the number density, σ is the collisional cross-section, and v_rel is the typical relative speed between particles. The törmäysaika is the reciprocal of the rate, τ = 1/Γ. For hard spheres with diameter d, σ ≈ π d^2, and v_rel is typically of order the thermal speed, v_th ∼ sqrt(kT/m). Thus, τ ≈ 1/(n π d^2 v_rel). In real systems, cross-sections and relative velocities depend on the interaction potential and temperature, so τ must be evaluated accordingly.

The concept extends beyond ideal gases. In plasmas, collision times are influenced by long-range Coulomb interactions and may involve Coulomb logarithms. In dense or strongly interacting media, correlations, quantum effects, or collective behavior modify the simple picture.

Relation to spatial scale is given by the mean free path l ≈ ⟨v⟩ τ, where ⟨v⟩ is a characteristic particle speed. If l is small compared to the system size, kinetic theory reliably describes transport. Conversely, very long törmäysaika implies infrequent collisions and weak coupling. In astrophysics, direct physical collisions between stars are rare except in extremely dense star clusters, where they can influence core dynamics.